question_answer 1) In ruby laser, the stimulated emission is due to transition from
A)
metastable state to any lower state
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B)
any higher state to lower state
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C)
metastable state to ground state
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D)
any higher state to ground state
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question_answer 2) A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is
A)
uniform throughout the pipe but not zero
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B)
zero only along the axis of the pipe
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C)
zero at any point inside the pipe
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D)
maximum at the centre and minimum at the edge
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question_answer 3) A convex lens made of glass has focal length 0.15 m in air. If the refractive index of glass is \[\frac{3}{2}\] and that of water is \[\frac{4}{3}\], the focal length of lens when immersed in water is
A)
0.45 m
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B)
0.15 m
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C)
0.30 m
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D)
0.6 m
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question_answer 4) Two sources are said to be coherent if they produce waves
A)
having a constant phase difference
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B)
of equal wavelength
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C)
of equal speed
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D)
having same shape of wave front
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question_answer 5) Three resistors \[1\,\Omega ,\,2\,\Omega \] and \[3\,\Omega \] are connected to form a triangle. Across \[3\,\Omega \] resistor a \[3\,\Omega \] battery is connected. The current through \[3\,\Omega \] resistor is
A)
0.75 A
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B)
1 A
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C)
2 A
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D)
1.5 A
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question_answer 6) In a common emitter amplifier the input signal is applied across
A)
anywhere
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B)
emitter-collector
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C)
collector-base
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D)
base-emitter
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question_answer 7) In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is
A)
\[\frac{1}{{{e}^{2}}}\]
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B)
\[\frac{1}{e}\]
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C)
e
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D)
\[{{e}^{2}}\]
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question_answer 8) A ray of light is incident on a surface of glass slab at an angle \[{{45}^{o}}\]. If the lateral shift produced per unit thickness is \[\frac{1}{\sqrt{3}}m\], the angle of refraction produced is
A)
\[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
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B)
\[{{\tan }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\]
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C)
\[{{\sin }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\]
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D)
\[{{\tan }^{-1}}\left( \frac{2}{\sqrt{3}-1} \right)\]
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question_answer 9) Ferromagnetic materials used in a transformer must have
A)
low permeability and high hysterisis loss
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B)
high permeability and low hysterisis loss
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C)
high permeability and high hysterisis loss
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D)
low permeability and low hysterisis loss
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question_answer 10) According to Newton's corpuscular theory, the speed of light is
A)
same in all the media
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B)
lesser in rarer medium
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C)
lesser in denser medium
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D)
independent of the medium
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question_answer 11) For the constructive interference the path difference between the two interfering waves must be equal to
A)
\[\left( 2n+1 \right)\lambda \]
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B)
\[2n\pi \]
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C)
\[n\lambda \]
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D)
\[\left( 2n+1 \right)\frac{\pi }{2}\]
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question_answer 12) The accurate measurement of emf can be obtained using
A)
multimeter
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B)
voltmeter
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C)
voltameter
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D)
potentiometer
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question_answer 13) The kinetic energy of an electron gets tripled, then the de-Broglie wavelength associated with it changes by a factor
A)
\[\frac{1}{3}\]
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B)
\[\sqrt{3}\]
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C)
\[\frac{1}{\sqrt{3}}\]
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D)
3
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question_answer 14) Which of the following is not a thermodynamic coordinate?
A)
Gas constant (R)
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B)
Pressure (p)
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C)
Volume (V)
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D)
Temperature (T)
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question_answer 15) Two solid pieces, one of steel and the other of aluminium when immersed completely in water have equal weights. When the solid pieces are weighed in air
A)
the weight of aluminium is half the weight of steel
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B)
steel piece will weigh more
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C)
they have the same weight
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D)
aluminium piece will weigh more
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question_answer 16) The amount of energy released when one microgram of matter is annihilated is
A)
25 kWh
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B)
\[9\times {{10}^{10}}kWh\]
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C)
\[3\times {{10}^{10}}kWh\]
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D)
\[0.5\times {{10}^{5}}kWh\]
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question_answer 17) The number of significant figures in the numbers \[4.8000\times {{10}^{4}}\] and 48000.50 are respectively
A)
5 and 6
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B)
5 and 7
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C)
2 and 7
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D)
2 and 6
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question_answer 18) \[\beta \]-decay means emission of electron from
A)
innermost electron orbit
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B)
a stable nucleus
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C)
outermost electron orbit
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D)
radioactive nucleus
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question_answer 19) An electric heater rated 220 V and 550 W is connected to AC mains. The current drawn by it is
