question_answer 1) An object accelerates from rest to a velocity 27.5 m/s in 10 s, then the distance covered after next 10 s is:
A)
550 m
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B)
137.5 m
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C)
412.5 m
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D)
175 m
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question_answer 2) The position vector of a particle is \[\mathbf{\vec{r}}=(a\,\cos \,\omega t)\mathbf{\hat{i}}\,+(a\,\sin \,\omega t)\mathbf{\hat{j}}\] The velocity vector of the particle is:
A)
parallel to position vector
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B)
perpendicular to position vector
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C)
directed towards the origin
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D)
directed away from the origin
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question_answer 3) If a person sitting in a train moving with a constant velocity along a straight line, throws a ball vertically upwards, then:
A)
ball will fall onwards the train
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B)
ball will return to throwers hand
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C)
ball will not return to throwers hand
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D)
none of the above
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question_answer 4) A stone thrown at an angle \[\theta \] to the horizontal reaches a maximum height H. Then the time of flight of stone will be:
A)
\[\sqrt{\frac{2H}{g}}\]
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B)
\[2\sqrt{\frac{2H}{g}}\]
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C)
\[\frac{2\sqrt{2H\sin \theta }}{g}\]
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D)
\[\frac{\sqrt{2H\sin \theta }}{g}\]
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question_answer 5) At the height 80 m, an aeroplane is moved with 150 m/s. A bomb is dropped from it, so as to hit a target. At what distance from the target should the bomb be dropped? \[(g=10\,m/{{s}^{2}})\]
A)
605.3 m
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B)
600 m
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C)
80 m
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D)
230 m
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question_answer 6) A spring has length I and spring constant k. If spring is divided in two equal pans then spring constant of each part is:
A)
\[k\]
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B)
\[\frac{k}{2}\]
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C)
\[2k\]
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D)
\[4k\]
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question_answer 7) A body is moving along a rough horizontal surface with an initial velocity 6 m/s. If the body comes to rest after travelling a distance 9 m, then the coefficient of sliding friction will be:
A)
0.4
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B)
0.2
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C)
0.6
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D)
0.8
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question_answer 8) If two soap bubbles of different radii are connected by a tube:
A)
air flows from the bigger bubble to the smaller bubble till the sizes become equal
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B)
air flows from bigger bubble to the smaller bubble till the sizes are interchanged
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C)
air flows from the smaller bubble to the bigger
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D)
there is no flow of air
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question_answer 9) If the momentum of body is increased by 100%, then the percentage increase in the kinetic energy will be:
A)
330%
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B)
225%
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C)
200%
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D)
300%
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question_answer 10) Water falls from a height 500 m. The rise in temperature of water at bottom if whole of the energy remains in water, will be : (specific heat of water is c = 4.2 kJ/kg)
A)
\[0.23{}^\circ C\]
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B)
\[1.16{}^\circ C\]
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C)
\[0.96{}^\circ C\]
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D)
\[1.02{}^\circ C\]
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question_answer 11) A bullet of mass 0.1 kg is fired with a speed of 100 m/s. The mass of gun being 50 kg. Then, the velocity of recoil become:
A)
0.05 m/s
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B)
0.5 m/s
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C)
0.1 m/s
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D)
0.2 m/s
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question_answer 12) A body of mass M moves with velocity v and collides elastically with another body of mass m (M >> m) at rest, then the velocity of body of mass m is:
A)
\[v\]
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B)
\[\text{2v}\]
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C)
\[\text{v/2}\]
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D)
zero
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question_answer 13) If torque is zero then:
A)
angular momentum is conserved
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B)
linear momentum is conserved
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C)
energy is conserved
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D)
angular momentum is not conserved
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question_answer 14) A solid sphere, a hollow sphere and a disc having same mass and radius roll down the same inclined plane from rest. Which one will reach the ground in least time?
A)
Solid sphere
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B)
Hollow sphere
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C)
Disc
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D)
All will reach in same time
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question_answer 15) In simple harmonic motion maximum velocity is at:
A)
extreme position
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B)
half of extreme position
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C)
equilibrium position
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D)
between extreme and equilibrium position
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question_answer 16)
A ball is thrown from a point with a speed
A)
Yes, \[60{}^\circ \]
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B)
Yes, \[30{}^\circ \]
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C)
No
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D)
Yes, \[45{}^\circ \]
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question_answer 17) The ratio of root mean square velocities of \[{{O}_{3}}\] And \[{{O}_{2}}\] is:
A)
1 : 1
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B)
2 : 3
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C)
3 : 2
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D)
\[\sqrt{2}:\sqrt{3}\]
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question_answer 18) If mass of He is 4 times that of hydrogen, then mean velocity of He is:
A)
2 times of H-mean value
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B)
\[\frac{1}{2}\]times of H-mean value
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C)
4 times of H-mean value
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D)
same as H-mean value
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question_answer 19) A wire elongates by \[l\] mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):
A)
\[l\]
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B)
2\[l\]
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C)
zero
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D)
\[l\]/2
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question_answer 20) First law of thermodynamics is a consequence of the conservation of:
A)
energy
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B)
charge
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C)
heat
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D)
all of these
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question_answer 21) An ideal heat engine exhausting heat at \[77{}^\circ C\] is to have 30% efficiency. It must take heat at:
A)
\[127{}^\circ C\]
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B)
\[227{}^\circ C\]
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C)
\[327{}^\circ C\]
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D)
\[673{}^\circ C\]
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question_answer 22) A liquid cools from \[50{}^\circ C\] to \[45{}^\circ C\] in 5 min and from \[45{}^\circ C\] to \[41.5{}^\circ C\] in the next 5 min. The temperature of the surrounding is:
A)
\[27{}^\circ C\]
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B)
\[40.3{}^\circ C\]
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C)
\[23.3{}^\circ C\]
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D)
\[33.3{}^\circ C\]
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question_answer 23) At \[127{}^\circ C\], radiated energy is \[2.7\times {{10}^{-3}}\text{J/s}\text{.}\] At what temperature radiated energy is 4.32 \[4.32\times {{10}^{6}}\text{J/s?}\]?
