question_answer 1) If the velocity of light c, gravitational constant G and Plancks constant h are chosen as fundamental units, the dimensions of length L in the new system is:
A)
\[[{{h}^{1}}{{c}^{1}}{{G}^{-1}}]\]
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B)
\[[{{h}^{1/2}}{{c}^{1/2}}{{G}^{-1/2}}]\]
done
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C)
\[[{{h}^{1}}{{c}^{-3}}{{G}^{1}}]\]
done
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D)
\[[{{h}^{1/2}}{{c}^{-3/2}}{{G}^{1/2}}]\]
done
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E)
done
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question_answer 2) A plate has a length\[5\pm 0.1\text{ }cm\]and breadth\[2\pm 0.01\text{ }cm\]. Then the area of the plate is:
A)
\[10\pm 0.1\text{ }c{{m}^{2}}\]
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B)
\[10\pm 0.01\text{ }c{{m}^{2}}\]
done
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C)
\[10\pm 0.001\text{ }c{{m}^{2}}\]
done
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D)
\[10\pm 1\text{ }c{{m}^{2}}\]
done
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E)
\[10c{{m}^{2}}\]
done
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question_answer 3) A ball hangs from a string inside a train moving along a horizontal straight track. The string is observed to incline towards the rear of the train making a constant small angle with the vertical. It shows that the train is:
A)
moving with a uniform acceleration
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B)
moving with a uniform velocity
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C)
moving with a uniform retardation
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D)
moving with an acceleration which is increasing uniformly
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E)
at rest
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question_answer 4) A particle moves along Y-axis in such a way that its y-coordinate varies with time t according to the relation\[y=3+5t+7{{t}^{2}}\]. The initial velocity and acceleration of the particle are respectively:
A)
\[14m{{s}^{-1}},\text{ }-5m{{s}^{-2}}\]
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B)
\[19m{{s}^{-1}},-9m{{s}^{-2}}\]
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C)
\[-14m{{s}^{-1}},-5m{{s}^{-2}}\]
done
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D)
\[3m{{s}^{-1}},-5m{{s}^{-2}}\]
done
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E)
\[5m{{s}^{-1}},14m{{s}^{-2}}\]
done
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question_answer 5) An object travels north with a velocity of \[10\text{ }m{{s}^{-1}}\]and then speeds up to a velocity of \[25\text{ }m{{s}^{-1}}\]in 5 s. The acceleration of the object in these 5 s is:
A)
\[3\text{ }m{{s}^{-1}}\]in north direction
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B)
\[3\text{ }m{{s}^{-2}}\]in north direction
done
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C)
\[\text{15 }m{{s}^{-2}}\] in north direction
done
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D)
\[\text{3 }m{{s}^{-2}}\]in south direction
done
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E)
\[\text{10 }m{{s}^{-2}}\] in north direction
done
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question_answer 6) An automobile in travelling at 50 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 90 km/h, all other conditions remaining same and assuming no skidding, the minimum stopping distance in metres is:
A)
72
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B)
92.5
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C)
102.6
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D)
129.6
done
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E)
139.6
done
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question_answer 7) A rifle shoots a bullet with a muzzle velocity of 500 ms1 at a small target 50 m away. To hit the target the rifle must be aimed (take g = 10 \[m{{s}^{-2}}\]):
A)
exactly at the target
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B)
10 cm below the target
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C)
10 cm above the target
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D)
5 cm below the target
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E)
5 cm above the target
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question_answer 8) The centripetal acceleration of particle of mass m moving with a velocity v in a circular orbit of radius r is:
A)
\[{{v}^{2}}/r\]along the radius, towards the centre
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B)
\[{{v}^{2}}/r\]along the radius, away from the centre
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C)
\[m{{v}^{2}}/r\]along the radius, away from the centre
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D)
\[m{{v}^{2}}/r\]along the radius, towards the centre
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E)
\[vr\]along the radius away from the centre
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question_answer 9) An\[\alpha -\]particle of mass m suffers one dimensional elastic collision with a nucleus of unknown mass. After the collision the\[\alpha -\]particle is scattered directly backwards losing 75% of its kinetic energy. Then the mass of the nucleus is:
A)
m
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B)
2m
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C)
3m
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D)
1m
done
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E)
5m
done
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question_answer 10) While driving a car around a curve of 200 m radius, the driver notices that a simple pendulum hung to the roof of the car is making an angle of \[15{}^\circ \]to the horizontal. The speed of the car in km/h is:
A)
60.5
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B)
72.5
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C)
82.5
done
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D)
92.5
done
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E)
106.5
done
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question_answer 11) A stationary body of mass m explodes into three parts having masses in the ratio 1 : 3 : 3. The two fractions with equal masses move at right angles to each other with a velocity of \[1.5\text{ }m{{s}^{-1}}\]Then the velocity of the third body is:
A)
\[4.5\sqrt{2}m{{s}^{-1}}\]
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B)
\[5\,m{{s}^{-1}}\]
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C)
\[5\sqrt{32}m{{s}^{-1}}\]
done
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D)
\[1.5\,m{{s}^{-1}}\]
done
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E)
\[1\,m{{s}^{-1}}\]
done
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question_answer 12) In a simple pendulum the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle 6 with the vertical. Then:
A)
\[\theta =30{}^\circ \]
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B)
\[\theta =45{}^\circ \]
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C)
\[\theta =60{}^\circ \]
done
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D)
\[\theta ={{\cos }^{-1}}(1/3)\]
done
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E)
\[\theta ={{\cos }^{-1}}(2/3)\]
done
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question_answer 13) An object of mass m falls on to a spring of constant k from h. Then the spring undergoes compression by a length\[x\]. The maximum compression x is given by the equation:
A)
\[mgh=\frac{1}{2}k{{x}^{2}}\]
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B)
\[mgh(h+x)=\frac{1}{2}k{{x}^{2}}\]
done
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C)
\[mg(h+x)=-kx\]
done
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D)
\[mgh=-kx\]
done
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E)
\[mgh=-\frac{1}{2}k{{x}^{2}}\]
done
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question_answer 14) A rocket of initial mass 1000 kg ejects mass at a constant rate of 10 kg/s with constant relative speed of\[11\text{ }m{{s}^{-1}}\]. Neglecting gravity, the acceleration of the rocket 1 min after the blast is:
A)
\[11/40\,m{{s}^{-2}}\]
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B)
\[22/40\,m{{s}^{-2}}\]
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C)
\[1.1/40\,m{{s}^{-2}}\]
done
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D)
\[1\,m{{s}^{-2}}\]
done
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E)
\[11/60\,\,m{{s}^{-2}}\]
done
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question_answer 15) An elastic ball is dropped from a height h and it rebounds many times from the floor. If the coefficient of restitution is e, the time interval between the second and the third impact, is:
A)
\[ev/g\]
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B)
\[{{e}^{2}}v/g\]
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C)
\[{{e}^{2}}\sqrt{\left( \frac{8h}{g} \right)}\]
done
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D)
\[{{e}^{2}}\sqrt{\left( \frac{h}{g} \right)}\]
done
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E)
\[{{e}^{2}}\sqrt{\left( \frac{2h}{g} \right)}\]
done
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question_answer 16) An object of mass m is attached to light string which passess through a hollow tube. The object is set into rotation in a horizontal circle of radius,\[{{r}_{1}}\]. If the string is pulled shortening the radius to\[{{r}_{2}}\], the ratio of new kinetic energy to the original kinetic energy is:
A)
\[{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]
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B)
\[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\]
done
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C)
\[\frac{{{r}_{1}}}{{{r}_{2}}}\]
done
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D)
\[\frac{{{r}_{2}}}{{{r}_{1}}}\]
done
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E)
1
done
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question_answer 17) Total angular momentum of a rotating body remains constant, if the net torque acting on the body is:
A)
zero
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B)
maximum
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C)
minimum
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D)
unity
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E)
equal to the total angular momentum about a parallel axis
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question_answer 18) A car is racing on a circular track of 180 m radius with a speed of\[32\text{ }m{{s}^{-1}}\]. What should be the banking angle of the road to avoid changes of skidding of the vehicle at this speed without taking into consideration the friction between the tyre and the road?
A)
\[45{}^\circ \]
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B)
\[60{}^\circ \]
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C)
\[30{}^\circ \]
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D)
\[15{}^\circ \]
done
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E)
\[25{}^\circ \]
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question_answer 19) When a ceiling fan is switched on it makes 10 rotations in the first 3s. The number of rotations it makes in the next 3 s, assuming uniform angular acceleration is:
A)
40
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B)
30
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C)
20
done
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D)
10
done
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E)
50
done
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question_answer 20) A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to 1/3rd the escape velocity for that planet. The maximum height attained by the body is:
A)
R/2
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B)
R/3
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C)
R/S
done
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D)
R/8
done
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E)
R/9
done
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question_answer 21) A man weighs 80 kg on earth surface. The height above ground where he will weigh 40 kg, is: (radius of earth is 6400 km)
A)
0.31 times r
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B)
0.41 times r
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C)
0.51 times r
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D)
0.61 times r
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E)
0.82 times r
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question_answer 22) An adulterated sample of milk has a density of \[1032\text{ }kg{{m}^{-3}},\]while pure milk has a density of\[1080\text{ }kg{{m}^{-3}}\]. Then the volume of pure milk in a sample of 10 L of adulterated milk is:
A)
0.5 L
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B)
1.0 L
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C)
2.0 L
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D)
3.0 L
done
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E)
4.0 L
done
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question_answer 23) Typical silt (hard mud) particle of radius 20 um is on the top of lake water, its density is \[2000\text{ }kg/{{m}^{3}}\]and the viscosity of lake water is 1.0 mPa, density is \[1000\,kg/{{m}^{3}}\]. If the lake is still (has no internal fluid motion). The terminal speed with which the particle hits the bottom of the lake is ... mm/s.
A)
0.67
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B)
0.77
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C)
0.87
done
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D)
0.97
done
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E)
1.07
done
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question_answer 24) A solid sphere and a hollow sphere, both of the same size and same mass roll down an inclined plane. Then:
A)
solid sphere reaches the ground first
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B)
hollow sphere reaches the ground first
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C)
both spheres reach the ground at the same time
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D)
the time at which the spheres reach the ground cannot be specified by the given data
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E)
the hollow sphere will not roll down
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question_answer 25) If P is the pressure, V the volume, R the gas constant, k the Boltzmann constant and T the absolute temperature, then the number of molecules in the given mass of the gas is given by:
A)
\[\frac{PV}{RT}\]
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B)
\[\frac{PV}{kT}\]
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C)
\[\frac{PR}{T}\]
done
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D)
\[PV\]
done
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E)
\[\frac{V}{T}\]
done
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question_answer 26) An air bubble is released from the bottom of a pond and is found to expand to thrice its original volume as it reached the surface. If the atmospheric pressure is 100 kPa, the absolute pressure at the bottom of lake in kPa is ...(assume no temperature variation):
A)
33.3
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B)
50.0
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C)
100.0
done
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D)
200.0
done
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E)
300.0
done
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question_answer 27) During an adiabatic process, the volume of a gas is found to be inversely proportional to the root of its absolute temperature. The ratio \[{{C}_{p}}/{{C}_{V}}\]for the gas is:
A)
5/3
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B)
4/3
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C)
3/2
done
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D)
5/4
done
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E)
7/4
done
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question_answer 28) 1 g of steam at\[100{}^\circ C\]and equal mass of ice at \[0{}^\circ C\]are mixed. The temperature of the mixture in steady state will be (latent heat of steam\[=540\text{ }cal/g,\]latent heat of ice = 80 \[cal/g\]):
A)
\[50{}^\circ C\]
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B)
\[100{}^\circ C\]
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C)
\[67{}^\circ C\]
done
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D)
\[33{}^\circ C\]
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E)
\[0{}^\circ C\]
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question_answer 29) The work done by a gas is maximum when it expands:
A)
isothermally
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B)
adiabatically
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C)
isentropically
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D)
isobarically
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E)
isochorically
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question_answer 30) A tuning fork of frequency 580 Hz is employed to produce transverse waves on a long rope. The distance between the nearest crusts is found to be 20 cm. The velocity of the wave is:
A)
\[58\text{ }m{{s}^{-1}}\]
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B)
\[580\text{ }m{{s}^{-1}}\]
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C)
\[20\text{ }m{{s}^{-1}}\]
done
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D)
\[\text{29 }m{{s}^{-1}}\]
done
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E)
\[116\,m{{s}^{-1}}\]
done
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question_answer 31) A heavy brass sphere is hung from a weightless inelastic spring and as a simple pendulum its time period of oscillation is T. When the sphere is immersed in a non-viscous liquid of density 1/10 that of brass, it will act as a simple pendulum of period:
A)
\[T\]
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B)
\[\frac{10}{9}T\]
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C)
\[\sqrt{\left( \frac{9}{10} \right)}T\]
done
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D)
\[\sqrt{\left( \frac{10}{9} \right)}T\]
done
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E)
\[\frac{9}{100}T\]
done
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question_answer 32) The distance travelled by a sound wave when a tuning fork completes 25 vib in 16.5 m. If the frequency of the tuning fork is 500 Hz, find the velocity of sound.