A)
0.8 A
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B)
2.5 A
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C)
0.4 A
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D)
1.25 A
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question_answer 20) A body of mass m moving along a straight line covers half the distance with a speed of \[2\text{ }m{{s}^{-1}}\]. The remaining half of the distance is covered in two equal time intervals with a speed of \[3\text{ }m{{s}^{-1}}\] and \[5\text{ }m{{s}^{-1}}\] respectively. The average speed of the particle for the entire journey is
A)
\[\frac{3}{8}m{{s}^{-1}}\]
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B)
\[\frac{3}{8}m{{s}^{-1}}\]
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C)
\[\frac{4}{3}m{{s}^{-1}}\]
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D)
\[\frac{16}{3}m{{s}^{-1}}\]
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question_answer 21) The moment of inertia of a circular ring of radius r and mass M about diameter is
A)
\[\frac{2}{5}M{{r}^{2}}\]
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B)
\[\frac{M{{r}^{2}}}{4}\]
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C)
\[\frac{M{{r}^{2}}}{2}\]
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D)
\[\frac{M{{r}^{2}}}{12}\]
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question_answer 22) A body of mass 0.05 kg is observed to fall with an acceleration of \[9.5\text{ }m{{s}^{-2}}\]. The opposing force of air on the body is \[(g=9.8\text{ }m{{s}^{-2}})\]
A)
0.015 N
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B)
0.15 N
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C)
0.030 N
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D)
zero
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question_answer 23) The colloidal solution in which both the dispersed phase and dispersion medium are liquids are called
A)
emulsions
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B)
gels
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C)
foams
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D)
liquid crystals
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question_answer 24) In fog, photographs of the objects taken with infrared radiations are more clear than those obtained during visible light because
A)
\[I-R\] radiation has lesser wavelength than visible radiation
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B)
scattering of \[I-R\] light is more than visible light
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C)
the intensity of \[I-R\] light from the object is less
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D)
scattering of \[I-R\] light is less than visible light
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question_answer 25) Three concurrent co-planar forces 1 N, 2 N and 3 N acting along different directions on a body
A)
can keep the body in equilibrium if 2 N and 3 N act at right angle
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B)
can keep the body in equilibrium if 1 N and 2 N act at right angle
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C)
cannot keep the body in equilibrium
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D)
can keep the body in equilibrium in 1 N and 3 N act at an acute angle
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question_answer 26) Sound waves transfer
A)
only energy not momentum
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B)
energy
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C)
momentum
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D)
Both (a) and (b)
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question_answer 27)
Two rectangular \[0.15\text{ }m{{s}^{-1}}\] blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of spring constant \[10.8\text{ }N{{m}^{-1}}\] and are placed on a fricrionless horizontal surface. The block A was given an initial velocity of \[0.15\text{ }m{{s}^{-1}}\] in the direction shown in the figure. The maximum compression of the spring during motion is
A)
0.01 m
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B)
0.02 m
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C)
0.05 m
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D)
0.03 m
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question_answer 28) G P Thomson experimentally confirmed the existence of matter waves by the phenomena
A)
diffraction
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B)
refraction
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C)
polarisation
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D)
scattering
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question_answer 29) The resistance of a wire at 300 K is found to be \[0.3\,\Omega \]. If the temperature coefficient of resistance of wire is \[1.5\times {{10}^{-3}}{{K}^{-1}}\], the temperature at which the resistance becomes \[0.6\,\,\Omega \] is
A)
720 K
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B)
345 K
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C)
993 K
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D)
690 K
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question_answer 30)
The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is
A)
225 J
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B)
200 J
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C)
400 J
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D)
175 J
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question_answer 31) Two luminous point sources separated by a certain distance are at 10 km from an observer. If the aperture of his eye is \[2.5\times {{10}^{-3}}m\] and the wavelength of light used is 500 nm, the distance of separation between the point sources just seen to be resolved is
A)
12.2 m
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B)
24.2 m
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C)
2.44 m
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D)
1.22 m
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question_answer 32) A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4 m distance from the hinges for opening or closing the door is
A)
1.2 N
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B)
3.6 N
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C)
2.4 N
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D)
4 N
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question_answer 33) \[0.1\text{ }{{m}^{3}}\] of water at \[{{80}^{o}}C\] is mixed with \[0.3\text{ }{{m}^{3}}\]of water at \[{{60}^{o}}C\]. The final temperature of the mixture is
A)
\[{{65}^{o}}C\]
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B)
\[{{70}^{o}}C\]
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C)
\[{{60}^{o}}C\]
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D)
\[{{75}^{o}}C\]
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question_answer 34) The spectral series of the hydrogen atom that lies in the visible region of the electromagnetic spectrum
A)
Paschen
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B)
Balmer
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C)
Lyman
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D)
Brackett
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question_answer 35)
A graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph curve OC represents
A)
isochoric process
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B)
isothermal process
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C)
isobaric process
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D)
adiabatic process
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question_answer 36) Which of the following statement does not hold good for thermal radiation?