A)
400 K
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B)
4000 K
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C)
80000 K
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D)
40000 K
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question_answer 24) If wave equation is \[y=0.08\sin \frac{2\pi }{\lambda }(200t-x),\]then the velocity of the wave will be :
A)
400 \[\sqrt{2}\] m/s
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B)
200 \[\sqrt{2}\] m/s
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C)
400 m/s
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D)
200 m/s
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question_answer 25) A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been used to form the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object?
A)
20 cm
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B)
30 cm
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C)
60 cm
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D)
80 cm
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question_answer 26) A man having height 6 m, observes image of 2 m height erect, then mirror used is:
A)
concave
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B)
convex
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C)
plane
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D)
none of these
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question_answer 27) Which of the following statements is true?
A)
If wavelength of light increases then frequency also increases
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B)
If energy increases then frequency also increases
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C)
Frequency of red light is greater than frequency of blue light
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D)
If energy increases then frequency decreases
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question_answer 28) If focal lengths of the objective and the eye piece of a telescope be\[{{f}_{0}}\]and\[{{f}_{e}}\] respectively, then its magnification is :
A)
\[\frac{1}{2}({{f}_{0}}+{{f}_{e}})\]
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B)
\[{{f}_{0}}/{{f}_{e}}\]
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C)
\[({{f}_{0}}+{{f}_{e}})\]
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D)
\[{{f}_{0}}\times {{f}_{e}}\]
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question_answer 29) Near and far points of human eye are:
A)
25 cm and infinite
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B)
50 cm and 100 cm
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C)
25 cm and 50 cm
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D)
0 cm and 25 cm
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question_answer 30) Work done in carrying a charge around an equipotential surface will:
A)
increase
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B)
decrease
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C)
zero
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D)
infinity
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question_answer 31) An air parallel plate capacitor has capacity C. The capacity and distance between plates are doubled when immersed in a liquid then dielectric constant of the liquid is:
A)
1
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B)
2
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C)
3
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D)
4
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question_answer 32) If the potential of a capacitor having capacity \[6\,\mu F\] is increased from 10 V to 20V, then increase in its energy is:
A)
\[\text{12 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{J}\]
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B)
\[\text{9 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-4}}}\text{J}\]
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C)
\[\text{4}\text{.5 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{J}\]
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D)
\[\text{2}\text{.25 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-6}}}\text{J}\]
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question_answer 33) The resistance of a bulb filament is 100\[\Omega \] at a temperature of \[100{}^\circ C\]. If its temperature coefficient of resistance be \[0.005/{}^\circ C\], its resistance will become 200\[\Omega \] at a temperature of:
A)
\[300{}^\circ C\]
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B)
\[400{}^\circ C\]
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C)
\[500{}^\circ C\]
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D)
\[200{}^\circ C\]
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question_answer 34) A galvanometer of resistance \[22.8\,\,\Omega \] measures 1 A. How much shunt should be used, so that it can be used to measure 20 A?
A)
\[1\,\Omega \]
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B)
\[2\,\,\Omega \]
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C)
\[1.2\,\,\Omega \]
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D)
\[2.2\,\,\Omega \]
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question_answer 35) If an ammeter is joined in parallel through a circuit, it can be damaged due to excess:
A)
resistance
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B)
current
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C)
voltage
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D)
none of these
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question_answer 36) The heat produced by a 100 W heater in 2 min will be equal to:
A)
\[\text{12 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{3}}}\text{J}\]
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B)
\[\text{10 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{3}}}\text{J}\]
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C)
\[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{3}}}\text{J}\]
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D)
\[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{3}}}\text{J}\]
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question_answer 37) Two wires have resistances R and 2R. When both are joining in series and in parallel, then ratio of heats generated in these situations on applying the same voltage, is:
A)
2 : 1
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B)
1 : 2
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C)
2 : 9
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D)
9 : 2
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question_answer 38) The current in a coil decreases from 1 A to 0.2 A in 10 s. The coefficient of self-inductance, if induced emf is 0.4 V, is:
A)
5 H
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B)
3 H
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C)
4 H
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D)
2 H
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question_answer 39) Cyclotron is a device which is used to:
A)
measure the charge
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B)
measure the voltage
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C)
accelerate protons
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D)
accelerate electrons
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question_answer 40) In L - R circuit, resistance is 8 \[\Omega \] and inductive reactance is \[\Omega ,\] then impedance is:
A)
\[2\Omega \]
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B)
\[14\Omega \]
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C)
\[4\Omega \]
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D)
\[10\Omega \]
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question_answer 41) According to Maxwells hypothesis, changing electric field gives rise to:
A)
magnetic field
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B)
pressure gradient
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C)
charge
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D)
voltage
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question_answer 42) Dimensions of Plancks constant is:
A)
\[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
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B)
\[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
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C)
\[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-1}}\text{T }\!\!]\!\!\text{ }\]
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D)
\[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{-1}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
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question_answer 43) In any fission process the ratio mass of fission products mass of parent nucleus
A)
less than 1
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B)
greater than 1
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C)
equal to 1
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D)
depends on the mass of parent nucleus
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question_answer 44) If in a nuclear fusion process, the masses of the fusing nuclei be \[{{m}_{1}}\] and \[{{m}_{2}}\] and the mass of the resultant nucleus be \[{{m}_{3,}}\] then:
A)
\[{{m}_{3}}={{m}_{1}}+{{m}_{2}}\]
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B)
\[{{m}_{3}}=({{m}_{1}}-{{m}_{2}})\]
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C)
\[{{m}_{3}}<({{m}_{1}}+{{m}_{2}})\]
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D)
\[{{m}_{3}}>({{m}_{1}}+{{m}_{2}})\]
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question_answer 45) In BJT, maximum current flows in which or the following?