A)
\[350\text{ }m{{s}^{-1}}\]
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B)
\[330\text{ }m{{s}^{-1}}\]
done
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C)
\[300\text{ }m{{s}^{-1}}\]
done
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D)
\[450\text{ }m{{s}^{-1}}\]
done
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E)
\[500\text{ }m{{s}^{-1}}\]
done
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question_answer 33) Two instruments having stretched strings are being played in unison. When the tension of one of the instruments is increased by 1%, 3 beats are produced in 2s. The initial frequency of vibration of each wire is:
A)
300 Hz
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B)
500 Hz
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C)
1000 Hz
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D)
400 Hz
done
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E)
600 Hz
done
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question_answer 34) Three point charges 1C, 2C and 3C are placed at the corners of an equilateral triangle of side 1m. The work done in bringing these charges to the vertices of a smaller similar triangle of side 0.5 m is:
A)
\[2.7\times {{10}^{10}}J\]
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B)
\[9.9\times {{10}^{10}}J\]
done
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C)
\[10.8\times {{10}^{10}}J\]
done
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D)
\[5.4\times {{10}^{10}}J\]
done
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E)
zero
done
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question_answer 35)
The capacitors A and B have identical geometry. A material with a dielectric constant 3 is present between the plates of B. The potential difference across A and B are respectively:
A)
2.5V, 7.5 V
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B)
2V, 8V
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C)
8V, 2V
done
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D)
7.5V, 2.5V
done
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E)
3V, 2V
done
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question_answer 36) An electric bulb is marked 100 W, 230 V. If the supply voltage drops to 115 V, what is the total energy produced by the bulb in 10 min?
A)
30 kJ
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B)
20 kJ
done
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C)
15 kJ
done
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D)
10 kJ
done
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E)
5kJ
done
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question_answer 37) A circular coil carrying a current has a radius R. The ratio of magnetic induction at the centre of the coil and at a distance equal to \[\sqrt{3}R\]from the centre of the coil on the axis is:
A)
\[1:1\]
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B)
\[1:2\]
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C)
\[2:1\]
done
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D)
\[1:8\]
done
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E)
\[8:1\]
done
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question_answer 38) The examples of diamagnetic, paramagnetic and ferromagnetic materials are respectively:
A)
copper, aluminium, iron
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B)
aluminium, copper, iron
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C)
copper, iron, aluminium
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D)
aluminium, iron, copper
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E)
iron, aluminium, copper
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question_answer 39)
In the Wheatstones bridge shown below, in order to balance the bridge we must have:
A)
\[{{R}_{1}}=3\,\Omega ,{{R}_{2}}=3\,\Omega \]
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B)
\[{{R}_{1}}=6\,\Omega ,{{R}_{2}}=1.5\,\Omega \]
done
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C)
\[{{R}_{1}}=1.5\,\Omega ,{{R}_{2}}=\]any finite value
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D)
\[{{R}_{1}}=3\,\,\Omega ,{{R}_{2}}=\]any finite value
done
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E)
\[{{R}_{2}}=1.5\,\,\Omega ,{{R}_{1}}=\]any finite value
done
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question_answer 40)
Four\[10\,\mu F\]capacitors are connected to a 500 V supply as shown in the figure. The equivalent capacitance of the network is:
A)
\[40\,\mu F\]
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B)
\[20\,\mu F\]
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C)
\[13.3\,\mu F\]
done
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D)
\[10\,\mu F\]
done
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E)
\[2.5\,\mu F\]
done
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question_answer 41) A resistor is constructed as hollow cylinder of dimensions\[{{r}_{a}}=0.5\,cm\]and\[{{r}_{b}}=1.0\,cm\]and\[\rho =3.5\times {{10}^{-5}}\Omega m\]. The resistance of the configuration for the length of 5 cm cylinder is ... \[\times {{10}^{-3}}\Omega \].
A)
7.42
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B)
10.56
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C)
14.38
done
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D)
16.48
done
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E)
18.29
done
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question_answer 42)
The resistances are connected as shown in the figure below. Find the equivalent resistance between the points A and B.
A)
\[205\,\Omega \]
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B)
\[10\,\Omega \]
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C)
\[3.5\,\Omega \]
done
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D)
\[5\,\Omega \]
done
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E)
\[3\,\Omega \]
done
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question_answer 43)
The figure below shows a 2.0 V potentiometer used for the determination of internal resistance of a 2.5 V cell. The balance point of the cell in the open circuit is 75 cm. When a resistor of\[10\,\Omega \]is used in the external circuit of the cell, the balance point shifts to 65 cm length of potentiometer wire. Then the internal resistance of the cell is:
A)
\[2.5\,\,\Omega \]
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B)
\[2.0\,\,\Omega \]
done
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C)
\[1.54\,\,\Omega \]
done
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D)
\[1.0\,\,\Omega \]
done
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E)
\[0.5\,\,\Omega \]
done
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question_answer 44) An electric heater boils 1 kg of water in a time\[{{t}_{1}}\]. Another heater boils the same amount of water in a time\[{{t}_{2}}\]. When the two heaters are connected in parallel, the time required by them together to boil the same amount of water is:
A)
\[{{t}_{1}}+{{t}_{2}}\]
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B)
\[{{t}_{1}}{{t}_{2}}\]
done
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C)
\[\frac{{{t}_{1}}+{{t}_{2}}}{2}\]
done
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D)
\[\frac{{{t}_{1}}-{{t}_{2}}}{2}\]
done
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E)
\[\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}\]
done
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question_answer 45)
Two thin metallic strips, carrying current in the direction shown, cross each other perpendicularly without touching but being close to each other, as shown in the figure. The regions which contain some points of zero magnetic induction are:
A)
I and II
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B)
I and III
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C)
I and IV
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D)
II and III
done
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E)
II and IV
done
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question_answer 46) The force on a conductor of length\[l\]placed in a magnetic field of magnitude B and carrying a current I is given by (\[\theta \]is the angle, the conductor makes with the direction of B):
A)
\[F=I\,l\,B\sin \theta \]
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B)
\[F={{I}^{2}}\,l\,{{B}^{2}}\sin \theta \]
done
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C)
\[F=I\,l\,B\cos \theta \]
done
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D)
\[F=\frac{{{I}^{2}}l}{B}\sin \theta \]
done
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E)
\[F=\frac{{{I}^{2}}l}{B}\cos \theta \]
done
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question_answer 47) A needle made of bismuth is suspended freely in a magnetic field. The angle which the needle makes with the magnetic field is:
A)
\[0{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[90{}^\circ \]
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D)
\[180{}^\circ \]
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E)
any angle with which it is placed
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question_answer 48) The resonant frequency of an LCR circuit occurs at a frequency equal to:
A)
\[\frac{1}{LC}\]
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B)
\[\frac{1}{\sqrt{LC}}\]
done
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C)
\[\frac{1}{LCR}\]
done
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D)
\[\frac{1}{CR}\]
done
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E)
\[\frac{1}{\sqrt{LCR}}\]
done
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question_answer 49) An AC is given by\[i={{i}_{1}}\cos \omega t+{{i}_{2}}\sin \omega t\]The rms current is given by:
A)
\[\frac{{{i}_{1}}+{{i}_{2}}}{\sqrt{2}}\]
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B)
\[\frac{{{i}_{1}}-{{i}_{2}}}{\sqrt{2}}\]
done
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C)
\[\sqrt{\left( \frac{i_{1}^{2}+i_{2}^{2}}{2} \right)}\]
done
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D)
\[\sqrt{\left( \frac{i_{1}^{2}-i_{2}^{2}}{2} \right)}\]
done
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E)
\[\frac{{{i}_{1}}{{i}_{2}}}{\sqrt{2}}\]
done
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question_answer 50) The coefficient of mutual inductance between the primary and secondary of the coil is 5 H. A current of 10 A is cut off in 0.5 s. The induced emf is:
A)
1 V
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B)
10 V
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C)
5 V
done
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D)
100 V
done
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E)
50V
done
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question_answer 51) If a transformer of an audio amplifier has output impedance\[8000\,\Omega \]and the speaker has input impedance of \[8\Omega \], the primary and secondary turns of this transformer connected between the output of amplifier and to loud speaker should have the ratio:
A)
\[1000:1\]
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B)
\[100:1\]
done
clear
C)
\[1:32\]
done
clear
D)
\[32:1\]
done
clear
E)
\[1:1000\]
done
clear
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question_answer 52) In the electromagnetic spectrum, the visible spectrum lies between:
A)
radio waves and microwaves
done
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B)
infrared and ultraviolet rays
done
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C)
microwaves and infrared spectrum
done
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D)
X-ray and \[\gamma \]-ray spectrum
done
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E)
ultraviolet and X-ray spectrum
done
clear
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question_answer 53) Maxwell in his famous equation of electromagnetism introduced the concept:
A)
AC current
done
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B)
DC current
done
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C)
displacement current
done
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D)
impedance
done
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E)
reactance
done
clear
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question_answer 54) Out of the following electromagnetic radiations, which has the shortest wavelength?