A)
The wavelength changes when it travels from one medium to another
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B)
The frequency changes when it travels from one medium to another
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C)
The speed changes when it travels from one medium to another
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D)
They travel in straight line in a given medium
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question_answer 37)
A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at
A)
D
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B)
B
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C)
A
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D)
C
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question_answer 38)
Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N. For a streamline flow of liquid the rate of liquid flow is
A)
changing continuously with time
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B)
greater at M than at N
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C)
greater at N than at M
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D)
same at M and N
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question_answer 39) A resistor and a capacitor are connected in series with an AC source. If the potential drop across the capacitor is 5 V and that across resistor is 12 V, then applied voltage is
A)
13 V
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B)
17 V
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C)
5 V
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D)
12 V
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question_answer 40) The amount of heat energy radiated by a metal at temperature T is E. When the temperature is increased to 3T, energy radiated is
A)
81 E
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B)
9 E
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C)
3 E
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D)
27 E
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question_answer 41) The angle of minimum deviation for an incident light ray on an equilateral prism is equal to its refracting angle. The refractive index of its material is
A)
\[\frac{1}{\sqrt{2}}\]
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B)
\[\sqrt{3}\]
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C)
\[\frac{\sqrt{3}}{2}\]
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D)
\[\frac{3}{2}\]
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question_answer 42)
In the following combinations of logic gates, the outputs of A, B and C are respectively
A)
0, 1, 1
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B)
0, 1, 0
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C)
1, 1, 0
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D)
1, 0, 1
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question_answer 43) A stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points P and Q are at a distance of 4 m and 9 m respectively from the source. The ratio of amplitudes of the waves at P and Q is
A)
\[\frac{3}{2}\]
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B)
\[\frac{4}{9}\]
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C)
\[\frac{2}{3}\]
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D)
\[\frac{9}{4}\]
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question_answer 44) A galvanometer of resistance \[240\text{ }\Omega \] allows only 4% of the main current after connecting a shunt resistance. The value of the shunt resistance is
A)
\[10\text{ }\Omega \]
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B)
\[20\text{ }\Omega \]
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C)
\[8\text{ }\Omega \]
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D)
\[5\text{ }\Omega \]
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question_answer 45) The phenomena in which proton flips is
A)
nuclear magnetic resonance
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B)
lasers
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C)
radioactivity
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D)
nuclear fusion
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question_answer 46) \[y=3\sin \,\pi \left( \frac{t}{2}-\frac{x}{4} \right)\] represents an equation of a progressive wave, where t is in second and \[x\] is in metre. The distance travelled by the wave in 5 s is
A)
8 m
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B)
10 m
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C)
5 m
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D)
32 m
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question_answer 47) According to the quark model, it is possible to build all the hadrons using
A)
2 quarks and 3 antiquarks
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B)
3 quarks and 2 antiquarks
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C)
3 quarks and 3 antiquarks
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D)
2 quarks and 2 antiquarks
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question_answer 48) An \[\alpha \]-particle of mass \[6.4\times {{10}^{-27}}kg\] and charge \[3.2\times {{10}^{-19}}C\] is situated in a uniform electric field of \[1.6\times 10s\text{ }V{{m}^{-1}}\]. The velocity of the particle at the end of \[2\times {{10}^{-2}}m\] path when it starts from rest is