A)
Emitter region
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B)
Base region
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C)
Collector region
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D)
Equal in all the regions
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question_answer 46) In frequency modulated wave:
A)
frequency varies with time
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B)
amplitude varies with time
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C)
both frequency and amplitude vary with time
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D)
both frequency and amplitude are constant
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question_answer 47) The total energy of an electron in the first excited state of hydrogen is about -3.4 eV. Its kinetic energy in this state is:
A)
- 3.4 eV
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B)
- 6.8 eV
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C)
6.8 eV
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D)
3.4 eV
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question_answer 48) If \[{{\lambda }_{v,}}{{\lambda }_{x}}\]and \[{{\lambda }_{m}}\]represent the wavelengths of visible light, X-rays and microwaves respectively, then:
A)
\[{{\lambda }_{m}}>{{\lambda }_{x}}>{{\lambda }_{v}}\]
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B)
\[{{\lambda }_{v}}>{{\lambda }_{m}}>{{\lambda }_{x}}\]
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C)
\[{{\lambda }_{m}}>{{\lambda }_{v}}>{{\lambda }_{x}}\]
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D)
\[{{\lambda }_{v}}>{{\lambda }_{x}}>{{\lambda }_{m}}\]
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question_answer 49) The manifestation of band structure in solids is due to:
A)
Heisenbergs uncertainty principle
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B)
Paulis exclusion principle
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C)
Bohrs correspondence principle
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D)
Boltzmanns law
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question_answer 50) An electric power station transmits 100 MW power through long and thin cable. If the transmission is at (i) 20000 V, (ii) 200 V, in which case would be less power loss?
A)
In (i) only
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B)
In (ii) only
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C)
In each case, power loss is zero
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D)
Data is insufficient
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question_answer 51)
Arrange the following as increase in oxidation number: (i)\[M{{n}^{2+}}\] (ii) \[Mn{{O}_{2}}\] (iii) \[KMn{{O}_{4}}\] (iv) \[{{K}_{2}}Mn{{O}_{4}}\]
A)
\[(i)>(ii)>(iii)>(iv)\]
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B)
\[(i)<(ii)<(iv)>(iii)\]
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C)
\[(ii)<(iii)<(i)<(iv)\]
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D)
\[(iii)>(i)>(iv)>(ii)\]
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question_answer 52) \[S-S\]bond is not present in:
A)
\[{{H}_{2}}{{S}_{2}}{{O}_{4}}\]
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B)
\[{{H}_{2}}{{S}_{2}}{{O}_{6}}\]
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C)
\[{{H}_{2}}{{S}_{2}}{{O}_{8}}\]
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D)
None of these
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question_answer 53) A radioactive substance after 48 days remains 25% of initial then find disintegration constant:
A)
\[2.89\times {{10}^{-2}}{{T}^{-1}}\]
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B)
\[3.89\times {{10}^{-3}}{{T}^{-1}}\]
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C)
\[4.89\times {{10}^{-2}}{{T}^{-1}}\]
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D)
None of these
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question_answer 54) Correct order of reactivity:
A)
\[{{I}_{2}}>B{{r}_{2}}>C{{l}_{2}}>{{F}_{2}}\]
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B)
\[B{{r}_{2}}>{{I}_{2}}>C{{l}_{2}}>{{F}_{2}}\]
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C)
\[C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}>{{F}_{2}}\]
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D)
\[{{F}_{2}}>C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}\]
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question_answer 55) Three elements A, B and C having reduction potential \[-1.5,-0.5\] and \[1.5\,V\]respectively then arrange them in correct order according to reducing power:
A)
\[A>B>C\]
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B)
\[~B>A>C\]
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C)
\[~C>B>A\]
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D)
\[~B>C>A\]
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question_answer 56) The standard reduction potential \[{{E}^{o}}\]for the half reactions are as: \[Zn\xrightarrow{{}}Z{{n}^{2+}}+2{{e}^{-}},{{E}^{o}}=0.76\,V\] \[Cu\xrightarrow{{}}C{{u}^{2+}}+2{{e}^{-}},{{E}^{o}}=0.34\,V\] The emf for the cell reaction: \[Zn+C{{u}^{2+}}\xrightarrow{{}}Z{{n}^{2}}+Cu\]
A)
\[0.42\,V\]
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B)
\[-0.42\,\,V\]
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C)
\[-1.1\,V\]
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D)
\[1.1\,V\]
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question_answer 57) Variable oxidation state and degenerated orbital shows:
A)
s-block element
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B)
p-block element
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C)
d-block element
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D)
all of these
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question_answer 58) Which of the following is more acidic in nature?
A)
\[HClO\]
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B)
\[~HCl{{O}_{2}}\]
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C)
\[~HCl{{O}_{3}}\]
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D)
\[~HCl{{O}_{4}}\]
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question_answer 59) Unit of the constant of zero order reaction is:
A)
\[\text{tim}{{\text{e}}^{-1}}\]
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B)
\[\text{mol}\,{{L}^{-1}}\,{{s}^{-1}}\]
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C)
\[L\,mo{{l}^{-1}}{{s}^{-1}}\]
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D)
\[\text{L}\,mo{{l}^{-1}}{{s}^{-1}}\]
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question_answer 60) Mole fraction of a solute in benzene is 0.2 then find molality of solute:
A)
3.2
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B)
2
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C)
4
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D)
3.6
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question_answer 61) What amount of water is added in 40 mL of \[\text{NaOH}\,\text{(0}\text{.1 N)}\]which is neutralized by 50 mL of \[\text{HCl}\,\text{(0}\text{.2 N)}\]
A)
80 mL
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B)
60 mL
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C)
40 mL
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D)
90 mL
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question_answer 62) Slope between PV and P at constant temperature is:
A)
zero
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B)
1
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C)
\[\frac{1}{2}\]
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D)
\[\frac{1}{\sqrt{2}}\]
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question_answer 63) When pressure is applied to the equilibrium system ice\[\]water. Which of the following phenomenon will happen?