A)
Radio waves
done
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B)
Infrared
done
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C)
Ultraviolet
done
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D)
Visible light
done
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E)
X-rays
done
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question_answer 55) In Youngs double slit experiment, the width of one of the slits is slowly increased to make it twice the width of the other slit. Then in the interference pattern:
A)
the intensity of maxima increase while that of minima decrease
done
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B)
the intensities of both maxima and minima decrease
done
clear
C)
the intensities of both maxima and minima remain the same
done
clear
D)
the intensity of maxima decrease while that of minima increase
done
clear
E)
the intensities of both maxima and minima increase
done
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question_answer 56) Two coherent sources whose intensity ratio is \[81:1\]produce interference fringes. The ratio of minimum to maximum intensity, i.e., \[{{I}_{\min }}:{{I}_{\max }}\]is:
A)
\[16:25\]
done
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B)
\[9:1\]
done
clear
C)
\[1:9\]
done
clear
D)
\[25:16\]
done
clear
E)
\[5:4\]
done
clear
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question_answer 57) An infinitely long rod lies along the axis of concave mirror of focal length\[f\]. The near end of the rod is at a distance\[x>f\]from the mirror. Then the length of the image of the rod is:
A)
\[\frac{{{f}^{2}}}{x+f}\]
done
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B)
\[\frac{{{f}^{2}}}{x}\]
done
clear
C)
\[\frac{xf}{x-f}\]
done
clear
D)
\[\frac{xf}{x+f}\]
done
clear
E)
\[\frac{{{f}^{2}}}{x-f}\]
done
clear
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question_answer 58) A beaker containing a liquid appears to be half when it is actually two third full. The refractive index of liquid is:
A)
7/6
done
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B)
6/5
done
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C)
3/2
done
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D)
5/4
done
clear
E)
4/3
done
clear
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question_answer 59) If\[{{h}_{1}}\]and\[{{h}_{2}}\]are the heights of the images in conjugate position of a convex lens, then the height of the object is:
A)
\[{{h}_{1}}+{{h}_{2}}\]
done
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B)
\[{{h}_{1}}-{{h}_{2}}\]
done
clear
C)
\[{{h}_{1}}/{{h}_{2}}\]
done
clear
D)
\[\sqrt{{{h}_{1}}{{h}_{2}}}\]
done
clear
E)
\[{{h}_{1}}{{h}_{2}}\]
done
clear
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question_answer 60) The power of the combination of a convex lens of focal length 50 cm and concave lens of focal length 40 cm is:
A)
\[+1\text{ }D\]
done
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B)
\[-1\,D\]
done
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C)
zero
done
clear
D)
\[+\,0.5D\]
done
clear
E)
\[-\,0.5D\]
done
clear
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question_answer 61) Image formed by a convex lens is virtual and erect when the object is placed:
A)
at F
done
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B)
between F and the lens
done
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C)
at 2F
done
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D)
beyond 2 F
done
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E)
at infinity
done
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question_answer 62) The rest mass of photon is:
A)
\[\frac{hv}{c}\]
done
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B)
\[\frac{hv}{{{c}^{2}}}\]
done
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C)
\[\frac{hc}{\lambda }\]
done
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D)
zero
done
clear
E)
\[\frac{h}{\lambda }\]
done
clear
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question_answer 63) A charged oil drop of mass \[9.75\times {{10}^{-15}}kg\] and charge\[30\times {{10}^{-16}}C\]is suspended in a uniform electric field existing between two parallel plates. The field between the plates, taking \[(g=10\text{ }m{{s}^{-2}})\]is:
A)
3.25 V/m
done
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B)
300 V/m
done
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C)
325 V/m
done
clear
D)
32.5 V/m
done
clear
E)
3000 V/m
done
clear
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question_answer 64) If the wavelength of incident light changes from 400 nm to 300 nm, the stopping potential for photoelectrons emitted from a surface becomes approximately:
A)
1.0V greater
done
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B)
1.0V smaller
done
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C)
0.5V greater
done
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D)
0.5V smaller
done
clear
E)
0. IV greater
done
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question_answer 65) Let the potential energy of hydrogen atom in the ground state be regarded as zero. Then its potential energy in the first excited state will be:
A)
20.4 eV
done
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B)
13.6 eV
done
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C)
3.4 eV
done
clear
D)
6.8 eV
done
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E)
10.2 eV
done
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View Answer play_arrow
question_answer 66) Two radioactive nuclides\[x\]and y have half-lives 1 h and 2 h respectively. Initially the samples have equal number of nuclei. After 4 h the ratio of the numbers of\[x\]and y is:
A)
\[\frac{1}{2}\]
done
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B)
2
done
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C)
\[\frac{1}{4}\]
done
clear
D)
1
done
clear
E)
\[\frac{1}{16}\]
done
clear
View Answer play_arrow
question_answer 67) \[_{92}{{U}^{238}}\]decays successively to from\[_{90}T{{h}^{234}},\]\[_{91}P{{a}^{234}}{{,}_{92}}{{U}^{234}}{{,}_{90}}T{{h}^{230}}{{,}_{88}}R{{a}^{226}}\]during the reaction the number of\[\alpha -\]particles emitted is:
A)
4
done
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B)
3
done
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C)
5
done
clear
D)
2
done
clear
E)
1
done
clear
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question_answer 68) Let\[{{n}_{e}}\]and\[{{n}_{h}}\]represent the number density of electrons and holes in a semiconductor. Then:
A)
\[{{n}_{e}}>{{n}_{h}}\]if the semiconductor is intrinsic
done
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B)
\[{{n}_{e}}<{{n}_{h}}\]if the semiconductor is intrinsic
done
clear
C)
\[{{n}_{e}}\ne {{n}_{h}}\]if the semiconductor is intrinsic
done
clear
D)
\[{{n}_{e}}={{n}_{h}}\]if the semiconductor is intrinsic
done
clear
E)
\[{{n}_{e}}={{n}_{h}}\]if the semiconductor is extrinsic
done
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question_answer 69) In a n-p-n transistor amplifier, the collector current is 9 mA. If 90% of the electrons from the emitter reach the collector, then:
A)
\[\alpha =0.9,\beta =9.0\]
done
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B)
the base current is 10 mA
done
clear
C)
the emitter current is 1 mA
done
clear
D)
\[\alpha =9.0,\text{ }\beta =0.9\]
done
clear
E)
\[\alpha =0.99,\text{ }\beta =99.0\]
done
clear
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question_answer 70) In a properly biased transistor:
A)
both depletion layers are equally large
done
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B)
both depletion layers are equally small
done
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C)
emitter-base depletion layer is large but base-collector depletion layer is small
done
clear
D)
emitter-base depletion layer is small but base-collector depletion layer is large
done
clear
E)
both depletion layers vanish
done
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View Answer play_arrow
question_answer 71) A dim star of magnitude\[+14.5\]explodes into a nova of magnitude\[+2\]. The factor by which the brightness of the star has increased is:
A)
12.5
done
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B)
\[{{10}^{2}}\]
done
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C)
\[{{10}^{3}}\]
done
clear
D)
\[{{10}^{4}}\]
done
clear
E)
\[{{10}^{5}}\]
done
clear
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question_answer 72) If the sun becomes twice as hot:
A)
the output of radiated energy will be eight times larger
done
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B)
it will radiate predominantly in the infrared
done
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C)
it will radiate predominantly in the ultraviolet
done
clear
D)
the output of the radiated energy will be eight times smaller
done
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E)
the frequency spectrum of the radiated energy will not alter
done
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question_answer 73) The standard adopted for the determination of atomic weight of elements is based on:
A)
\[{{H}^{1}}\]
done
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B)
\[{{C}^{12}}\]
done
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C)
\[{{O}^{16}}\]
done
clear
D)
\[{{S}^{32}}\]
done
clear
E)
\[C{{l}^{35}}\]
done
clear
View Answer play_arrow
question_answer 74) Law of multiple proportions is illustrated by one of the following pairs:
A)
\[{{H}_{2}}S\]and\[S{{O}_{2}}\]
done
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B)
\[N{{H}_{3}}\] and \[N{{O}_{2}}\]
done
clear
C)
\[N{{a}_{2}}S\]and\[N{{a}_{2}}O\]
done
clear
D)
\[BeO\] and\[BeC{{l}_{2}}\]
done
clear
E)
\[{{N}_{2}}O\]and \[NO\]
done
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View Answer play_arrow
question_answer 75) Paramagnetism of oxygen is explained on the basis of its electronic configuration of:
A)
\[{{({{\pi }^{*}}2{{p}_{x}})}^{1}}{{(\pi 2{{p}_{y}})}^{1}}\]
done
clear
B)
\[{{({{\pi }^{*}}2{{p}_{y}})}^{1}}{{({{\pi }^{*}}2{{p}_{z}})}^{1}}\]
done
clear
C)
\[{{({{\sigma }^{*}}2s)}^{1}}{{(\pi 2{{p}_{y}})}^{1}}\]
done
clear
D)
\[{{({{\sigma }^{*}}2s)}^{1}}{{(\pi 2{{p}_{y}})}^{1}}\]
done
clear
E)
\[{{(\pi 2{{p}_{x}})}^{1}}{{(\pi 2{{p}_{y}})}^{1}}\]
done
clear
View Answer play_arrow
question_answer 76) The van der Waals equation for a real gas is given by the formula\[\left( P+\frac{{{n}^{2}}a}{{{V}^{2}}} \right)\]\[(V-nb)=\]\[nRT,\]where\[P,V,T\]and\[n\]are the pressure, volume, temperature and the number of moles of the gas. Which one is the correct interpretation for the parameter a?
A)
The parameter a accounts for the finite size of the molecule, not included temperature in the ideal gas law
done
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B)
The parameter a accounts for the shape of gas phase molecules
done
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C)
The parameter a accounts for intermolecular interactions present in the molecule
done
clear
D)
The parameter a has no physical significance and van der Waals introduced it as a numerical correction factor only
done
clear
E)
The parameter is a correction factor to the volume of the container
done
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View Answer play_arrow
question_answer 77) Avogadros hypothesis states that:
A)
the ideal gas consists of a large number of small particles called molecules
done
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B)
under the same conditions of temperature and pressure equal volumes of gases contain the same number of molecules
done
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C)
volume of a definite quantity of gas at constant pressure is directly proportional to absolute temperature
done
clear
D)
a given mass of gas at constant pressure is directly proportional to absolute temperature
done
clear
E)
for a definite mass of gas at constant temperature the volume is inversely proportional to its pressure
done
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question_answer 78) The observation that the ground state of nitrogen atom has 3 unpaired electrons in its electronic configuration and not otherwise is associated with:
A)
Paulis exclusion principle
done
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B)
Hunds rule of maximum multiplicity
done
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C)
Heisenbergs uncertainty relation
done
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D)
Ritz combination principle
done
clear
E)
Valence bond method
done
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View Answer play_arrow
question_answer 79) Which of the following overlaps leads to bonding?
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
E)
done
clear
View Answer play_arrow
question_answer 80) In the periodic table metallic character of elements shows one of the following trend:
A)
decreases down the group and increases across the period
done
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B)
increases down the group and decreases across the period
done
clear
C)
increases across the period and also down the group
done
clear
D)
decreases across the period and also down the group
done
clear
E)
decreases down the group and remains constant across the period
done
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question_answer 81) Which of the following statements is correct?
A)
All carbon to carbon bonds contain a\[\sigma -\]bond and one or more\[\pi -\]bonds
done
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B)
All carbon to hydrogen bonds are\[\pi -\]bonds
done
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C)
All oxygen to hydrogen bonds are hydrogen bonds
done
clear
D)
All carbon to hydrogen bonds are \[\sigma -\]bonds
done
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E)
All carbon to carbon bonds are\[\sigma -\]bonds
done
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View Answer play_arrow
question_answer 82) An example of a polar covalent compound is:
A)
\[KCl\]
done
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B)
\[NaCl\]
done
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C)
\[CC{{l}_{4}}\]
done
clear
D)
\[HCl\]
done
clear
E)
\[C{{H}_{4}}\]
done
clear
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question_answer 83) If\[117g\text{ }NaCl\]is dissolved in 1000 got water the concentration of the solution is said to be:
A)
2 molar
done
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B)
2 molal
done
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C)
1 normal
done
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D)
1 molal
done
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E)
2 normal
done
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question_answer 84) A solution of 4.5 g of a pure non-electrolyte in 100 g of water was found to freeze at\[0.465{}^\circ C\]. The molecular weight of the solute is closest to: \[({{k}_{f}}=1.86)\]
A)
135.0
done
clear
B)
172.0
done
clear
C)
90.0
done
clear
D)
86.2
done
clear
E)
180.0
done
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question_answer 85) The enthalpy of vaporization of substance is \[840\text{ }J\text{ m}o{{l}^{-1}}\]and its boiling point is\[-173{}^\circ C\]. Its entropy of vaporization is:
A)
\[42\text{ }J\text{ }mo{{l}^{-1}}{{K}^{-1}}\]
done
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B)
\[21\text{ }J\text{ }mo{{l}^{-1}}{{K}^{-1}}\]
done
clear
C)
\[84\text{ }J\text{ m}o{{l}^{-1}}{{K}^{-1}}\]
done
clear
D)
\[8.4\text{ }J\text{ mo}{{l}^{-1}}{{K}^{-1}}\]
done
clear
E)
\[0.028\text{ }J\text{ }mo{{l}^{-1}}{{K}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 86) Given the following thermochemical equations: \[Zn+\frac{1}{2}{{O}_{2}}\xrightarrow[{}]{{}}ZnO+84,000\,cal\] \[Hg+\frac{1}{2}{{O}_{2}}\xrightarrow[{}]{{}}HgO+21,700\,cal\] Accordingly the heat of reaction for the following reaction, \[Zn+HgO\xrightarrow[{}]{{}}Hg+\]heat is:
A)
105, 700 cal
done
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B)
61, 000 cal
done
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C)
105, 000 cal
done
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D)
60, 000 cal
done
clear
E)
62, 300 cal
done
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question_answer 87) A saturated solution of\[Ca{{F}_{2}}\]is\[2\times {{10}^{-4}}mol/L\] Its solubility product constant is:
A)
\[2.6\times {{10}^{-9}}\]
done
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B)
\[4\times {{10}^{-8}}\]
done
clear
C)
\[8\times {{10}^{-12}}\]
done
clear
D)
\[3.2\times {{10}^{-11}}\]
done
clear
E)
\[8\times {{10}^{-10}}\]
done
clear
View Answer play_arrow
question_answer 88) For the reaction\[{{H}_{2}}(g)+{{I}_{2}}(g)2HI(g),\]the equilibrium constants expressed in terms of concentrations\[{{K}_{c}}\]and in terms of partial pressures\[{{K}_{p}},\]are related as:
A)
\[{{K}_{p}}={{K}_{c}}{{(RT)}^{2}}\]
done
clear
B)
\[{{K}_{p}}={{K}_{c}}{{(RT)}^{-2}}\]
done
clear
C)
\[{{K}_{p}}={{K}_{c}}\]
done
clear
D)
\[{{K}_{c}}={{K}_{p}}(RT)\]
done
clear
E)
\[{{K}_{c}}={{K}_{p}}{{(RT)}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 89) Which of the following\[1:1\]mixture will act as buffer solution?
A)
\[HCl\]and \[NaOH\]
done
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B)
\[KOH\] and \[C{{H}_{3}}COOH\]
done
clear
C)
\[C{{H}_{3}}COOH\] and \[NaCl\]
done
clear
D)
\[C{{H}_{3}}COONa\] and \[N{{H}_{4}}OH\]
done
clear
E)
\[C{{H}_{3}}COOH\] and\[C{{H}_{3}}COONa\]
done
clear
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question_answer 90) What is potential of platinum wire dipped into a solution of\[0.1\,M\,in\,S{{n}^{2+}}\]and\[0.01\,M\,in\,S{{n}^{4+}}\]?
A)
\[E{}^\circ \]
done
clear
B)
\[E{}^\circ +0.059\]
done
clear
C)
\[E{}^\circ +\frac{0.059}{2}\]
done
clear
D)
\[E{}^\circ -0.059\]
done
clear
E)
\[E{}^\circ -2\times 0.59\]
done
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question_answer 91) In one of the following reactions\[HN{{O}_{3}}\]does not behave as an oxidizing agent. Identify it:
A)
\[{{I}_{2}}+10HN{{O}_{3}}\xrightarrow{{}}2HI{{O}_{3}}+10N{{O}_{2}}\]\[+4{{H}_{2}}O\]
done
clear
B)
\[3Cu+8HN{{O}_{3}}\xrightarrow{{}}3Cu{{(N{{O}_{3}})}_{2}}\]\[+2NO+4{{H}_{2}}O\]
done
clear
C)
\[4Zn+10HN{{O}_{3}}\xrightarrow[{}]{{}}4Zn{{(N{{O}_{3}})}_{2}}\]\[+N{{H}_{4}}N{{O}_{3}}+3{{H}_{2}}O\]
done
clear
D)
\[N{{O}_{3}}+3F{{e}^{2+}}+4{{H}^{+}}\xrightarrow[{}]{{}}NO\]\[+3F{{e}^{3+}}+2{{H}_{2}}O\]
done
clear
E)
\[2HN{{O}_{3}}+{{P}_{2}}{{O}_{5}}\xrightarrow{{}}2HP{{O}_{3}}+{{N}_{2}}{{O}_{5}}\]
done
clear
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question_answer 92) Which of the following statement is not correct?