A)
\[2~\sqrt{3}\times {{10}^{5}}m{{s}^{-1}}\]
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B)
\[8\times {{10}^{5}}m{{s}^{-1}}\]
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C)
\[16\times {{10}^{5}}m{{s}^{-1}}\]
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D)
\[4\times {{10}^{5}}m{{s}^{-1}}\]
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question_answer 49) A cylindrical tube open at both the ends has a fundamental frequency of 390 Hz in air. If \[\frac{1}{4}th\] of the tube is immersed vertically in water the fundamental frequency of air column is
A)
260 Hz
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B)
130 Hz
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C)
390 Hz
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D)
520 Hz
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question_answer 50) The surface temperature of the stars is determined using
A)
Planck's law
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B)
Wien's displacement law
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C)
Rayleigh-Jeans law
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D)
Kirchhoff?s law
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question_answer 51)
The charge deposited on 4\[\mu \]F capacitor in the circuit is
A)
\[6\times {{10}^{-6}}C\]
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B)
\[12\times {{10}^{-6}}C\]
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C)
\[24\times {{10}^{-6}}C\]
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D)
\[36\times {{10}^{-6}}C\]
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question_answer 52) A parallel beam of light is incident on a converging lens parallel to its principal axis. As one moves away from the lens on the other side of the principal axis, the intensity of light
A)
first decreases and then increases
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B)
continuously increases
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C)
continuously decreases
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D)
first increases and then decreases
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question_answer 53) Continuous emission spectrum is produced by
A)
incandescent electric lamp
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B)
mercury vapour lamp
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C)
sodium vapour lamp
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D)
polyatomic substances
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question_answer 54) A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength \[I\] is passed through the coil, the magnetic field at its centre is
A)
\[\frac{{{\mu }_{0}}nI}{\left( b-a \right)}{{\log }_{e}}\frac{a}{b}\]
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B)
\[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}\]
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C)
\[\frac{2{{\mu }_{0}}nI}{b}\]
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D)
\[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}{{\log }_{e}}\frac{b}{a}\]
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question_answer 55) A ray of light is incident on a plane mirror at an angle of \[{{60}^{o}}\]. The angle of deviation produced by the mirror is
A)
\[{{120}^{o}}\]
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B)
\[{{30}^{o}}\]
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C)
\[{{60}^{o}}\]
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D)
\[{{90}^{o}}\]
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question_answer 56) The electric potential at any point \[x,y,z\] in metres is given by \[V=3{{x}^{2}}\]. The electric field at a point (2, 0, 1) is
A)
\[12\text{ }V{{m}^{-1}}\]
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B)
\[-6\text{ }V{{m}^{-1}}\]
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C)
\[6\text{ }V{{m}^{-1}}\]
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D)
\[-12V{{m}^{-1}}\]
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question_answer 57) Young's double slit experiment gives interference fringes of width 0.3 mm. A thin glass plate made of material of refractive index 1.5 is kept in the path of light from one of the slits, then the fringe width becomes
A)
zero
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B)
0.3 mm
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C)
0.45 mm
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D)
0.15 mm
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question_answer 58)
Near a circular loop of conducting wire as shown in the figure an electron moves along a straight line. The direction of the induced current if any in the loop is
A)
variable
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B)
clockwise
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C)
anticlockwise
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D)
zero
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question_answer 59) Hydrogen atom from excited state comes to the ground stage by emitting a photon of wavelength\[\lambda \]. If R is the Rydberg constant, the principal quantum number n of the excited state is