A)
More ice will be formed
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B)
Water will evaporate
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C)
More water will be formed
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D)
Equilibrium will not be formed
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question_answer 64) For\[A\xrightarrow{{}}B,\Delta H=4\,k\,cal\,mo{{l}^{-1}}\] \[\Delta S=10\,cal\,mo{{l}^{-1}}{{K}^{-1}}\]reaction is spontaneous when temperature can be:
A)
400 K
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B)
300 K
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C)
500 K
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D)
none of these
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question_answer 65) Degree of dissociation of \[N{{H}_{4}}OH\]in water is \[1.8\times {{10}^{-5}},\]then hydrolysis constant of \[N{{H}_{4}}Cl\]is:
A)
\[1.8\times {{10}^{-5}}\]
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B)
\[1.8\times {{10}^{-10}}\]
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C)
\[5.55\times {{10}^{-5}}\]
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D)
\[5.55\times {{10}^{-10}}\]
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question_answer 66) A current of strength 2.5A was passed through \[CuS{{O}_{4}}\]solution for 6 min 26s. The amount of copper deposited is: \[(\text{At}\text{.wt}\text{.of }Cu=63.5,1\text{ }F=96500\text{ }C)\]
A)
0.3175 g
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B)
3.175 g
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C)
0.635 g
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D)
6.35 g
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question_answer 67) The charge on an electron was discovered by:
A)
J. J. Thomson
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B)
Neil Bohr
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C)
James Chadwick
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D)
Mullikan
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question_answer 68) The normality of mixture obtained by mixing 100 mL of \[\text{0}\text{.2 M }{{\text{H}}_{\text{2}}}\text{S}{{\text{0}}_{\text{4}}}\text{+ 100 mL}\]of \[\text{0}\text{.2 M NaOH}\]is:
A)
0.2
done
clear
B)
0.01
done
clear
C)
0.1
done
clear
D)
0.3
done
clear
View Answer play_arrow
question_answer 69) The Bohrs orbit radius for the hydrogen atom \[(n=1)\] is approximately \[\text{0}\text{.53 }\overset{\text{o}}{\mathop{\text{A}}}\,\]. The radius for the first excited state \[(n=2)\] orbit is:
A)
\[\text{0}\text{.27 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
B)
\[\text{1}\text{.27 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
C)
\[\text{2}\text{.12 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
D)
\[\text{3}\text{.12 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
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question_answer 70) A gas has a vapour density 11.2. The volume occupied by \[\lg \]of the gas at NTP is:
A)
1 L
done
clear
B)
11.2 L
done
clear
C)
22.4 L
done
clear
D)
4 L
done
clear
View Answer play_arrow
question_answer 71) If \[n=3,\,l=0\]and \[m=0,\]then atomic number is:
A)
12 or 13
done
clear
B)
13 or 14
done
clear
C)
10 or 11
done
clear
D)
11 or 12
done
clear
View Answer play_arrow
question_answer 72) Which is not a colligative property?
A)
Osmotic pressure
done
clear
B)
Optical activity
done
clear
C)
Elevation in boiling point
done
clear
D)
Depression in freezing point
done
clear
View Answer play_arrow
question_answer 73) The rate constant of a first order reaction is\[3\times {{10}^{-6}}\] per second and initial concentration is 0.10 M. Then the initial rate of reaction is:
A)
\[3\times {{10}^{-6}}m{{s}^{-1}}\]
done
clear
B)
\[3\times {{10}^{-8}}m{{s}^{-1}}\]
done
clear
C)
\[3\times {{10}^{-7}}m{{s}^{-1}}\]
done
clear
D)
\[3\times {{10}^{-9}}m{{s}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 74) \[C{{H}_{2}}=C{{H}_{2}}(g)+{{H}_{2}}(g)\to C{{H}_{3}}-C{{H}_{3}}(g)\] The heat of reaction is [bond energy of \[C-C=80\,kcal,\,C=C=145\,kcal,\] \[C-H=98\,kcal,\,H-H=103\,kcal\]
A)
\[~-14\text{ kcal}\]
done
clear
B)
\[~-28\text{ kcal}\]
done
clear
C)
\[~-\,42\text{ kcal}\]
done
clear
D)
\[~-\,56\text{ kcal}\]
done
clear
View Answer play_arrow
question_answer 75) Tyndall effect is shown by:
A)
precipitate
done
clear
B)
sol
done
clear
C)
plasma
done
clear
D)
solution
done
clear
View Answer play_arrow
question_answer 76) If \[p{{K}_{a}}\]values of four adds are given below at \[25{{\,}^{o}}C\]the strongest acid is:
A)
2.0
done
clear
B)
2.5
done
clear
C)
3.0
done
clear
D)
4.0
done
clear
View Answer play_arrow
question_answer 77) The solubility of gas in liquid depends upon:
A)
the nature of gas
done
clear
B)
the temperature
done
clear
C)
the nature of solvent
done
clear
D)
all of the above
done
clear
View Answer play_arrow
question_answer 78) Write the IUPAC name of: \[C{{H}_{3}}-C{{H}_{2}}-\underset{C{{H}_{3}}}{\overset{OH}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{2}}-C{{H}_{3}}\]
A)
3- methylpentane-3-ol
done
clear
B)
3-hydroxyhexane
done
clear
C)
3-hydroxy-3-methyl pentane
done
clear
D)
all of the above
done
clear
View Answer play_arrow
question_answer 79) Natural rubber is polymer of:
A)
\[{{H}_{2}}C=\underset{Cl}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-CH=C{{H}_{2}}\]
done
clear
B)
\[{{H}_{2}}C=\overset{Cl}{\mathop{\overset{|}{\mathop{C}}\,}}\,-CH=C{{H}_{2}}\]
done
clear
C)
\[\overset{{{C}_{6}}{{H}_{5}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,=C{{H}_{2}}\]
done
clear
D)
\[{{(-C{{H}_{2}}-C{{H}_{2}}-)}_{n}}\]
done
clear
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question_answer 80) \[C{{H}_{3}}-C{{H}_{2}}-O-C{{H}_{2}}-C{{H}_{3}}\]reacts with hot and excess HI, then formed product is:
A)
\[C{{H}_{3}}-C{{H}_{2}}-I\]and \[C{{H}_{3}}C{{H}_{2}}OH\]
done
clear
B)
\[C{{H}_{3}}-C{{H}_{2}}-OH\]
done
clear
C)
\[C{{H}_{3}}-C{{H}_{2}}-I\]
done
clear
D)
none of the above
done
clear
View Answer play_arrow
question_answer 81) X compounds reacts with Na to give \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}},\] then compound X is:
A)
\[C{{H}_{3}}C{{H}_{2}}OH\]
done
clear
B)
\[C{{H}_{3}}C{{H}_{2}}-Cl\]
done
clear
C)
\[C{{H}_{3}}-C{{H}_{3}}\]
done
clear
D)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}OH\]
done
clear
View Answer play_arrow
question_answer 82) In the following compound, least number of mono chlorination is possible:
A)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]
done
clear
B)
\[C{{H}_{3}}-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C{{H}_{2}}-C{{H}_{3}}\]
done
clear
C)
\[C{{H}_{3}}-\underset{C{{H}_{3}}}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-H\]
done
clear
D)
\[C{{H}_{3}}-\underset{C{{H}_{3}}}{\overset{C{{H}_{3}}}{\mathop{\underset{|}{\overset{|}{\mathop{C}}}\,}}}\,-C{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 83) \[C{{H}_{3}}C{{H}_{2}}OH\]convert into \[C{{H}_{3}}CHO\]in the presence of:
A)
\[N{{a}_{2}}C{{r}_{2}}{{O}_{7}}\]and \[NaOH\]
done
clear
B)
\[N{{a}_{2}}C{{r}_{2}}{{O}_{7}}\]and dil. \[{{H}_{2}}S{{O}_{4}}\]
done
clear
C)
\[NaOH\]
done
clear
D)
Fe in presence of \[\text{NaOH}\]
done
clear
View Answer play_arrow
question_answer 84) Which of the following reactant give Tollens reagent and Fehlings solution test?