A)
In zero order reaction the rate of the reaction remains constant throughout
done
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B)
A second order reaction would become a pseudo first order reaction when one of the reactants is taken in large excess
done
clear
C)
The value of first order rate constant expends on the units of the concentration terms used
done
clear
D)
In a first order reaction the plot of log \[(\alpha -x)vs\]time gives a straight line
done
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E)
The value of\[{{t}_{1/2}}\]for a first order reaction is independent of initial concentration
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question_answer 93) Radioactive decay series of uranium is denoted as:
A)
\[4n+1\]
done
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B)
\[4n+2\]
done
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C)
\[4n\]
done
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D)
\[4n+3\]
done
clear
E)
\[4n+4\]
done
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View Answer play_arrow
question_answer 94) The number of isomeric hexanes is:
A)
5
done
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B)
2
done
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C)
3
done
clear
D)
4
done
clear
E)
6
done
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question_answer 95) The coagulating power of an electrolyte for arsenious sulphide decreases in the order:
A)
\[N{{a}^{+}}>A{{l}^{3+}}>B{{a}^{2+}}\]
done
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B)
\[PO_{4}^{3-}>SO_{4}^{2-}>C{{l}^{-}}\]
done
clear
C)
\[Cl>SO_{4}^{2-}>PO_{4}^{3-}\]
done
clear
D)
\[A{{l}^{3+}}>B{{a}^{2+}}>N{{a}^{+}}\]
done
clear
E)
\[N{{a}^{+}}>B{{a}^{2+}}>PO_{4}^{3-}\]
done
clear
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question_answer 96)
The two optical isomers given below, namely:
A)
enantiomers
done
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B)
geometrical isomers
done
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C)
diastereomers
done
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D)
structural isomers
done
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E)
conformational isomers
done
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View Answer play_arrow
question_answer 97) Which of the following statement is wrong?
A)
Using Lassaignes test nitrogen and sulphur present in organic compound can be tested
done
clear
B)
Using Beilsteins test the presence of halogen in a compound can be tested
done
clear
C)
In Lassaignes filtrate the nitrogen present in a organic compound is converted into\[NaCN\]
done
clear
D)
Lassaignes test fail to identify nitrogen in diazo compound
done
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E)
In the estimation of carbon, an organic compound is heated with\[CaO\]in a combustion tube
done
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View Answer play_arrow
question_answer 98) Cist-trans isomers generally:
A)
contain an asymmetric carbon atom
done
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B)
rotate the plane of polarized light
done
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C)
are enantiomorphs
done
clear
D)
contain a triple bond
done
clear
E)
contain double bonded carbon atoms
done
clear
View Answer play_arrow
question_answer 99) Wurtzs reaction involves the reduction of alkyl halide with:
A)
\[Zn/HCl\]
done
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B)
\[HI\]
done
clear
C)
\[Zn/Cu\]couple
done
clear
D)
Na in ether
done
clear
E)
\[Zn\]in an inert solvent
done
clear
View Answer play_arrow
question_answer 100) The reaction \[{{C}_{12}}{{H}_{26}}\xrightarrow[{}]{{}}{{C}_{6}}{{H}_{12}}+{{C}_{6}}{{H}_{14}}\]represent:
A)
substitution
done
clear
B)
synthesis
done
clear
C)
cracking
done
clear
D)
polymerization
done
clear
E)
addition
done
clear
View Answer play_arrow
question_answer 101) The compound that does not answer iodoform test is:
A)
ethanol
done
clear
B)
ethanol
done
clear
C)
methanol
done
clear
D)
propanone
done
clear
E)
acetophenone
done
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View Answer play_arrow
question_answer 102) Which one of the following compound reacts with chlorobenzene to produce DDT?
A)
Acetaldehyde
done
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B)
Nitrobenzene
done
clear
C)
m-chloroacetaldehyde
done
clear
D)
Trichloroacetaldehyde
done
clear
E)
Benzene
done
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View Answer play_arrow
question_answer 103) Conversion of benzaldehyde to 3-phenylprop-2-en-l-oic acid is:
A)
Perkin condensation
done
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B)
Claisen condensation
done
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C)
oxidative addition
done
clear
D)
Aldol condensation
done
clear
E)
none of the above
done
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View Answer play_arrow
question_answer 104) Which of the following compounds forms an addition compound with\[C{{H}_{3}}MgBr,\]which on hydrolysis produce a secondary alcohol?
A)
\[HCHO\]
done
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B)
\[C{{H}_{3}}CHO\] \[RCHO+Grignard\text{ }reagent\xrightarrow{{}}\] secondary alcohol
done
clear
C)
\[C{{H}_{3}}OC{{H}_{3}}\]
done
clear
D)
\[C{{H}_{3}}COC{{H}_{3}}\]
done
clear
E)
\[C{{H}_{3}}COOC{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 105)
Which of the following pairs are correctly matched? 1. Haber process Manufacture of ammonia 2. Leblanc process Manufacture of sulphuric acid 3. Birkeland-Eyde process Manufacture of nitric acid 4. Solvay process Manufacture of sodium carbonate
Select the correct answer using the codes given below:
A)
2, 3 and 4
done
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B)
1, 2, 3 and 4
done
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C)
1, 2 and 4
done
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D)
1, 2 and 3
done
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E)
1, 3 and 4
done
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View Answer play_arrow
question_answer 106) Which of the following compounds on treatment first with\[NaN{{O}_{2}}/HCl\]and then coupled with phenol produces p-hydroxyazobenzene?
A)
Nitrobenzene
done
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B)
Azobenzene
done
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C)
Phenol
done
clear
D)
Phenyl isocyanide
done
clear
E)
Aniline
done
clear
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question_answer 107) Initial setting of cement is mainly due to:
A)
hydration and gel formation
done
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B)
dehydration and gel formation
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C)
hydration and hydrolysis
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D)
dehydration and dehydrolysis
done
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E)
hydration and oxidation
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question_answer 108) A certain metal will liberate hydrogen from dilute acids. It will react with water to form hydrogen only when the metal is heated and the water is in the form of steam. The metal is probably:
A)
iron
done
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B)
potassium
done
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C)
copper
done
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D)
mercury
done
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E)
sodium
done
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question_answer 109) The number of \[\alpha \] and\[\beta \]particles emitted in the chain of reactions leading to the decay of \[_{92}^{238}U\]to\[_{82}^{206}Pb\]:
A)
\[8\beta \]particles and \[6\alpha \] particles
done
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B)
\[5\alpha \] particles and\[0\beta \]particles
done
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C)
\[8\alpha \] and\[6\beta \]particles
done
clear
D)
\[10\alpha \]particles and\[10\beta \]particles
done
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E)
\[5\alpha \]particles and\[2\beta \]particles
done
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question_answer 110) Hydrogen peroxide when added to a solution of potassium permanganate acidified with sulphuric acid:
A)
forms water only
done
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B)
acts as an oxidizing agent
done
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C)
acts as a reducing agent
done
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D)
reduces sulphuric acid
done
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E)
produces hydrogen
done
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question_answer 111) The equilibrium molecular structure of hydrogen peroxide is:
A)
Planar as given below
done
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B)
linear
done
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C)
tetrahedral
done
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D)
non planar
done
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E)
planar as given below
done
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question_answer 112) Consider the following compounds: 1. Sulphur dioxide 2. Hydrogen peroxide 3. Ozone Among these compounds identify those that can act as bleaching agent:
A)
1 and 3
done
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B)
2 and 3
done
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C)
1 and 2
done
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D)
1, 2 and 3
done
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E)
1 only
done
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question_answer 113) Alkali metals have high oxidation potential and hence, they behave as:
A)
oxidizing agents
done
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B)
Lewis bases
done
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C)
reducing agents
done
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D)
electrolytes
done
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E)
Bronsted bases
done
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question_answer 114) Water is oxidized to oxygen by:
A)
\[Cl{{O}_{2}}\]
done
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B)
\[KMn{{O}_{4}}\]
done
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C)
\[{{H}_{2}}{{O}_{2}}\]
done
clear
D)
fluorine
done
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E)
ozone
done
clear
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question_answer 115) Identify the incorrect statement:
A)
The molarity of a solution is independent of temperature
done
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B)
The tendency for catenation is much higher for carbon than for silicon
done
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C)
Nitriles and iso nitriles constitute metamers
done
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D)
t -butyl 1-carbocation has planar carbons and is very reactive
done
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E)
Zirconium and Hafnium are strikingly similar because of their almost same ionic radii
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question_answer 116) The magnetic momenta, of transition metals is related to the number of unpaired electrons, n as:
A)
\[\mu =n{{(n+2)}^{2}}\]
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B)
\[\mu ={{n}^{2}}(n+2)\]
done
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C)
\[\mu =n/(n+2)\]
done
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D)
\[\mu =n/\sqrt{(n+2)}\]
done
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E)
\[\mu =\sqrt{n+(n+2)}\]
done
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question_answer 117) Which one of the following statement is wrong?
A)
The IUPAC name of\[[Co{{(N{{H}_{3}})}_{6}}C{{l}_{3}}]\]is hexamine cobalt (III) chloride
done
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B)
Dibenzol peroxide is a catalyst in the polymerization of PVC
done
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C)
Borosilicate glass is heat resistant
done
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D)
Concentrated\[HN{{O}_{3}}\]can be safely transported in aluminium containers
done
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E)
\[p{{K}_{a}}\]of trichloroacetic acid is less than that of acetic acid
done
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question_answer 118) Which of the following is not a thermoplastic?
A)
Polystyrene
done
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B)
Teflon
done
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C)
Polyvinyl chloride
done
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D)
Nylon 6, 6
done
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E)
Novalac
done
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question_answer 119) Which set is the correct pairing set (or contains complementary pairs) responsible for the structure of DNA? (A-adenine, G-guanine, C-cytosine, T-thymine, U-uracil)
A)
A-T, G-C
done
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B)
A-C, G-T
done
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C)
A-G, C-T
done
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D)
A-U, G-C
done
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E)
T-U, G-C
done
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question_answer 120) Barbituric acid and its derivatives are well known as:
A)
tranquilizers
done
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B)
antiseptics
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C)
analgesics
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D)
antipyretics
done
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E)
antibiotic
done
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question_answer 121) If\[f(x)={{\log }_{x}}({{\log }_{e}}x),\]then\[f(x)\]at\[x=e\]is equal to:
A)
1
done
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B)
2
done
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C)
0
done
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D)
\[e\]
done
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E)
\[1/e\]
done
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question_answer 122) The number of terms in the expansion of \[{{(a+b+c)}^{10}}\]is:
A)
11
done
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B)
21
done
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C)
55
done
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D)
66
done
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E)
44
done
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question_answer 123) For what value of\[\lambda ,\]the system of equations \[x+y+z=6,\text{ }x+2y+3z=10,\]\[x+2y+\lambda z=10\]is consistent?