A)
\[\sqrt{\frac{\lambda R}{\lambda R-1}}\]
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B)
\[\sqrt{\frac{\lambda }{\lambda R-1}}\]
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C)
\[\sqrt{\frac{\lambda {{R}^{2}}}{\lambda R-1}}\]
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D)
\[\sqrt{\frac{\lambda R}{\lambda -1}}\]
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question_answer 60) The magnetic dipole moment of a current loop is independent of
A)
magnetic field in which it is lying
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B)
number of turns
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C)
area of the loop
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D)
current in the loop
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question_answer 61) The correct statement with regard to \[H_{2}^{+}\] and \[H_{2}^{-}\] is
A)
both \[H_{2}^{+}\] and \[H_{2}^{-}\] are equally stable
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B)
both \[H_{2}^{+}\] and \[H_{2}^{-}\] do not exist
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C)
Ha is more stable than \[H_{2}^{+}\]
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D)
\[H_{2}^{+}\] is more stable than \[H_{2}^{-}\]
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question_answer 62) Arrange the following in the increasing order of their bond order \[{{O}_{2}},O_{2}^{+},O_{2}^{-}\] and \[O_{2}^{2-}\]
A)
\[O_{2}^{2-},O_{2}^{-},{{O}_{2}},O_{2}^{+}\]
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B)
\[O_{2}^{2-},O_{2}^{-},O_{2}^{+},{{O}_{2}}\]
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C)
\[O_{2}^{+},{{O}_{2}},O_{2}^{-},O_{2}^{2-}\]
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D)
\[{{O}_{2}},O_{2}^{+},O_{2}^{-},O_{2}^{2-}\]
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question_answer 63) 2 g of a radioactive sample having half-life of 15 days was synthesized on 1st Jan 2009. The amount of the sample left behind on 1st March, 2009 (including both the days) is
A)
0 g
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B)
0.125 g
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C)
1 g
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D)
0.5 g
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question_answer 64) For a chemical reaction \[A\to B\], the rate of the reaction is \[2\times {{10}^{-3}}\,mol\,\,d{{m}^{-3}}{{s}^{-1}}\] when the initial concentration is \[0.05\,mol\,d{{m}^{-3}}\]. The rate of the same reaction is \[1.6\times {{10}^{-2}}mol\,d{{m}^{-3}}{{s}^{-1}}\] when the initial concentration is \[0.1\text{ }mol\text{ }d{{m}^{-3}}\]. The order of the reaction is
A)
2
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B)
0
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C)
3
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D)
1
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question_answer 65)
For the decomposition of a compound AB at 600 K, the following data were obtained [AB] mol \[d{{m}^{-3}}\] Rate of decomposition of AB in mol \[d{{m}^{-3}}{{s}^{-1}}\] 0.20 \[2.75\times {{10}^{-8}}\] 0.40 \[11.0\times {{10}^{-8}}\] 0.60 \[24.75\times {{10}^{-8}}\]
The order for the decomposition of AB is
A)
1.5
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B)
0
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C)
1
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D)
2
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question_answer 66) The rate equation for a reaction \[A\to B\] is\[r=k{{[A]}^{0}}\]. If the initial concentration of the reactant is a mol \[d{{m}^{-3}}\], the half-life period of the reaction is
A)
\[\frac{a}{2k}\]
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B)
\[\frac{k}{a}\]
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C)
\[\frac{a}{k}\]
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clear
D)
\[\frac{2a}{k}\]
done
clear
View Answer play_arrow
question_answer 67) 30 cc of \[\frac{M}{3}HCl,\,20\,cc\] of \[\frac{M}{2}HN{{O}_{3}}\] and 40 cc of \[\frac{M}{4}NaOH\] solutions are mixed and the volume was made up to \[1\text{ }d{{m}^{3}}\]. The pH of the resulting solution is
A)
8
done
clear
B)
2
done
clear
C)
1
done
clear
D)
3
done
clear
View Answer play_arrow
question_answer 68) An aqueous solution containing 6.5 g of \[NaCl\]of 90% purity was subjected to electrolysis. After the complete electrolysis, the solution was evaporated to get solid \[NaOH\]. The volume of 1 M acetic acid required to neutralise \[NaOH\] obtained above is
A)
\[1000\text{ }c{{m}^{3}}\]
done
clear
B)
\[2000\text{ }c{{m}^{3}}\]
done
clear
C)
\[100\text{ }c{{m}^{3}}\]
done
clear
D)
\[200\text{ }c{{m}^{3}}\]
done
clear
View Answer play_arrow
question_answer 69) The standard electrode potential for the half cell reactions are \[Z{{n}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Zn;\,{{E}^{o}}=-0.76\,V\] \[F{{e}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Fe;\,{{E}^{o}}=-0.44\,V\] The emf of the cell reaction, \[F{{e}^{2+}}+Zn\xrightarrow{{}}Z{{n}^{2+}}+Fe\] is
A)
-0.32V
done
clear
B)
-1.20V
done
clear
C)
+ 1.20V
done
clear
D)
4-0.32 V
done
clear
View Answer play_arrow
question_answer 70) \[{{10}^{-6}}M\,NaOH\] is diluted 100 times. The pH of the diluted base is