A)
\[C{{H}_{3}}CHO\]
done
clear
B)
\[C{{H}_{3}}COOH\]
done
clear
C)
\[C{{H}_{3}}-\underset{O}{\mathop{\underset{||}{\mathop{C}}\,}}\,-C{{H}_{3}}\]
done
clear
D)
\[C{{H}_{3}}-C{{H}_{2}}COOH\]
done
clear
View Answer play_arrow
question_answer 85) The alcohol manufactured from water gas is:
A)
\[C{{H}_{3}}OH\]
done
clear
B)
\[{{C}_{2}}{{H}_{5}}OH\]
done
clear
C)
\[C{{H}_{3}}C{{H}_{2}}COOH\]
done
clear
D)
\[{{(C{{H}_{3}})}_{2}}CHOH\]
done
clear
View Answer play_arrow
question_answer 86) The most stable alkene is:
A)
\[{{R}_{2}}C=C{{R}_{2}}\]
done
clear
B)
\[RCH=CHR\]
done
clear
C)
\[C{{H}_{2}}=C{{H}_{2}}\]
done
clear
D)
\[RCH=C{{R}_{2}}\]
done
clear
View Answer play_arrow
question_answer 87) The most favorable condition for the manufacture of \[N{{H}_{3}}\]is:
A)
high temperature and high pressure
done
clear
B)
low temperature and low pressure
done
clear
C)
high temperature and low pressure
done
clear
D)
low temperature and high pressure
done
clear
View Answer play_arrow
question_answer 88) The conversion of benzaldehyde into benzyl alcohol takes place by:
A)
Fittig reaction
done
clear
B)
Wurtz Fittig reaction
done
clear
C)
Wurtz reaction
done
clear
D)
Cannizaros reaction
done
clear
View Answer play_arrow
question_answer 89) Paracetamol is an:
A)
antibiotic
done
clear
B)
antipyretic
done
clear
C)
antimalarial
done
clear
D)
analgesic
done
clear
View Answer play_arrow
question_answer 90) Benzaldehyde gives a positive test with:
A)
Toilers reagent
done
clear
B)
Fehling solution
done
clear
C)
Benedicts solution
done
clear
D)
all of the above
done
clear
View Answer play_arrow
question_answer 91) Which of the following is not soluble in \[NaOH\]?
A)
\[Fe{{(OH)}_{3}}\]
done
clear
B)
\[Zn{{(OH)}_{2}}\]
done
clear
C)
\[Al{{(OH)}_{3}}\]
done
clear
D)
\[Sn{{(OH)}_{2}}\]
done
clear
View Answer play_arrow
question_answer 92) Which of the following has least oxidation state of Fe?
A)
\[{{K}_{3}}[Fe{{(OH)}_{6}}]\]
done
clear
B)
\[{{K}_{2}}[Fe{{O}_{4}}]\]
done
clear
C)
\[FeS{{O}_{4}}{{(N{{H}_{4}})}_{2}}S{{O}_{4}}.6{{H}_{2}}O\]
done
clear
D)
\[{{[Fe{{(CN)}_{6}}]}^{3-}}\]
done
clear
View Answer play_arrow
question_answer 93) Green vitriol is formed by:
A)
\[Fe{{S}_{2}}+{{H}_{2}}O+{{O}_{2}}\]
done
clear
B)
\[Fe{{S}_{2}}+{{H}_{2}}O+C{{O}_{2}}\]
done
clear
C)
\[Fe{{S}_{2}}+CO+C{{O}_{2}}\]
done
clear
D)
\[Fe{{S}_{2}}+CO\]
done
clear
View Answer play_arrow
question_answer 94) \[NaOH+{{P}_{4}}+{{H}_{2}}O\xrightarrow{{}}\]?
A)
\[P{{H}_{3}}+Na{{H}_{2}}P{{O}_{2}}\]
done
clear
B)
\[P{{H}_{3}}+N{{a}_{2}}P{{O}_{4}}\]
done
clear
C)
\[P{{H}_{3}}+N{{a}_{2}}HP{{O}_{2}}\]
done
clear
D)
\[{{H}_{3}}P{{O}_{4}}+NaO\]
done
clear
View Answer play_arrow
question_answer 95) Slag is represented by:
A)
\[CaSi{{O}_{3}}\]
done
clear
B)
\[Si{{O}_{3}}\]
done
clear
C)
\[Ca{{(OH)}_{2}}\]
done
clear
D)
\[CaO\]
done
clear
View Answer play_arrow
question_answer 96) Which of the following is not a nucleophile?