A)
1
done
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B)
2
done
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C)
\[-1\]
done
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D)
3
done
clear
E)
\[-3\]
done
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question_answer 124) Let\[f(x)\]be twice differentiable such that\[f(x)=-f(x),f(x)=g(x),\]where\[f(x)\]and\[f(x)\]represent the first and second derivatives of\[f(x)\]respectively. Also, if\[h(x)={{[f(x)]}^{2}}+{{[g(x)]}^{2}}\]and\[h(5)=5,\]then\[h(10)\]is equal to:
A)
3
done
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B)
10
done
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C)
13
done
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D)
5
done
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E)
0
done
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question_answer 125) A straight line through P (1, 2) is such that its intercept between the axes is bisected at P. Its equation is:
A)
\[x+y=-1\]
done
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B)
\[x+y=3\]
done
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C)
\[x+2y=5\]
done
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D)
\[2x+y=4\]
done
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E)
none of these
done
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question_answer 126) The radius of any circle touching the lines \[3x-4y+5=0\]and\[6x-8y-9=0\]is:
A)
1.9
done
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B)
0.95
done
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C)
2.9
done
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D)
1.45
done
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E)
1.95
done
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question_answer 127) The point on the curve\[\sqrt{x}+\sqrt{y}=\sqrt{a},\]the normal at which is parallel to the\[x-\]axis, is:
A)
\[(0,0)\]
done
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B)
\[(0,a)\]
done
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C)
\[(a,0)\]
done
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D)
\[(a,a)\]
done
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E)
\[(-a,a)\]
done
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question_answer 128) If two circles of the same radius r and centres at (2,3) and (5,6) respectively cut orthogonally, then the value of r is:
A)
3
done
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B)
2
done
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C)
1
done
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D)
5
done
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E)
6
done
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question_answer 129) The equation to the sides of a triangle are \[x-3y=0,\text{ }4x+3y=5\]and\[3x+y=0\]. The line \[3x-4y=0\]passes through:
A)
the incentre
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B)
the centroid
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C)
the orthocentre
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D)
the circumcentre
done
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E)
none of these
done
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question_answer 130) For\[|x|<1,\]let\[y=1+x+{{x}^{2}}+.....\]to\[\infty ,\]then\[\frac{dy}{dx}-y\]is equal to:
A)
\[\frac{x}{y}\]
done
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B)
\[\frac{{{x}^{2}}}{{{y}^{2}}}\]
done
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C)
\[\frac{x}{{{y}^{2}}}\]
done
clear
D)
\[x{{y}^{2}}\]
done
clear
E)
\[\frac{x-1}{{{y}^{2}}}\]
done
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question_answer 131) If\[(-4,5)\]is one vertex and\[7x-y+8=0\]is one diagonal of a square, then the equation of the second diagonal is:
A)
\[x+3y=21\]
done
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B)
\[2x-3y=7\]
done
clear
C)
\[x+7y=31\]
done
clear
D)
\[2x+3y=21\]
done
clear
E)
\[x-3y=21\]
done
clear
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question_answer 132) The number of common tangents to two circles \[{{x}^{2}}+{{y}^{2}}=4\] and\[{{x}^{2}}+{{y}^{2}}-8x+12=0\]is:
A)
1
done
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B)
2
done
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C)
5
done
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D)
4
done
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E)
3
done
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question_answer 133) If\[y=lo{{g}^{n}}x,\]where\[lo{{g}^{n}}\]means\[log\text{ }log\text{ }log\text{ }...\](repeated n times), then \[x\text{ }log\text{ }x\text{ }lo{{g}^{2}}x\text{ }lo{{g}^{3}}x\text{ }...\text{ }lo{{g}^{n-1}}\text{ }x\text{ }lo{{g}^{n}}x\frac{dy}{dx}\] is equal to:
A)
\[\log x\]
done
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B)
\[x\]
done
clear
C)
\[\frac{1}{\log x}\]
done
clear
D)
\[1\]
done
clear
E)
\[{{\log }^{n}}x\]
done
clear
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question_answer 134) The focus of the parabola\[{{y}^{2}}-x-2y+2=0\]is:
A)
(1/4, 0)
done
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B)
(1, 2)
done
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C)
(5/4, 1)
done
clear
D)
(3/4, 5/2)
done
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E)
(1, 5/4)
done
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question_answer 135) The equation of the parabola with vertex at the origin and directrix\[y=2\]is:
A)
\[{{y}^{2}}=8x\]
done
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B)
\[{{y}^{2}}=-8x\]
done
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C)
\[{{y}^{2}}=\sqrt{8}x\]
done
clear
D)
\[{{x}^{2}}=8y\]
done
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E)
\[{{x}^{2}}=-8y\]
done
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question_answer 136) The point on the curve\[x{{y}^{2}}=1\]that is nearest to the origin, is:
A)
(1, 1)
done
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B)
(4, 1/2)
done
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C)
(1/4, 2)
done
clear
D)
\[({{2}^{1/6}},{{(1/2)}^{1/12}})\]
done
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E)
\[({{(1/2)}^{1/3}},{{2}^{1/6}})\]
done
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question_answer 137) The distance of the point A (2, 3, 4) from\[x-\]axis is:
A)
5
done
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B)
\[\sqrt{13}\]
done
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C)
\[2\sqrt{5}\]
done
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D)
\[5\sqrt{2}\]
done
clear
E)
none of these
done
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question_answer 138) The radius of the circle \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z-11=0\]and \[x+2y+2z-15=0\]is:
A)
\[\sqrt{3}\]
done
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B)
\[\sqrt{5}\]
done
clear
C)
\[\sqrt{7}\]
done
clear
D)
\[3\]
done
clear
E)
\[\sqrt{2}\]
done
clear
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question_answer 139) \[\int{{{x}^{2}}{{(ax+b)}^{-2}}dx}\]is equal to:
A)
\[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}\log (ax+b) \right)+c\]
done
clear
B)
\[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\]
done
clear
C)
\[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)+\frac{{{x}^{2}}}{a(ax+b)}+c\]
done
clear
D)
\[\frac{2}{{{a}^{2}}}\left( x+\frac{b}{a}\log (ax+b) \right)-\frac{{{x}^{2}}}{a(ax+b)}+c\]
done
clear
E)
\[\frac{2}{{{a}^{2}}}\left( x-\frac{b}{a}\log (ax+b) \right)+\frac{{{x}^{2}}}{a(ax+b)}+c\]
done
clear
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question_answer 140) If the co-ordinate of the vertices of a triangle ABC be\[A(-1,3,2),B(2,3,5)\]and \[C(3,5,-2),\] then\[\angle A\]is equal to:
A)
\[45{}^\circ \]
done
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B)
\[60{}^\circ \]
done
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C)
\[90{}^\circ \]
done
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D)
\[30{}^\circ \]
done
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E)
\[135{}^\circ \]
done
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question_answer 141) If\[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}|\overrightarrow{a}|=3,|\overrightarrow{b}|=5\]and\[|\overrightarrow{c}|=7,\]then the angle between\[\overrightarrow{a}\]and\[\overrightarrow{b}\]is:
A)
0
done
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B)
\[30{}^\circ \]
done
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C)
\[45{}^\circ \]
done
clear
D)
\[60{}^\circ \]
done
clear
E)
\[90{}^\circ \]
done
clear
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question_answer 142) If\[f(t)\]is an odd function, the\[\int_{0}^{x}{f(t)}\,dt\]is:
A)
an odd function
done
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B)
an even function
done
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C)
neither even nor odd
done
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D)
0
done
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E)
1
done
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question_answer 143) The projection of\[\hat{i}+3\text{ }\hat{j}+\hat{k}\]on\[2\hat{i}-3\text{ }\hat{j}+6\hat{k}\]is:
A)
1/7
done
clear
B)
\[-1/7\]
done
clear
C)
7
done
clear
D)
\[-7\]
done
clear
E)
1
done
clear
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question_answer 144) If\[\overrightarrow{a}\times \overrightarrow{b}=0\]and\[\overrightarrow{a}.\overrightarrow{b}=0\]then:
A)
\[\overrightarrow{a}\bot \overrightarrow{b}\]
done
clear
B)
\[\overrightarrow{a}|\,|\overrightarrow{b}\]
done
clear
C)
\[\overrightarrow{a}=0\]and\[\overrightarrow{b}=\overrightarrow{0}\]
done
clear
D)
\[\overrightarrow{a}=\overrightarrow{0}\]and\[\overrightarrow{b}=\overrightarrow{0}\]
done
clear
E)
cannot be determined
done
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question_answer 145) If the area bounded by the parabola\[y=2-{{x}^{2}}\]and the line\[x+y=0\]is A sq unit, then A equals:
A)
1/2
done
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B)
1/3
done
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C)
2/9
done
clear
D)
9/2
done
clear
E)
9
done
clear
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question_answer 146) The points\[A(4,5,1),B(0,-1,-1),C(3,9,4)\]and \[D(-4,4,4)\]are:
A)
collinear
done
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B)
coplanar
done
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C)
non-coplanar
done
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D)
non-collinear
done
clear
E)
non-collinear and non-coplanar
done
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question_answer 147) \[{{(\overrightarrow{a}\times \overrightarrow{b})}^{2}}\]is equal to:
A)
\[\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-(\overrightarrow{a}.\overrightarrow{b})\]
done
clear
B)
\[\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-{{(\overrightarrow{a}.\overrightarrow{b})}^{2}}\]
done
clear
C)
\[\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-2\,\,\overrightarrow{a}\,\,.\,\,\overrightarrow{b}\]
done
clear
D)
\[\overset{{{\to }^{2}}}{\mathop{a}}\,+\overset{{{\to }^{2}}}{\mathop{b}}\,-2\,\,\overrightarrow{a}\,\,.\,\,\overrightarrow{b}\]
done
clear
E)
none of the above
done
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question_answer 148) Let F denotes the family of ellipses whose centre is at the origin and major axis is the y-axis. Then, equation of the family F is:
A)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
done
clear
B)
\[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
done
clear
C)
\[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
done
clear
D)
\[\frac{{{d}^{2}}y}{d{{x}^{2}}}-\frac{dy}{dx}\left( x\frac{dy}{dx}-y \right)=0\]
done
clear
E)
\[xy\frac{{{d}^{2}}y}{d{{x}^{2}}}+\left( x\frac{dy}{dx}-y \right)=0\]
done
clear
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question_answer 149) The value of \[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\left[ \cos \left( \frac{\pi }{{{2}^{2}}} \right)+i\sin \left( \frac{\pi }{{{2}^{2}}} \right) \right]\] \[\left[ \cos \left( \frac{\pi }{{{2}^{3}}} \right)+i\sin \left( \frac{\pi }{{{2}^{3}}} \right) \right].....\infty \]is:
A)
\[-1\]
done
clear
B)
\[1\]
done
clear
C)
\[0\]
done
clear
D)
\[\sqrt{2}\]
done
clear
E)
\[-\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 150) If\[x+\frac{1}{x}=2\sin \alpha ,y+\frac{1}{y}=2\cos \beta ,\]then\[{{x}^{3}}{{y}^{3}}+\frac{1}{{{x}^{3}}{{y}^{3}}}\]is:
A)
\[2\cos 3(\beta -\alpha )\]
done
clear
B)
\[2\cos 3(\beta +\alpha )\]
done
clear
C)
\[2\sin 3(\beta -\alpha )\]
done
clear
D)
\[2\sin 3(\beta +\alpha )\]
done
clear
E)
\[\sin 3(\beta -\alpha )\]
done
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question_answer 151) Solution of the equation\[x{{\left( \frac{dy}{dx} \right)}^{2}}+2\sqrt{xy}\frac{dy}{dx}+y=0\]is:
A)
\[x+y=a\]
done
clear
B)
\[\sqrt{x}-\sqrt{y}=\sqrt{a}\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]
done
clear
D)
\[\sqrt{x}+\sqrt{y}=\sqrt{a}\]
done
clear
E)
\[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]
done
clear
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question_answer 152) A bag contains 5 white and 3 black balls and 4 balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is:
A)
1/196
done
clear
B)
2/7
done
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C)
1/7
done
clear
D)
13/56
done
clear
E)
3/7
done
clear
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question_answer 153) If \[\underset{x\to a}{\mathop{\lim }}\,\frac{{{a}^{x}}-{{x}^{a}}}{{{x}^{x}}-{{a}^{a}}}=-1,\]then a equals to:
A)
1
done
clear
B)
0
done
clear
C)
e
done
clear
D)
\[(1/e)\]
done
clear
E)
\[\infty \]
done
clear
View Answer play_arrow
question_answer 154) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}\]is equal to:
A)
0
done
clear
B)
1
done
clear
C)
1/2
done
clear
D)
\[-1/2\]
done
clear
E)
\[\infty \]
done
clear
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question_answer 155) \[\underset{x\to a}{\mathop{\lim }}\,\frac{\log (x-a)}{\log ({{e}^{x}}-{{e}^{a}})}\]is equal to:
A)
0
done
clear
B)
1
done
clear
C)
a
done
clear
D)
does not exist
done
clear
E)
\[-a\]
done
clear
View Answer play_arrow
question_answer 156) If\[f(x)=|x{{|}^{3}},\] then\[f(0)\] equals:
A)
0
done
clear
B)
1/2
done
clear
C)
\[-1\]
done
clear
D)
\[-1/2\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 157) \[\int{{{e}^{-\log x}}}dx\]is equal to:
A)
\[{{e}^{-\log x}}+c\]
done
clear
B)
\[-x{{e}^{-\log x}}+c\]
done
clear
C)
\[{{e}^{\log x}}+c\]
done
clear
D)
\[\log x+c\]
done
clear
E)
\[\log |x|+c\]
done
clear
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question_answer 158) The area cut off by the latus rectum from the parabola\[{{y}^{2}}=4ax\]is:
A)
\[(8/3)\text{ }a\text{ }sq\text{ }unit\]
done
clear
B)
\[(8/3)\,\sqrt{a}\,sq\,\] unit
done
clear
C)
\[(3/8)\text{ }{{a}^{2}}\text{ }sq\text{ }unit\]
done
clear
D)
\[(8/3)\text{ }{{a}^{3}}sq\text{ }unit\]
done
clear
E)
\[(8/3)\text{ }{{a}^{2}}\text{ }sq\text{ }unit\]
done
clear
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question_answer 159) The solution of differential equation \[(x+y)(dx-dy)=dx+dy\]is:
A)
\[x-y=k{{e}^{x-y}}\]
done
clear
B)
\[x+y=k{{e}^{x+y}}\]
done
clear
C)
\[x+y=k(x-y)\]
done
clear
D)
\[x-y=k{{e}^{x+y}}\]
done
clear
E)
\[x+y=k{{e}^{x-y}}\]
done
clear
View Answer play_arrow
question_answer 160) In how many ways can 8 students be arranged in a row?