A)
between 7 and 8
done
clear
B)
between 5 and 6
done
clear
C)
between 6 and 7
done
clear
D)
between 10 and 11
done
clear
View Answer play_arrow
question_answer 71) In the electrolysis of acidulated water, it is desired to obtain 1.12 cc of hydrogen per second under STP condition. The current to be passed is
A)
1.93 A
done
clear
B)
9.65 A
done
clear
C)
19.3 A
done
clear
D)
0.965 A
done
clear
View Answer play_arrow
question_answer 72) The one which decreases with dilution is
A)
molar conductance
done
clear
B)
conductance
done
clear
C)
specific conductance
done
clear
D)
equivalent conductance
done
clear
View Answer play_arrow
question_answer 73) Vapour pressure of pure ?A? is 70 mm of Hg at\[{{25}^{o}}C\]. It forms an ideal solution with ?B? in which mole fraction of A is 0.8. If the vapour pressure of the solution is 84 mm of Hg at\[{{25}^{o}}C\], the vapour pressure of pure ?B? at \[{{25}^{o}}C\] is
A)
28 mm
done
clear
B)
56 mm
done
clear
C)
70mm
done
clear
D)
140mm
done
clear
View Answer play_arrow
question_answer 74) A 6% solution of urea is isotonic with
A)
1 M solution of glucose
done
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B)
0.05 M solution of glucose
done
clear
C)
6% solution of glucose
done
clear
D)
25% solution of glucose
done
clear
View Answer play_arrow
question_answer 75) In countries nearer to polar region, the roads are sprinkled with \[CaC{{l}_{2}}\]. This is
A)
to minimise the wear and tear of the roads
done
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B)
to minimise the snow fall
done
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C)
to minimise pollution
done
clear
D)
to minimise the accumulation of dust on the road
done
clear
View Answer play_arrow
question_answer 76) For the reaction \[{{H}_{2}}O(l){{H}_{2}}O(g)\] at 373 K and 1 atm pressure
A)
\[\Delta H=0\]
done
clear
B)
\[\Delta E=0\]
done
clear
C)
\[\Delta H=T\Delta S\]
done
clear
D)
\[\Delta H=\Delta E\]
done
clear
View Answer play_arrow
question_answer 77) A compound of 'A' and 'B' crystallises in a cubic lattice in which 'A' atoms occupy the lattice points at the corners of the cube. The 'B' atoms occupy the centre of each face of the cube. The probable empirical formula of the compound is
A)
\[A{{B}_{2}}\]
done
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B)
\[{{A}_{3}}B\]
done
clear
C)
\[AB\]
done
clear
D)
\[A{{B}_{3}}\]
done
clear
View Answer play_arrow
question_answer 78) In electrophilic aromatic substitution reaction, the nitro group is meta directing because it
A)
decreases electron density at ortho and para positions
done
clear
B)
decreases electron density at meta position
done
clear
C)
increases electron density at meta position
done
clear
D)
increases electron density at ortho and para positions
done
clear
View Answer play_arrow
question_answer 79) \[C{{H}_{3}}COOH\xrightarrow{LiAl{{H}_{4}}}X\xrightarrow[{{300}^{o}}C]{Cu}Y\frac{Dilute}{naOH}\]In the above reaction Z is
A)
butanol
done
clear
B)
aldol
done
clear
C)
ketol
done
clear
D)
acetal
done
clear
View Answer play_arrow
question_answer 80) The best method for the conversion of an alcohol into an alkyl chloride is by treating the alcohol with
A)
\[PC{{l}_{3}}\]
done
clear
B)
\[PC{{l}_{5}}\]
done
clear
C)
\[SOC{{l}_{2}}\] in presence of pyridine
done
clear
D)
dry \[HCl\] in the presence of anhydrous \[ZnC{{l}_{2}}\]
done
clear
View Answer play_arrow
question_answer 81) The electrophile involved in the sulphonation of benzene is
A)
\[SO_{3}^{+}\]
done
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B)
\[SO_{3}^{2-}\]
done
clear
C)
\[H_{3}^{+}O\]
done
clear
D)
\[S{{O}_{3}}\]
done
clear
View Answer play_arrow
question_answer 82) The carbon-carbon bond length in benzene is
A)
in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{4}}\]
done
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B)
same as in \[{{C}_{2}}{{H}_{4}}\]
done
clear
C)
in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{2}}\]
done
clear
D)
in between \[{{C}_{2}}{{H}_{4}}\] and \[{{C}_{2}}{{H}_{2}}\]
done
clear
View Answer play_arrow
question_answer 83) The compound which is not formed during the dry distillation of a mixture of calcium formate and calcium acetate is
A)
methanal
done
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B)
propanal
done
clear
C)
propanone
done
clear
D)
ethanol
done
clear
View Answer play_arrow
question_answer 84) An organic compound X is oxidised by using acidified \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]. The product obtained reacts with phenyl hydrazine but does not answer silver mirror test. The possible structure of X is
A)
\[C{{H}_{3}}C{{H}_{2}}OH\]
done
clear
B)
\[C{{H}_{3}}\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{-C}}\,-C{{H}_{3}}\]
done
clear
C)
\[{{(C{{H}_{3}})}_{2}}CHOH\]
done
clear
D)
\[C{{H}_{3}}CHO\]
done
clear
View Answer play_arrow
question_answer 85) The reaction involved in the oil of winter green test is salicylic acid \[\xrightarrow[Conc.\,\,{{H}_{2}}S{{O}_{4}}]{\Delta }\] product. The product is treated with \[N{{a}_{2}}C{{O}_{3}}\]solution. The missing reagent in the above reaction is
A)
phenol
done
clear
B)
\[NaOH\]
done
clear
C)
ethanol
done
clear
D)
methanol
done
clear
View Answer play_arrow