A)
\[B{{F}_{3}}\]
done
clear
B)
\[N{{H}_{3}}\]
done
clear
C)
\[C{{N}^{-}}\]
done
clear
D)
\[O{{H}^{-}}\]
done
clear
View Answer play_arrow
question_answer 97) Fuming sulphuric acid is:
A)
\[{{H}_{2}}S{{O}_{4}}+S{{O}_{3}}\]
done
clear
B)
\[{{H}_{2}}S{{O}_{4}}+S{{O}_{2}}\]
done
clear
C)
\[{{H}_{2}}S{{O}_{4}}\]
done
clear
D)
\[{{H}_{2}}S{{O}_{4}}+S{{O}_{4}}\]
done
clear
View Answer play_arrow
question_answer 98) On strong heating \[MgC{{l}_{2}}.6{{H}_{2}}O,\]the product obtained is:
A)
\[MgC{{l}_{2}}\]
done
clear
B)
\[MgO\]
done
clear
C)
\[MgC{{l}_{2}}.2{{H}_{2}}O\]
done
clear
D)
\[MgC{{l}_{2}}.4{{H}_{2}}O\]
done
clear
View Answer play_arrow
question_answer 99) The highest first ionization potential is of:
A)
carbon
done
clear
B)
boron
done
clear
C)
oxygen
done
clear
D)
nitrogen
done
clear
View Answer play_arrow
question_answer 100) In sulphur detection of an organic compound, sodium nitroprusside solution is added to sodium extract. Formation of violet colour is due to:
A)
\[N{{a}_{3}}Fe{{(CN)}_{6}}\]
done
clear
B)
\[N{{a}_{3}}[Fe{{(CN)}_{5}}NOS]\]
done
clear
C)
\[Fe{{(CNS)}_{3}}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 101) The eccentricity of the ellipse\[9{{x}^{2}}+5{{y}^{2}}-30y=0\]is:
A)
1/3
done
clear
B)
2/3
done
clear
C)
3/4
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 102) The maximum value of \[12\sin \theta -9{{\sin }^{2}}\theta \]is:
A)
3
done
clear
B)
4
done
clear
C)
5
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 103) if \[\cos {{20}^{o}}=k\]and \[\cos x=2{{k}^{2}}-1,\]then the possible values of \[x\]between \[{{0}^{o}}\]and \[{{360}^{o}}\]are:
A)
\[{{140}^{o}}\]and\[{{270}^{o}}\]
done
clear
B)
\[{{40}^{o}}\]and\[{{140}^{o}}\]
done
clear
C)
\[{{40}^{o}}\]and \[{{320}^{o}}\]
done
clear
D)
\[{{50}^{o}}\]and \[{{130}^{o}}\]
done
clear
View Answer play_arrow
question_answer 104) \[\int_{{}}^{{}}{{{5}^{{{5}^{{{5}^{x}}}}}}.}{{5}^{{{5}^{x}}}}{{.5}^{x}}dx\]is equal to:
A)
\[\frac{{{5}^{{{5}^{x}}}}}{{{(log5)}^{3}}}+c\]
done
clear
B)
\[{{5}^{{{5}^{{{5}^{x}}}}}}{{(log5)}^{3}}+c\]
done
clear
C)
\[\frac{{{5}^{{{5}^{{{5}^{x}}}}}}}{{{(log5)}^{3}}}+c\]
done
clear
D)
none of these
done
clear
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question_answer 105) If \[\cos (\theta +\phi )=m\cos (\theta -\phi ),\]then \[\tan \theta \]is equal to:
A)
\[[(1+m)/(1-m)]\tan \phi \]
done
clear
B)
\[[(1-m)/(1+m)]\tan \phi \]
done
clear
C)
\[[(1-m)/(1+m)]cot\phi \]
done
clear
D)
\[[(1+m)/(1-m)]sec\phi \]
done
clear
View Answer play_arrow
question_answer 106) The value of \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sqrt{1+{{x}^{4}}}-(1+{{x}^{2}})}{{{x}^{2}}}\]is equal to
A)
0
done
clear
B)
\[-1\]
done
clear
C)
2
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 107) The roots of the equation \[|{{x}^{2}}-x-6|=x+2\]are
A)
\[-2,1,4\]
done
clear
B)
\[0,2,4\]
done
clear
C)
\[0,1,4\]
done
clear
D)
\[-2,2,4\]
done
clear
View Answer play_arrow
question_answer 108) The maximum number of real roots of the equation \[{{x}^{2n}}-1=0\]is:
A)
2
done
clear
B)
3
done
clear
C)
\[n\]
done
clear
D)
\[2n\]
done
clear
View Answer play_arrow
question_answer 109) If \[\alpha ,\beta ,\gamma \]are the angles when a directed line makes with the positive directions the coordinate axes, then \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma \]is equal to:
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 110) The first and last terms of an AP are a and \[l\] respectively. If S be the sum of all the terms of the AP, then common difference is:
A)
\[\frac{{{l}^{2}}-{{a}^{2}}}{2S-(l+a)}\]
done
clear
B)
\[\frac{{{l}^{2}}-{{a}^{2}}}{2S-(l-a)}\]
done
clear
C)
\[\frac{{{l}^{2}}+{{a}^{2}}}{2S+(l+a)}\]
done
clear
D)
\[\frac{{{l}^{2}}+{{a}^{2}}}{2S-(l+a)}\]
done
clear
View Answer play_arrow
question_answer 111) If the two lines of regression are\[x+4y=3\]and \[3x+y=5,\]then value of \[x\] for \[y=3\]is:
A)
\[\frac{2}{3}\]
done
clear
B)
\[-9\]
done
clear
C)
\[~-4\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 112) The value of the following determinant \[\left| \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ {{a}^{3}} & {{b}^{3}} & {{c}^{3}} \\ \end{matrix} \right|\]is:
A)
\[(a-b)(b-c)(c-a)(a+b+c)\]
done
clear
B)
\[abc(a+b)(b+c)(c+a)\]
done
clear
C)
\[(a-b)(b-c)(c-a)\]
done
clear
D)
none of the above
done
clear
View Answer play_arrow
question_answer 113) If \[A=\left[ \begin{matrix} 1 & 3 \\ 3 & 10 \\ \end{matrix} \right],\]then adjoint of A is:
A)
\[\left[ \begin{matrix} 10 & 3 \\ 3 & 1 \\ \end{matrix} \right]\]
done
clear
B)
\[\left[ \begin{matrix} 10 & -3 \\ -3 & 1 \\ \end{matrix} \right]\]
done
clear
C)
\[\left[ \begin{matrix} 1 & 3 \\ 3 & 10 \\ \end{matrix} \right]\]
done
clear
D)
\[\left[ \begin{matrix} -1 & -3 \\ -3 & 10 \\ \end{matrix} \right]\]
done
clear
View Answer play_arrow
question_answer 114) If \[y=1+x+{{x}^{2}}+{{x}^{3}}+...,\]\[x\]is equal to:
A)
\[\frac{y-1}{y}\]
done
clear
B)
\[\frac{1-y}{y}\]
done
clear
C)
\[\frac{y}{1-y}\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 115) \[1+\frac{3}{2}+\frac{5}{{{2}^{2}}}+\frac{7}{{{2}^{3}}}+....\infty \]is equal to:
A)
2
done
clear
B)
6
done
clear
C)
5
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 116) If \[{{a}_{r}}\]is the coefficient of \[{{x}^{r}}\] in the expansion of \[{{(1+x+{{x}^{2}})}^{n}},\]then \[{{a}_{1}}-2{{a}_{2}}+3{{a}_{2}}-...-2n{{a}_{2n}}\]is equal to:
A)
0
done
clear
B)
\[n\]
done
clear
C)
\[-n\]
done
clear
D)
\[2n\]
done
clear
View Answer play_arrow
question_answer 117) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{1/x}}}{{{e}^{1/x+1}}}\]is equal to:
A)
0
done
clear
B)
1
done
clear
C)
does not exist
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 118) If P is any point on the ellipse \[81{{x}^{2}}+144{{y}^{2}}-1944\] whose foci are S and S. Then \[SP+SP\] equals:
A)
3
done
clear
B)
\[4\sqrt{6}\]
done
clear
C)
36
done
clear
D)
324
done
clear
View Answer play_arrow
question_answer 119) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{2{{\sin }^{2}}3x}{{{x}^{2}}}\]is equal to:
A)
0
done
clear
B)
1
done
clear
C)
18
done
clear
D)
36
done
clear
View Answer play_arrow
question_answer 120) The solution of \[\frac{dy}{dx}+\sqrt{\left( \frac{1-{{y}^{2}}}{1-{{x}^{2}}} \right)}=0\]is:
A)
\[{{\tan }^{-1}}x+{{\cot }^{-1}}x=c\]
done
clear
B)
\[{{\sin }^{-1}}x+{{\sin }^{-1}}y=c\]
done
clear
C)
\[{{\sec }^{-1}}x+\cos e{{c}^{-1}}x=c\]
done
clear
D)
none of the above
done
clear
View Answer play_arrow
question_answer 121) If \[x=(cos\theta +\theta sin\theta )\] \[y=a(sin\theta -\theta cos\theta ),\]then\[\frac{dy}{dx}\]is equal to:
A)
\[\cos \theta \]
done
clear
B)
\[\tan \theta \]
done
clear
C)
\[\sec \theta \]
done
clear
D)
\[\cos ec\,\theta \]
done
clear
View Answer play_arrow
question_answer 122) \[\int_{1}^{x}{\frac{\log ({{x}^{2}})}{x}}dx\]is equal to:
A)
\[{{(\log x)}^{2}}\]
done
clear
B)
\[\frac{1}{2}{{(\log x)}^{2}}\]
done
clear
C)
\[\frac{\log {{x}^{2}}}{2}\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 123) The two regression lines are \[2x-7y+6=0\] and \[7x-2y+1=0.~\] The correlation coefficient between \[x\] and \[y\]is:
A)
\[-\frac{2}{3}\]
done
clear
B)
\[\frac{2}{7}\]
done
clear
C)
\[\frac{4}{9}\]
done
clear
D)
none of these
done
clear
View Answer play_arrow
question_answer 124) Simpsons one third rule for evolution\[\int_{a}^{b}{f(x)dx}\] requires the interval [a, b] to be divided into:
A)
an even number of sub-intervals of equal width
done
clear
B)
any number of sub-intervals
done
clear
C)
any number of sub-intervals of equal width
done
clear
D)
an odd number of sub-intervals of equal width
done
clear
View Answer play_arrow
question_answer 125) If \[\sin A=\sin B\]and \[\cos A=\cos B,\]then A is equal to:
A)
\[2n\pi +B\]
done
clear
B)
\[2n\pi -B\]
done
clear
C)
\[n\pi +B\]
done
clear
D)
\[n\pi +B{{(-1)}^{n}}B\]
done
clear
View Answer play_arrow
question_answer 126) The number of diagonals that can be drawn in a Dolygon 15 sides, is:
A)
16
done
clear
B)
60
done
clear
C)
90
done
clear
D)
80
done
clear
View Answer play_arrow
question_answer 127) \[\text{tan 1}{{\text{0}}^{\text{o}}}\text{+tan 3}{{\text{5}}^{\text{o}}}\text{+tan 1}{{\text{0}}^{\text{o}}}\text{ tan 3}{{\text{5}}^{\text{o}}}\]is equal to:
A)
0
done
clear
B)
\[\frac{1}{2}\]
done
clear
C)
\[-1\]
done
clear
D)
1
done
clear
View Answer play_arrow
question_answer 128) If \[\left| \begin{matrix} a+b & b+c & c+a \\ b+c & c+a & a+b \\ c+a & a+b & b+c \\ \end{matrix} \right|=k\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|\]then k is equal to:
A)
1
done
clear
B)
2
done
clear
C)
3
done
clear
D)
8
done
clear
View Answer play_arrow
question_answer 129) If \[a,b,c\]are in AP, then \[{{2}^{ax+1}},{{2}^{bx+1}},{{2}^{cx+1}},x\ne 0\]area in:
A)
AP
done
clear
B)
GP only when \[x>0\]
done
clear
C)
GP if \[x<0\]
done
clear
D)
GP
done
clear
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question_answer 130) If \[\alpha \]and \[\beta \]are the roots of the equation\[a{{x}^{2}}+bx+c=0,\]then \[(1+\alpha +{{\alpha }^{2}})(1+\beta +{{\beta }^{2}})\]is equal to:
A)
0
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B)
positive
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C)
negative
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D)
none of these
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question_answer 131) The angle between the tangents drawn from the origin to the circle\[{{(x-7)}^{2}}+{{(y+1)}^{2}}=25\] is:
A)
\[\frac{\pi }{3}\]
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B)
\[\frac{\pi }{6}\]
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C)
\[\frac{\pi }{2}\]
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D)
\[\frac{\pi }{8}\]
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question_answer 132) The area of the circle whose centre is at (1, 2) and passing through (4, 6) is
A)
\[5\pi \,\text{sq}\,\text{unit}\]
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B)
\[10\pi \,\text{sq}\,\text{unit}\]
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C)
\[25\,\pi \,\,\text{sq}\,\text{unit}\]
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D)
none of these
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question_answer 133) The curve represented by\[x=3(\cos t+\sin t),y=4(\cos t-\sin t)\]is:
A)
ellipse
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B)
parabola
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C)
hyperbola
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D)
circle
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question_answer 134) The line \[y=mx+1\]is a tangent to the parabola \[{{y}^{2}}=4x,\] if:
A)
\[m=1\]
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B)
\[~m=2\]
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C)
\[m=4\]
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D)
\[~m=3\]
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question_answer 135) \[f(x)=\left| \begin{matrix} {{x}^{3}} & {{x}^{4}} & 3{{x}^{2}} \\ 1 & -6 & 4 \\ p & {{p}^{2}} & {{p}^{3}} \\ \end{matrix} \right|,\] here p is a constant, then\[\frac{{{d}^{3}}f(x)}{d{{x}^{3}}}\]is:
A)
proportional to \[{{x}^{2}}\]
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B)
proportional to \[x\]
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C)
proportional to \[{{x}^{3}}\]
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D)
a constant
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question_answer 136) \[\int_{0}^{1.5}{[{{x}^{2}}]}\,dx\]is:
A)
\[4+2\sqrt{2}\]
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B)
\[2+\sqrt{2}\]
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C)
\[2-\sqrt{2}\]
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D)
none of these
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question_answer 137) The rational number which is equal to the number \[2.\overset{.}{\mathop{3}}\,\overset{.}{\mathop{5}}\,\overset{.}{\mathop{7}}\,\] with recurring decimal is:
A)
\[\frac{2355}{1001}\]
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B)