A)
\[8!\]
done
clear
B)
\[7!\]
done
clear
C)
8
done
clear
D)
7
done
clear
E)
\[2\times 7!\]
done
clear
View Answer play_arrow
question_answer 161) If the third term of a GP is P, then the product of the first 5 terms of the GP is:
A)
\[{{P}^{3}}\]
done
clear
B)
\[{{P}^{2}}\]
done
clear
C)
\[{{P}^{10}}\]
done
clear
D)
\[{{P}^{4}}\]
done
clear
E)
\[{{P}^{5}}\]
done
clear
View Answer play_arrow
question_answer 162) The sum to n terms of the series\[\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+.....\]is:
A)
\[\frac{{{3}^{n}}(2n+1)+1}{2({{3}^{n}})}\]
done
clear
B)
\[\frac{{{3}^{n}}(2n+1)-1}{2({{3}^{n}})}\]
done
clear
C)
\[\frac{{{3}^{n}}n-1}{2({{3}^{n}})}\]
done
clear
D)
\[\frac{{{3}^{n}}-1}{2}\]
done
clear
E)
\[\frac{{{3}^{n}}-n}{2({{3}^{n}})}\]
done
clear
View Answer play_arrow
question_answer 163) If\[\alpha \]and\[\beta \]are the solutions of the quadratic equation\[a{{x}^{2}}+bx+c=0\]such that\[\beta ={{\alpha }^{1/3}},\]then:
A)
\[{{(ac)}^{1/3}}+{{(ab)}^{1/3}}+c=0\]
done
clear
B)
\[{{({{a}^{3}}b)}^{1/4}}+{{(a{{b}^{3}})}^{1/4}}+c=0\]
done
clear
C)
\[{{({{a}^{3}}c)}^{1/4}}+{{(a{{c}^{3}})}^{1/4}}+b=0\]
done
clear
D)
\[{{({{a}^{4}}c)}^{1/3}}+{{(a{{c}^{4}})}^{1/3}}+b=0\]
done
clear
E)
\[{{({{a}^{3}}c)}^{1/4}}-{{(a{{c}^{3}})}^{1/4}}+b=0\]
done
clear
View Answer play_arrow
question_answer 164) \[^{20}{{C}_{4}}+{{2.}^{20}}{{C}_{3}}{{+}^{20}}{{C}_{2}}{{-}^{22}}{{C}_{18}}\]is equal to:
A)
0
done
clear
B)
1242
done
clear
C)
7315
done
clear
D)
6345
done
clear
E)
3340
done
clear
View Answer play_arrow
question_answer 165) If \[x=\frac{\left[ \begin{align} & 729+6(2)(243)+15(4)(81)+20(8)(27) \\ & +15(16)(9)+6(32)3+64 \\ \end{align} \right]}{1+4(4)+6(16)+4(64)+256}\] then \[\sqrt{x}-\frac{1}{\sqrt{x}}\]is equal to:
A)
0.2
done
clear
B)
4.8
done
clear
C)
1.02
done
clear
D)
5.2
done
clear
E)
25
done
clear
View Answer play_arrow
question_answer 166) Along a road lie an odd number of stones placed at intervals of 10 m. These stones have to be assembled around the middle stone. A person can carry only one stone at a time. A man started the job with one of the end stones by carrying them in succession. In carrying all the stones, the man covered a total distance of 3 km. Then the total number of stones is:
A)
20
done
clear
B)
25
done
clear
C)
12
done
clear
D)
24
done
clear
E)
50
done
clear
View Answer play_arrow
question_answer 167) If \[a=1+2+4+...\]to n terms, \[b=1+3+9+...\]to n terms and \[c=1+5+25+...\]to n terms, then \[\left| \begin{matrix} a & 2b & 4c \\ 2 & 2 & 2 \\ {{2}^{n}} & {{3}^{n}} & {{5}^{n}} \\ \end{matrix} \right|\]equals:
A)
\[{{(30)}^{n}}\]
done
clear
B)
\[{{(10)}^{n}}\]
done
clear
C)
\[0\]
done
clear
D)
\[{{2}^{n}}+{{3}^{n}}+{{5}^{n}}\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 168) The matrix \[\left| \begin{matrix} 5 & 10 & 3 \\ -2 & -4 & 6 \\ -1 & -2 & b \\ \end{matrix} \right|\]is a singular matrix, if b is equal to:
A)
\[-3\]
done
clear
B)
3
done
clear
C)
0
done
clear
D)
for any value of b
done
clear
E)
for no value of b
done
clear
View Answer play_arrow
question_answer 169) Let N be the number of quadratic equations with coefficients from {0, 1, 2, ..., 9} such that zero is a solution of each equation. Then the value of N is:
A)
infinite
done
clear
B)
29
done
clear
C)
90
done
clear
D)
900
done
clear
E)
81
done
clear
View Answer play_arrow
question_answer 170) For non-singular square matrices A, B and C of the same order,\[{{(A{{B}^{-1}}C)}^{-1}}\]is equal to:
A)
\[{{A}^{-1}}B{{C}^{-1}}\]
done
clear
B)
\[{{C}^{-1}}{{B}^{-1}}{{A}^{-1}}\]
done
clear
C)
\[CB{{A}^{-1}}\]
done
clear
D)
\[{{C}^{-1}}B{{A}^{-1}}\]
done
clear
E)
\[{{C}^{-1}}BA\]
done
clear
View Answer play_arrow
question_answer 171) The points\[(1,1),(-5,5)\]and\[(13,\lambda )\]lie on the same straight line, if\[\lambda \]is equal to:
A)
7
done
clear
B)
\[-7\]
done
clear
C)
\[\pm 7\]
done
clear
D)
0
done
clear
E)
14
done
clear
View Answer play_arrow
question_answer 172) If\[n=1,\text{ }2,\text{ }3,\text{ }....\]then\[\cos \alpha \cos 2\alpha \cos 4\alpha .....\cos {{2}^{n-1}}\alpha \] is equal to:
A)
\[\frac{\sin 2n\alpha }{2n\sin \alpha }\]
done
clear
B)
\[\frac{\sin {{2}^{n}}\alpha }{{{2}^{n}}\sin {{2}^{n-1}}\alpha }\]
done
clear
C)
\[\frac{\sin {{4}^{n-1}}\alpha }{{{4}^{n-1}}\sin \alpha }\]
done
clear
D)
\[\frac{\sin {{2}^{n}}\alpha }{{{2}^{n}}\sin \alpha }\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 173) If the lines \[3x+4y+1=0,\text{ }5x+\lambda y+3=0\] and \[2x+y-1=0\]are concurrent, then \[\lambda \] is equal to:
A)
\[-8\]
done
clear
B)
8
done
clear
C)
4
done
clear
D)
\[-4\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 174) If the equation\[k{{x}^{2}}-2xy-{{y}^{2}}-2x+2y=0\]represents a pair of lines, then k is equal to:
A)
2
done
clear
B)
\[-2\]
done
clear
C)
\[-5\]
done
clear
D)
5
done
clear
E)
3
done
clear
View Answer play_arrow
question_answer 175) Let \[A=\left[ \begin{matrix} {{\cos }^{2}}\theta & \sin \theta \cos \theta \\ \cos \theta \sin \theta & {{\sin }^{2}}\theta \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix} {{\cos }^{2}}\phi & \sin \phi \cos \phi \\ \cos \phi \sin \phi & {{\sin }^{2}}\phi \\ \end{matrix} \right]\]then\[AB=0\]if:
A)
\[\theta =n\phi ,n=0,1,2,....\]
done
clear
B)
\[\theta +\phi =n\pi ,n=0,1,2,....\]
done
clear
C)
\[\theta =\phi +(2n+1)\frac{\pi }{2},n=0,1,2,....\]
done
clear
D)
\[\theta =\phi +n\frac{\pi }{2},n=0,1,2,....\]
done
clear
E)
\[\theta =\phi +3n\frac{\pi }{2},n=0,1,2,....\]
done
clear
View Answer play_arrow
question_answer 176) If the area of the circle \[4{{x}^{2}}+4{{y}^{2}}-8x+16y+k=0\]is\[9\pi \]sq unit, then the value of k is:
A)
4 sq unit
done
clear
B)
16 sq unit
done
clear
C)
\[-16\]sq unit
done
clear
D)
\[\pm 16\] sq unit
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 177) If a focal chord of the parabola\[{{y}^{2}}=ax\]is \[2x-y-8=0,\]then the equation of the directrix is:
A)
\[x+4=0\]
done
clear
B)
\[x-4=0\]
done
clear
C)
\[y-4=0\]
done
clear
D)
\[y+4=0\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 178) Let\[X=\left[ \begin{matrix} {{x}_{1}} \\ {{x}_{2}} \\ {{x}_{3}} \\ \end{matrix} \right],A=\left[ \begin{matrix} 1 & -1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1 \\ \end{matrix} \right]\]and\[B=\left[ \begin{matrix} 3 \\ 1 \\ 4 \\ \end{matrix} \right]\]. If\[AX=B,\]then\[X\]is equal to:
A)
\[\left[ \begin{matrix} 1 \\ 2 \\ 3 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} -1 \\ -2 \\ 3 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} -1 \\ -2 \\ -3 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} -1 \\ 2 \\ 3 \\ \end{matrix} \right]\]
done
clear
E)
\[\left[ \begin{matrix} 0 \\ 2 \\ 1 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 179) A line make angles of\[45{}^\circ \]and\[60{}^\circ \]with the \[x-\]axis and the z-axis respectively. The angle made by it with y-axis is:
A)
\[30{}^\circ \,or\text{ }150{}^\circ \]
done
clear
B)
\[60{}^\circ \,or\text{ }120{}^\circ \]
done
clear
C)
\[45{}^\circ \,or\text{ }135{}^\circ \]
done
clear
D)
\[90{}^\circ \]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 180) If\[a=\frac{\pi }{18}\]rad then\[\cos a+\cos 2a+...+\cos 18a\] is equal to:
A)
0
done
clear
B)
\[-1\]
done
clear
C)
1
done
clear
D)
\[\pm 1\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 181) If\[\sec \theta +\tan \theta =k,\cos \theta \]equals to:
A)
\[\frac{{{k}^{2}}+1}{2k}\]
done
clear
B)
\[\frac{2k}{{{k}^{2}}+1}\]
done
clear
C)
\[\frac{k}{{{k}^{2}}+1}\]
done
clear
D)
\[\frac{k}{{{k}^{2}}-1}\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 182) \[\underset{x\to \frac{\pi }{6}}{\mathop{\lim }}\,\frac{2{{\sin }^{2}}x+\sin x-1}{2{{\sin }^{2}}x-3\sin x+1}\]is equal to:
A)
3
done
clear
B)
\[-3\]
done
clear
C)
6
done
clear
D)
0
done
clear
E)
9
done
clear
View Answer play_arrow
question_answer 183) If the function\[f(x)\]is defined by \[f(x)=a+bx\]and\[{{f}^{r}}=fff\text{ }...\](repeated r times), then \[{{f}^{r}}(x)\]is equal to:
A)
\[a+{{b}^{r}}x\]
done
clear
B)
\[ar+{{b}^{r}}x\]
done
clear
C)
\[ar+b{{x}^{r}}\]
done
clear
D)
\[a({{b}^{r}}-1)+{{b}^{r}}x\]
done
clear
E)
\[a\left( \frac{{{b}^{r}}-1}{b-1} \right)+{{b}^{r}}x\]
done
clear
View Answer play_arrow
question_answer 184) If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is:
A)
a constant
done
clear
B)
\[\propto {{s}^{2}}\]
done
clear
C)
\[\propto \frac{1}{{{s}^{2}}}\]
done
clear
D)
\[\propto s\]
done
clear
E)
\[\propto \frac{1}{s}\]
done
clear
View Answer play_arrow
question_answer 185) If \[f(x)=\frac{1-x}{1+x}(x\ne -1),\]then\[{{f}^{-1}}(x)\]W equals to:
A)
\[f(x)\]
done
clear
B)
\[\frac{1}{f(x)}\]
done
clear
C)
\[-f(x)\]
done
clear
D)
\[-\frac{1}{f(x)}\]
done
clear
E)
not defined
done
clear
View Answer play_arrow
question_answer 186) Domain of the function\[f(x)={{\sin }^{-1}}({{\log }_{2}}x)\]in the set of real numbers is:
A)
\[\{x:1\le x\le 2\}\]
done
clear
B)
\[\{x:1\le x\le 3\}\]
done
clear
C)
\[\{x:-1\le x\le 2\}\]
done
clear
D)
\[\left\{ x:\frac{1}{2}\le x\le 2 \right\}\]
done
clear
E)
\[\left\{ x:-\frac{1}{2}\le x\le 2 \right\}\]
done
clear
View Answer play_arrow
question_answer 187) If \[\omega \] is a complex cube root of unity, then \[\frac{a+b\omega +c{{\omega }^{2}}}{c+a\omega +b{{\omega }^{2}}}+\frac{c+a\omega +b{{\omega }^{2}}}{a+b\omega +c{{\omega }^{2}}}+\frac{b+c\omega +a{{\omega }^{2}}}{b+c{{\omega }^{4}}+a{{\omega }^{5}}}\] is equal to:
A)
\[1\]
done
clear
B)
\[\omega \]
done
clear
C)
\[{{\omega }^{2}}\]
done
clear
D)
\[-1\]
done
clear
E)
0
done
clear
View Answer play_arrow
question_answer 188) If\[\alpha ,\beta \]and\[\gamma \]are angles such that\[\tan \alpha +\tan \beta +\tan \gamma =\tan \alpha .\tan \beta .\tan \gamma \]and\[x=\cos \alpha +i\sin \alpha ,y=\cos \beta +i\sin \beta \]and\[z=\cos \gamma +i\sin \gamma ,\]then\[xyz\]is equal to:
A)
1, but not\[-1\]
done
clear
B)
\[-1\], but not 1
done
clear
C)
\[1\]or\[-1\]
done
clear
D)
0
done
clear
E)
\[i\]
done
clear
View Answer play_arrow
question_answer 189) If\[\alpha \]and\[\beta \]are complex cube roots of unity and \[x=a\alpha +b\beta ,\text{ }y=a+b,\text{ }z=\alpha \beta +b\alpha ,\]then\[xyz\] is equal to:
A)
\[a+b\]
done
clear
B)
\[a-b\]
done
clear
C)
\[{{a}^{2}}+{{c}^{2}}\]
done
clear
D)
\[{{a}^{2}}-{{b}^{2}}\]
done
clear
E)
\[{{a}^{3}}+{{b}^{3}}\]
done
clear
View Answer play_arrow
question_answer 190) If a, b and c are distinct positive real numbers in AP, then the roots of the equation \[a{{x}^{2}}+2bx+c=0\]are:
A)
imaginary
done
clear
B)
rational and equal
done
clear
C)
rational and distinct
done
clear
D)
irrational
done
clear
E)
real, may be rational or irrational
done
clear
View Answer play_arrow
question_answer 191) If a, b and c are in AP, then which one of the following is not true?