question_answer 86) The compound which forms acetaldehyde when heated with dilute \[NaOH\], is
A)
1, 1-dichloroethane
done
clear
B)
1, 1, 1-trichloroethane
done
clear
C)
1-chloroethane
done
clear
D)
1, 2-dichloroethane
done
clear
View Answer play_arrow
question_answer 87) Arrange the following in the increasing order of their basic strengths\[C{{H}_{3}}N{{H}_{2}},\,{{(C{{H}_{3}})}_{2}}NH\], \[{{(C{{H}_{3}})}_{3}}N,\,N{{H}_{3}}\]
A)
\[N{{H}_{3}}<{{(C{{H}_{3}})}_{3}}N<{{(C{{H}_{3}})}_{2}}NH<C{{H}_{3}}N{{H}_{2}}\]
done
clear
B)
\[N{{H}_{3}}<{{(C{{H}_{3}})}_{3}}N<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]
done
clear
C)
\[{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]
done
clear
D)
\[C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH<{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 88) The one which has least iodine value is
A)
sunflower oil
done
clear
B)
ginger oil
done
clear
C)
ghee
done
clear
D)
groundnut oil
done
clear
View Answer play_arrow
question_answer 89) A diabetic person carries a packet of glucose with him always, because
A)
glucose reduces the blood sugar level slowly
done
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B)
glucose increases the blood sugar level slowly
done
clear
C)
glucose reduces the blood sugar level
done
clear
D)
glucose increases the blood sugar level almost instantaneously
done
clear
View Answer play_arrow
question_answer 90) There are 20 naturally occurring amino acids. The maximum number of tripeptides that can be obtained is
A)
8000
done
clear
B)
6470
done
clear
C)
7465
done
clear
D)
5360
done
clear
View Answer play_arrow
question_answer 91) Cooking is fast in a pressure cooker, because
A)
food particles are effectively smashed
done
clear
B)
water boils at higher temperature inside the pressure cooker
done
clear
C)
food is cooked at constant volume
done
clear
D)
loss of heat due to radiation is minimum
done
clear
View Answer play_arrow
question_answer 92) The ore that is concentrated by froth floatation process is
A)
zincite
done
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B)
cinnabar
done
clear
C)
bauxite
done
clear
D)
malachite
done
clear
View Answer play_arrow
question_answer 93) The correct set of four quantum numbers for outermost electron of potassium \[(Z=19)\] is
A)
\[4,1,0,\frac{1}{2}\]
done
clear
B)
\[3,1,0,\frac{1}{2}\]
done
clear
C)
\[4,0,0,\frac{1}{2}\]
done
clear
D)
\[3,0,0,\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 94) A body of mass \[x\] kg is moving with a velocity of \[100\,\,m{{s}^{-1}}\]. Its de-Broglie wavelength is\[6.62\times {{10}^{-35}}m\]. Hence, \[x\] is \[(h=6.62\times {{10}^{-34}}Js)\]
A)
0.1 kg
done
clear
B)
0.25 kg
done
clear
C)
0.15 kg
done
clear
D)
0.2 kg
done
clear
View Answer play_arrow
question_answer 95) The correct order of ionisation energy of C, N, O, F is
A)
\[F<O<N<C\]
done
clear
B)
\[F<N<C<O\]
done
clear
C)
\[C<N<O<F\]
done
clear
D)
\[C<O<N<F\]
done
clear
View Answer play_arrow
question_answer 96) The oxide of an element whose electronic configuration is \[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{1}}\] is
A)
neutral
done
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B)
amphoteric
done
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C)
basic
done
clear
D)
acidic
done
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View Answer play_arrow
question_answer 97) The characteristic not related to alkali metal is
A)
high ionisation energy
done
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B)
their ions are isoelectronic with noble gases
done
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C)
low melting point
done
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D)
low electronegativity
done
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question_answer 98) Among the following, the compound that contains ionic, covalent and coordinate linkage is
A)
\[N{{H}_{3}}\]
done
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B)
\[N{{H}_{4}}Cl\]
done
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C)
\[NaCl\]
done
clear
D)
\[CaO\]
done
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View Answer play_arrow
question_answer 99) A covalent molecule \[A{{B}_{3}}\] has pyramidal structure. The number of lone pair and bond pair of electrons in the molecule are respectively
A)
2 and 2
done
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B)
0 and 4
done
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C)
3 and 1
done
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D)
1 and 3
done
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question_answer 100) Excess of carbon dioxide is passed through 50 mL of 0.5 M calcium hydroxide solution. After the completion of the reaction, the solution was evaporated to dryness. The solid calcium carbonate was completely neutralised with N hydrochloric acid. The volume of hydrochloric acid required is (Atomic mass of calcium = 40)
A)
\[300\,\,c{{m}^{3}}\]
done
clear
B)
\[200\,\,c{{m}^{3}}\]
done
clear
C)
\[500\,\,c{{m}^{3}}\]
done
clear
D)
\[400\,\,c{{m}^{3}}\]
done
clear
View Answer play_arrow
question_answer 101) A bivalent metal has an equivalent mass of 32. The molecular mass of the metal nitrate is
A)
182
done
clear
B)
168
done
clear
C)
192
done
clear
D)