\[\frac{2370}{997}\]
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C)
\[\frac{2355}{999}\]
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D)
none of these
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question_answer 138) The differential coefficient of\[f(\log x)\]w.r.t\[x,\] where \[f(x)=\log x\]is:
A)
\[\frac{x}{\log x}\]
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B)
\[\frac{\log x}{x}\]
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C)
\[{{(x\log x)}^{-1}}\]
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D)
none of these
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question_answer 139) There are six vertices of a regular hexagon are chosen at random, then the possibility that the triangle with three vertices is equilateral, is equal to:
A)
\[\frac{1}{2}\]
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B)
\[\frac{1}{3}\]
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C)
\[\frac{1}{10}\]
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D)
\[\frac{1}{20}\]
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question_answer 140) The number of vectors of unit length perpendicular to the two vectors \[a=(1,1,0)\] and \[b=(0,1,1)\]is:
A)
one
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B)
two
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C)
three
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D)
infinite
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question_answer 141) Three identical dice are rolled. The probability that same number will appear on each of them will be:
A)
\[\frac{1}{6}\]
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B)
\[\frac{1}{36}\]
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C)
\[\frac{1}{18}\]
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D)
\[\frac{3}{28}\]
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question_answer 142) If sets A and B are defined as \[A=\{(x,y):y={{e}^{x}},x\in R\}\]and \[B=\{(x,y):y=x,x\in R\}\]then
A)
\[B\subset A\]
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B)
\[A\subset B\]
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C)
\[A\cap B=\phi \]
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D)
\[A\cup B=A\]
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question_answer 143) Given \[A={{\sin }^{2}}\theta +{{\cos }^{4}}\theta ,\]then for all real value of \[\theta :\]
A)
\[1\le A\le 2\]
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B)
\[\frac{3}{4}\le A\le 1\]
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C)
\[\frac{13}{16}\le A<1\]
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D)
\[\frac{3}{4}\le A\le \frac{13}{16}\]
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question_answer 144) If the vectors \[a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k},\hat{i}+\hat{j}+c\hat{k}\] \[(a\ne 1,b\ne 1,c\ne 1)\]are coplanar, then the value of \[\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\]:is
A)
0
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B)
1
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C)
-1
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D)
2
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question_answer 145) A lady gives a dinner party for six guest. The number of ways in which they may be selected from among ten friends, if two of the friends will not attends the party together, is:
A)
112
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B)
140
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C)
164
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D)
none of these
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question_answer 146) Remainder of \[{{x}^{64}}+\text{ }{{x}^{27}}+1\]divided by \[x+1\] is:
A)
0
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B)
1
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C)
2
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D)
3
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question_answer 147) If the imaginary part of\[\frac{2z+1}{iz+1}\] is \[-2,\] then the locus of the point represented by z is a:
A)
circle
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B)
straight line
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C)
parabola
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D)
none of these
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question_answer 148) If\[{{z}_{1}},{{z}_{2}},{{z}_{3}}\] are in AP(\[{{z}_{1}},{{z}_{2}},{{z}_{3}}\]are complex numbers), then they lies on a :
A)
circle
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B)
straight line
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C)
parabola
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D)
none of these
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question_answer 149) Area of the region bounded by the curve \[y=\tan x,\]tangent drawn to the curve at \[x=\frac{\pi }{4}\] and the \[x-\]axis is:
A)
\[\log \sqrt{2}\,\text{sq}\,\text{unit}\]
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B)
\[\left( \log \sqrt{2}+\frac{1}{4} \right)\,\text{sq}\,\text{unit}\]
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C)
\[\left( \log \sqrt{2}-\frac{1}{4} \right)\text{sq}\,\text{unit}\]
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D)
\[\frac{1}{4}\text{sq}\,\text{unit}\]
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question_answer 150) The number of values of \[x\] in the interval \[[0,2\pi ],\]where the function\[f(x)=\cos x\]\[+\,\cos \sqrt{2x}\] attains its maximum, is:
A)
0
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B)
1
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C)
2
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D)
infinite
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at an angle of projection\[\theta \].From the same point and at the same instant, a person starts running with a constant speed \[\frac{{{v}_{0}}}{2}\] to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