A)
\[\frac{k}{a},\frac{k}{b}\]and\[\frac{k}{c}\]are in HP
done
clear
B)
\[a+k,\text{ }b+k\] and\[c+k\] are in AP
done
clear
C)
\[ka,kb\] and\[kc\]are in AP
done
clear
D)
\[{{a}^{2}},\text{ }{{b}^{2}}\]and\[{{c}^{2}}\]are in AP
done
clear
E)
\[a+b,\text{ }c+a\]and\[b+c\]are in AP
done
clear
View Answer play_arrow
question_answer 192) If\[{{z}_{1}},{{z}_{2}}\]and\[{{z}_{3}}\]are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are\[{{z}_{1}},{{z}_{2}}\]and\[{{z}_{3}}\]taken in order, is:
A)
\[{{z}_{1}}-{{z}_{2}}+{{z}_{3}}\]
done
clear
B)
\[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}\]
done
clear
C)
\[\frac{1}{3}({{z}_{1}}-{{z}_{2}}+{{z}_{3}})\]
done
clear
D)
\[\frac{1}{3}({{z}_{1}}+{{z}_{2}}-{{z}_{3}})\]
done
clear
E)
\[\frac{1}{3}({{z}_{1}}-{{z}_{2}}-{{z}_{3}})\]
done
clear
View Answer play_arrow
question_answer 193) \[\sqrt{4},\sqrt[4]{4},\sqrt[8]{4},\sqrt[16]{4},....\]to\[\infty \]are roots of the equation:
A)
\[{{x}^{2}}-4=0\]
done
clear
B)
\[{{x}^{2}}-4x+6=0\]
done
clear
C)
\[{{x}^{2}}-5x+4=0\]
done
clear
D)
\[{{x}^{2}}-3x+2=0\]
done
clear
E)
\[{{x}^{2}}-x=0\]
done
clear
View Answer play_arrow
question_answer 194) If\[{{a}_{1}},{{a}_{2}},{{a}_{3}},.....,{{a}_{n}}\]are the n arithmetic means between a and b, then\[2\sum\limits_{i=1}^{n}{{{a}_{i}}}\]equals:
A)
\[ab\]
done
clear
B)
\[n(a+b)\]
done
clear
C)
\[nab\]
done
clear
D)
\[\frac{(a+b)}{n}\]
done
clear
E)
\[\frac{n(a+b)}{ab}\]
done
clear
View Answer play_arrow
question_answer 195) Let a, b be the solutions of\[{{x}^{2}}+px+1=0\]and c, d be the solutions of\[{{x}^{2}}+qx+1=0\]. If \[(a-c)(b-c)\]and\[(a+d)(b+d)\]are the solutions of\[{{x}^{2}}+ax+\beta =0,\]then \[\beta \] equals:
A)
\[p+q\]
done
clear
B)
\[p-q\]
done
clear
C)
\[{{p}^{2}}+{{q}^{2}}\]
done
clear
D)
\[{{p}^{2}}-{{q}^{2}}\]
done
clear
E)
\[{{q}^{2}}-{{p}^{2}}\]
done
clear
View Answer play_arrow
question_answer 196) The \[x-\]co-ordinate of the incentre of the triangle where the mid points of the sides are (0, 1), (1,1) and (1, 0), is:
A)
\[2+\sqrt{2}\]
done
clear
B)
\[1+\sqrt{2}\]
done
clear
C)
\[2-\sqrt{2}\]
done
clear
D)
\[1-\sqrt{2}\]
done
clear
E)
\[3-\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 197) Which one of the following is true?
A)
\[\sin ({{\cos }^{-1}}x)=\cos ({{\sin }^{-1}}x)\]
done
clear
B)
\[\sec ({{\tan }^{-1}}x)=\tan ({{\sec }^{-1}}x)\]
done
clear
C)
\[\cos ({{\tan }^{-1}}x)=\tan ({{\cos }^{-1}}x)\]
done
clear
D)
\[\tan ({{\sin }^{-1}}x)=\sin ({{\tan }^{-1}}x)\]
done
clear
E)
all of these
done
clear
View Answer play_arrow
question_answer 198) If\[{{\tan }^{-1}}a+{{\tan }^{-1}}b={{\sin }^{-1}}1-{{\tan }^{-1}}c,\]then:
A)
\[a+b+c=abc\]
done
clear
B)
\[ab+bc+ca=abc\]
done
clear
C)
\[\frac{1}{a}+\frac{1}{b}+\frac{1}{c}-\frac{1}{abc}=0\]
done
clear
D)
\[ab+bc+ca=a+b+c\]
done
clear
E)
none of the above
done
clear
View Answer play_arrow
question_answer 199) Two consecutive sides of a parallelogram are \[4x+5y=0\] and\[7x+2y=0\]. One diagonal of the parallelogram is\[11x+7y=9\]. If the other diagonal is\[ax+by+c=0,\]then:
A)
\[a=-1,b=-1,c=2\]
done
clear
B)
\[a=1,b=-1,c=0\]
done
clear
C)
\[a=-1,b=-1,c=0\]
done
clear
D)
\[a=1,b=1,c=0\]
done
clear
E)
\[a=-1,b=-1,c=1\]
done
clear
View Answer play_arrow
question_answer 200) The number of values of \[\theta \] in the interval\[[-\pi ,\pi ]\]satisfying the equation\[cos\theta +sin2\theta =0\]is:
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
4
done
clear
E)
many
done
clear
View Answer play_arrow
question_answer 201) From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24, is:
A)
\[\frac{6}{25}\]
done
clear
B)
\[\frac{1}{4}\]
done
clear
C)
\[\frac{1}{6}\]
done
clear
D)
\[\frac{2}{5}\]
done
clear
E)
\[\frac{4}{5}\]
done
clear
View Answer play_arrow
question_answer 202) If the line\[x+y-1=0\]is a tangent to the parabola\[{{y}^{2}}-y+x=0,\]then the point of contact is:
A)
(0, 1)
done
clear
B)
\[(1,0)\]
done
clear
C)
\[(0,-1)\]
done
clear
D)
\[(-1,0)\]
done
clear
E)
\[(0,-1)\]
done
clear
View Answer play_arrow
question_answer 203) If\[f(x)=\left\{ \begin{matrix} \frac{2x-1}{\sqrt{1+x}-1}, & -1\le x<\infty ,x\ne 0 \\ k, & x=0 \\ \end{matrix} \right.\] is continuous everywhere, then k is equal to :
A)
\[\frac{1}{2}\log 2\]
done
clear
B)
\[\log 4\]
done
clear
C)
\[\log 8\]
done
clear
D)
\[\log 2\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 204) If\[\sec \left( \frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}} \right)={{e}^{a}},\]then\[\frac{dy}{dx}\]is equal to:
A)
\[\frac{{{y}^{2}}}{{{x}^{2}}}\]
done
clear
B)
\[\frac{y}{x}\]
done
clear
C)
\[\frac{x}{y}\]
done
clear
D)
\[\frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\]
done
clear
E)
\[0\]
done
clear
View Answer play_arrow
question_answer 205) The curve represented by the equation \[4{{x}^{2}}+16{{y}^{2}}-24x-32y-12=0\]is:
A)
a parabola
done
clear
B)
a pair of straight lines
done
clear
C)
an ellipse with eccentricity ½
done
clear
D)
an ellipse with eccentricity\[\sqrt{3}/2\]
done
clear
E)
a hyperbola with eccentricity 3/2
done
clear
View Answer play_arrow
question_answer 206) It\[{{\sin }^{-1}}x+{{\sin }^{-1}}y=\frac{\pi }{2},\]then\[\frac{dy}{dx}\]is equal to:
A)
\[\frac{x}{y}\]
done
clear
B)
\[-\frac{x}{y}\]
done
clear
C)
\[\frac{y}{x}\]
done
clear
D)
\[-\frac{y}{x}\]
done
clear
E)
none of these
done
clear
View Answer play_arrow
question_answer 207) The maximum value of\[\frac{\log x}{x}\]is equal to:
A)
\[\frac{2}{e}\]
done
clear
B)
\[\frac{1}{e}\]
done
clear
C)
\[e\]
done
clear
D)
\[1\]
done
clear
E)
\[\frac{e}{2}\]
done
clear
View Answer play_arrow
question_answer 208) \[ax+by-{{a}^{2}}=0,\]where a, b are non-zero, is the equation to the straight line perpendicular to a line \[l\]and passing through the point where (crosses the\[x-\]axis. Then equation to the line\[l\]is:
A)
\[\frac{x}{b}-\frac{y}{a}=1\]
done
clear
B)
\[\frac{x}{a}-\frac{y}{b}=1\]
done
clear
C)
\[\frac{x}{b}+\frac{y}{a}=ab\]
done
clear
D)
\[\frac{x}{a}-\frac{y}{b}=ab\]
done
clear
E)
\[\frac{x}{a}+\frac{y}{b}=ab\]
done
clear
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question_answer 209) \[\int{\frac{{{a}^{x/2}}}{\sqrt{{{a}^{-x}}-{{a}^{x}}}}}dx\]is equal to:
A)
\[\frac{1}{\log a}{{\sin }^{-1}}({{a}^{x}})+c\]
done
clear
B)
\[\frac{1}{\log a}{{\tan }^{-1}}({{a}^{x}})+c\]
done
clear
C)
\[2\sqrt{{{a}^{-x}}-{{a}^{x}}}+c\]
done
clear
D)
\[\log ({{a}^{x}}-1)+c\]
done
clear
E)
\[{{\sin }^{-1}}({{a}^{x}})+c\]
done
clear
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question_answer 210) If\[g(x)=\frac{f(x)-f(-x)}{2}\]defined over\[[-3,\text{ }3]\] and\[f(x)=2{{x}^{2}}-4x+1,\]then\[\int_{-3}^{3}{g(x)}dx\]is equal to:
A)
0
done
clear
B)
4
done
clear
C)
\[-4\]
done
clear
D)
8
done
clear
E)
none of these
done
clear
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question_answer 211) Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors \[2\hat{i}+4\hat{j}-5\hat{k}\]and\[\hat{i}+2\hat{j}+3\hat{k}\] respectively. Then, if a is a unit vector parallel to AC then a equals:
A)
\[\frac{1}{3}(3\hat{i}-6\hat{j}-2\hat{k})\]
done
clear
B)
\[\frac{1}{3}(3\hat{i}+6\hat{j}+2\hat{k})\]
done
clear
C)
\[\frac{1}{3}(3\hat{i}-6\hat{j}-3\hat{k})\]
done
clear
D)
\[\frac{1}{7}(3\hat{i}+6\hat{j}-2\hat{k})\]
done
clear
E)
\[\frac{1}{7}(3\hat{i}+5\hat{j}-3\hat{k})\]
done
clear
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question_answer 212) The solution of\[\frac{dy}{dx}+1=\cos ec(x+y)\]is:
A)
\[\cos (x+y)+x=c\]
done
clear
B)
\[\cos (x+y)=c\]
done
clear
C)
\[\sin (x+y)+x=c\]
done
clear
D)
\[\sin (x+y)+\sin (x+y)=c\]
done
clear
E)
\[x-\cos (x+y)=c\]
done
clear
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question_answer 213) Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are:
A)
\[7,6\]
done
clear
B)
\[6,3\]
done
clear
C)
\[6,4\]
done
clear
D)
\[7,4\]
done
clear
E)
\[3,7\]
done
clear
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question_answer 214) Let\[\overrightarrow{a}\]and\[\overrightarrow{b}\]be two unit vectors such that angle between them is\[60{}^\circ \]. Then\[|\overrightarrow{a}-\overrightarrow{b}|\]is equal to:
A)
\[\sqrt{5}\]
done
clear
B)
\[\sqrt{3}\]
done
clear
C)
\[0\]
done
clear
D)
\[1\]
done
clear
E)
\[\sqrt{2}\]
done
clear
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question_answer 215) Two numbers within the brackets denote the ranks of 10 students of a class in two subjects\[(1,10),(2,9),(3,8),(4,7),(5,6),(6,5)(7,4),(8,3)\]\[(9,2),(10,1),\]then rank correlation coefficient is:
A)
\[0\]
done
clear
B)
\[-1\]
done
clear
C)
\[1\]
done
clear
D)
\[0.5\]
done
clear
E)
\[-0.5\]
done
clear
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question_answer 216) \[\int{\frac{\sin x}{\sin (x-a)}}dx\]is equal to:
A)
\[x\cos a-\sin a.\log (x-a)+c\]
done
clear
B)
\[x\sin a+c\]
done
clear
C)
\[x\sin a+\sin a.\log \sin (x-a)+c\]
done
clear
D)
\[x\cos a+\sin a.\log \sin (x-a)+c\]
done
clear
E)
\[x\cos a+\cos a.\log \sin (x-a)+c\]
done
clear
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question_answer 217) If\[a=\hat{i}+2\hat{j}+3\hat{k},\]and \[\overrightarrow{b}=\hat{i}\times (\overrightarrow{a}\times \hat{i})+\hat{j}\times (\overrightarrow{a}\times \hat{j})+\overrightarrow{k}\times (\overrightarrow{a}\times \hat{k}),\] then length of \[\vec{b}\] is equal to
A)
\[\sqrt{12}\]
done
clear
B)
\[2\sqrt{12}\]
done
clear
C)
\[3\sqrt{14}\]
done
clear
D)
\[3\sqrt{12}\]
done
clear
E)
\[2\sqrt{14}\]
done
clear
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question_answer 218) \[\int{\frac{f(x)}{f(x)\log [f(x)]}}dx\]is equal to:
A)
\[\frac{f(x)}{\log f(x)}+c\]
done
clear
B)
\[f(x).\log f(x)+c\]
done
clear
C)
\[\log [\log f(x)]+c\]
done
clear
D)
\[\frac{1}{\log [\log f(x)]}+c\]
done
clear
E)
\[\frac{\log f(x)}{f(x)}+c\]
done
clear
View Answer play_arrow
question_answer 219) \[\int{\frac{{{e}^{x}}}{(2+{{e}^{x}})({{e}^{x}}+1)}}dx\]is equal to:
A)
\[\log \left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c\]
done
clear
B)
\[\log \left( \frac{{{e}^{x}}+2}{{{e}^{x}}+1} \right)+c\]
done
clear
C)
\[\left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c\]
done
clear
D)
\[\left( \frac{{{e}^{x}}+2}{{{e}^{x}}+1} \right)+c\]
done
clear
E)
\[\frac{1}{2}\log \left( \frac{{{e}^{x}}+1}{{{e}^{x}}+2} \right)+c\]
done
clear
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question_answer 220) For any angle\[\theta ,\]the expression\[\frac{2\cos 8\theta +1}{2\cos \theta +1}\]is equal to:
A)
\[(2\cos \theta +1)(2\cos 2\theta +1)(2\cos 4\theta +1)\]
done
clear
B)
\[(\cos \theta -1)(\cos 2\theta -1)(\cos 4\theta -1)\]
done
clear
C)
\[(2\cos \theta -1)(2\cos 2\theta -1)(2\cos 4\theta -1)\]
done
clear
D)
\[(2\cos \theta +1)(2\cos 2\theta +1)(2\cos 4\theta +1)\]
done
clear
E)
\[(2\cos \theta -1)(2\cos 2\theta -1)(2\cos 4\theta +1)\]
done
clear
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question_answer 221) If\[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta d\theta ,}\]then\[{{I}_{8}}+{{I}_{6}}\]is equal to:
A)
\[\frac{1}{7}\]
done
clear
B)
\[\frac{1}{4}\]
done
clear
C)
\[\frac{1}{5}\]
done
clear
D)
\[\frac{1}{6}\]
done
clear
E)
\[\frac{1}{2}\]
done
clear
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question_answer 222) The order of the differential equation \[{{\left( \frac{{{d}^{2}}y}{d{{x}^{2}}} \right)}^{3}}={{\left( 1+\frac{dy}{dx} \right)}^{1/2}}\]is:
A)
2
done
clear
B)
3
done
clear
C)
\[\frac{1}{2}\]
done
clear
D)
4
done
clear
E)
6
done
clear
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question_answer 223) If\[m\tan (\theta -30{}^\circ )=n\tan (\theta +120{}^\circ ),\]then\[\cos 2\theta \]equals:
A)
\[\frac{m+n}{m-n}\]
done
clear
B)
\[\frac{m-n}{m+n}\]
done
clear
C)
\[\frac{m-n}{2(m+n)}\]
done
clear
D)
\[\frac{m+n}{2(m-n)}\]
done
clear
E)
\[\frac{2(m+n)}{m-n}\]
done
clear
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question_answer 224) The integrating factor of the differential equation\[\cos x\left( \frac{dy}{dx} \right)+y\sin x=1\]is:
A)
\[cos\text{ }x\]
done
clear
B)
\[tan\text{ }x\]
done
clear
C)
\[sin\text{ }x\]
done
clear
D)
\[cot\text{ }x\]
done
clear
E)
\[sec\text{ }x\]
done
clear
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question_answer 225) Solution of the differential equation \[\tan y.{{\sec }^{2}}xdx+\tan x.{{\sec }^{2}}ydy=0\] is:
A)
\[tan\text{ }x+tan\text{ }y=k\]
done
clear
B)
\[tan\text{ }x-tan\text{ }y=k\]
done
clear
C)
\[(tan\text{ }x/tan\text{ }y)=k\]
done
clear
D)
\[tan\text{ }x.tan\text{ }y=k\]
done
clear
E)
None of the above
done
clear
View Answer play_arrow
question_answer 226) \[{{\tan }^{-1}}\left( \frac{m}{2} \right)-{{\tan }^{-1}}\left( \frac{m-n}{m+n} \right)\] is equal to:
A)
\[\frac{\pi }{4}\]
done
clear
B)
\[\frac{\pi }{2}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{\pi }{8}\]
done
clear
E)
\[\frac{2\pi }{3}\]
done
clear
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question_answer 227) A class has 175 students. The following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?
A)
35
done
clear
B)
48
done
clear
C)
60
done
clear
D)
22
done
clear
E)
30
done
clear
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question_answer 228) Let S be the set of all real numbers. Then the relation\[R=\{(a,b):1+ab>0\}\]on S is:
A)
reflexive and symmetric but not transitive
done
clear
B)
reflexive and transitive but not symmetric
done
clear
C)
symmetric and transitive but not reflexive
done
clear
D)
reflexive, transitive and symmetric
done
clear
E)
none of the above is true
done
clear
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question_answer 229) For the principal value branch of the graph of the function\[y={{\sin }^{-1}}x,-1\le x\le 1,\]which among the following is a true statement?
A)
graph is symmetric about the\[x-\]axis
done
clear
B)
graph is symmetric about the y-axis
done
clear
C)
graph is not continuous
done
clear
D)
the line\[x=1\]is a tangent
done
clear
E)
the line y = 1 is a tangent
done
clear
View Answer play_arrow
question_answer 230) Let\[f\left( x+\frac{1}{x} \right)={{x}^{2}}+\frac{1}{{{x}^{2}}},x\ne 0,\]then\[f(x)\] equals to:
A)
\[{{x}^{2}}\]
done
clear
B)
\[{{x}^{2}}-1\]
done
clear
C)
\[{{x}^{2}}-2\]
done
clear
D)
\[{{x}^{2}}+1\]
done
clear
E)
\[{{x}^{2}}+2\]
done
clear
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question_answer 231) A point P which represents a complex number z moves such that\[|z-{{z}_{1}}|=|z-{{z}_{2}}|,\]then its locus is:
A)
a circle with centre\[{{z}_{1}}\]
done
clear
B)
a circle with centre\[{{z}_{2}}\]
done
clear
C)
a circle with centre\[z\]
done
clear
D)
an ellipse
done
clear
E)
perpendicular bisector of line joining\[{{z}_{1}}\] and\[{{z}_{2}}\]
done
clear
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question_answer 232) The probability that in a family of 5 members, exactly 2 members have birthday on Sunday, is:
A)
\[\frac{12\times {{5}^{3}}}{{{7}^{5}}}\]
done
clear
B)
\[\frac{10\times {{6}^{2}}}{{{7}^{5}}}\]
done
clear
C)
\[\frac{2}{5}\]
done
clear
D)
\[\frac{10\times {{6}^{3}}}{{{7}^{5}}}\]
done
clear
E)
\[1\]
done
clear
View Answer play_arrow
question_answer 233) \[\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{{{(\sin \theta +i\cos \theta )}^{5}}}\]is equal to:
A)
\[\cos \theta -i\sin \theta \]
done
clear
B)
\[\sin \theta -i\cos \theta \]
done
clear
C)
\[\cos 9\theta -i\sin 9\theta \]
done
clear
D)
\[\sin 9\theta -i\cos 9\theta \]
done
clear
E)
\[\cos \theta +i\sin \theta \]
done
clear
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question_answer 234) The quadratic equation whose roots are twice the roots of\[2{{x}^{2}}-5x+2=0\]is:
A)
\[8{{x}^{2}}-10x+2=0\]
done
clear
B)
\[{{x}^{2}}-5x+4=0\]
done
clear
C)
\[2{{x}^{2}}-5x+2=0\]
done
clear
D)
\[{{x}^{2}}-10x+6=0\]
done
clear
E)
none of the above
done
clear
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question_answer 235) Standard deviation of the first\[2n+1\]natural numbers is equal to:
A)
\[\sqrt{\frac{n(n+1)}{2}}\]
done
clear
B)
\[\sqrt{\frac{n(n+1)(2n+1)}{3}}\]
done
clear
C)
\[\sqrt{\frac{n(n+1)}{3}}\]
done
clear
D)
\[\sqrt{\frac{n(n-1)}{2}}\]
done
clear
E)
\[2n+1\]
done
clear
View Answer play_arrow
question_answer 236) If\[\alpha +\beta =4\]and\[{{\alpha }^{3}}+{{\beta }^{3}}=44,\]then\[\alpha ,\beta \]are the roots of the equation.
A)
\[2{{x}^{2}}-7x+6=0\]
done
clear
B)
\[3{{x}^{2}}+9x+11=0\]
done
clear
C)
\[9{{x}^{2}}-27x+20=0\]
done
clear
D)
\[4{{x}^{2}}+22x+15=0\]
done
clear
E)
\[3{{x}^{2}}-12x-5=0\]
done
clear
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question_answer 237) The coefficient of\[x\]in\[{{x}^{2}}+px+q=0\]was taken as 17 in place of 13 and its roots were found to be\[-2\]and\[-15\]The roots of the original equation are:
A)
3, 7
done
clear
B)
\[-3,7\]
done
clear
C)
\[-3,-7\]
done
clear
D)
\[3,10\]
done
clear
E)
\[-3,-10\]
done
clear
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question_answer 238) If\[g(x)=\min (x,{{x}^{2}})\]where\[x\]is a real number, then:
A)
\[g(x)\]is an increasing function
done
clear
B)
\[g(x)\]is a decreasing function
done
clear
C)
\[g(x)\] is a constant function
done
clear
D)
\[g(x)\]is a continuous function except at\[x=0\]
done
clear
E)
\[g(x)\]is a continuous function except at \[x=0\]and\[x=1\]
done
clear
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question_answer 239) If\[^{n}{{C}_{3}}=220,\]then n equals to:
A)
10
done
clear
B)
11
done
clear
C)
12
done
clear
D)
9
done
clear
E)
8
done
clear
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question_answer 240) A polygon has 54 diagonals. Number of sides of this polygon is:
A)
12
done
clear
B)
15
done
clear
C)
16
done
clear
D)
9
done
clear
E)
14
done
clear
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