188
done
clear
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question_answer 102) The rms velocity of molecules of a gas of density \[4\,kg\,{{m}^{-3}}\] and pressure \[1.2\times {{10}^{5}}N{{m}^{-2}}\] is
A)
\[300\,\,m{{s}^{-1}}\]
done
clear
B)
\[900\,\,m{{s}^{-1}}\]
done
clear
C)
\[120\,\,m{{s}^{-1}}\]
done
clear
D)
\[600\,\,m{{s}^{-1}}\]
done
clear
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question_answer 103) 0.5 mole of each of \[{{H}_{2}},S{{O}_{2}}\] and \[C{{H}_{4}}\] are kept in a container. A hole was made in the container. After 3 h, the order of partial pressures in the container will be
A)
\[pS{{O}_{2}}>p{{H}_{2}}>pC{{H}_{4}}\]
done
clear
B)
\[pS{{O}_{2}}>pC{{H}_{4}}>p{{H}_{2}}\]
done
clear
C)
\[p{{H}_{2}}>pS{{O}_{2}}>pC{{H}_{4}}\]
done
clear
D)
\[p{{H}_{2}}>pC{{H}_{4}}>pS{{O}_{2}}\]
done
clear
View Answer play_arrow
question_answer 104) The enthalpy of formation of \[N{{H}_{3}}\] is\[-46\,\,kJ\,\,mo{{l}^{-1}}\]. The enthalpy change for the reaction \[2N{{H}_{3}}(g)\xrightarrow{{}}{{N}_{2}}(g)+3{{H}_{2}}(g)\] is
A)
+184 kJ
done
clear
B)
+23 kJ
done
clear
C)
+92 kJ
done
clear
D)
+46 kJ
done
clear
View Answer play_arrow
question_answer 105) 5 moles of \[S{{O}_{2}}\] and 5 moles of \[{{O}_{2}}\] are allowed to react. At equilibrium, it was found that 60% of \[S{{O}_{2}}\] is used up. If the partial pressure of the equilibrium mixture is one atmosphere, the partial pressure of \[{{O}_{2}}\] is
A)
0.82 atm
done
clear
B)
0.52 atm
done
clear
C)
0.21 atm
done
clear
D)
0.41 atm
done
clear
View Answer play_arrow
question_answer 106) \[2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)\] The equilibrium constant of the above reaction is 6.4 at 300 K. If 0.25 mole each of \[{{H}_{2}}\] and \[{{I}_{2}}\] are added to the system, the equilibrium constant will be
A)
6.4
done
clear
B)
0.8
done
clear
C)
3.2
done
clear
D)
1.6
done
clear
View Answer play_arrow
question_answer 107) Rate of physical adsorption increases with
A)
decrease in surface area
done
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B)
decrease in temperature
done
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C)
decrease in pressure
done
clear
D)
increase in temperature
done
clear
View Answer play_arrow
question_answer 108) IUPAC name of \[{{(C{{H}_{3}})}_{2}}CCl\] is
A)
n-butyl chloride
done
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B)
3-chloro butane
done
clear
C)
2-chloro 2-methyl propane
done
clear
D)
t-butyl chloride
done
clear
View Answer play_arrow
question_answer 109) Lucas test is associated with
A)
aldehydes
done
clear
B)
phenols
done
clear
C)
carboxylic acids
done
clear
D)
alcohols
done
clear
View Answer play_arrow
question_answer 110) An organic compound on heating with CuO produces \[C{{O}_{2}}\] but no water. The organic compound may be
A)
carbon tetrachloride
done
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B)
chloroform
done
clear
C)
methane
done
clear
D)
ethyl iodide
done
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View Answer play_arrow
question_answer 111) The condensation polymer among the following is
A)
rubber
done
clear
B)
protein
done
clear
C)
PVC
done
clear
D)
polyethene
done
clear
View Answer play_arrow
question_answer 112) The order of stability of metal oxides is
A)
\[A{{l}_{2}}{{O}_{3}}<MgO<F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}\]
done
clear
B)
\[C{{r}_{2}}{{O}_{3}}<MgO<A{{l}_{2}}{{O}_{3}}<F{{e}_{2}}{{O}_{3}}\]
done
clear
C)
\[F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<MgO\]
done
clear
D)
\[F{{e}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<MgO\]
done
clear
View Answer play_arrow
question_answer 113) The temperature of the slag zone in the metallurgy of iron using blast furnace is
A)
\[1200-{{1500}^{o}}C\]
done
clear
B)
\[1500-{{1600}^{o}}C\]
done
clear
C)
\[400-{{700}^{o}}C\]
done
clear
D)
\[800-{{1000}^{o}}C\]
done
clear
View Answer play_arrow
question_answer 114) The function of \[Fe{{(OH)}_{3}}\] in the contact process is
A)
to remove arsenic impurity
done
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B)
to detect colloidal impurity
done
clear
C)
to remove moisture
done
clear
D)
to remove dust particles
done
clear
View Answer play_arrow
question_answer 115) In which of the following, \[N{{H}_{3}}\] is not used?
A)
Tollen's reagent
done
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B)
Nessler's reagent
done
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C)
Group reagent for the analysis of IV group basic radicals
done
clear
D)
Group reagent for the analysis of III group basic radicals
done
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View Answer play_arrow
question_answer 116) Argon is used
A)
in filling airships
done
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B)
to obtain low temperature
done
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C)
in high temperature welding
done
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D)
in radiotherapy for treatment of cancer
done
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View Answer play_arrow
question_answer 117) The incorrect statement in respect of chromyl chloride test is
A)
formation of red vapours
done
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B)
formation of lead chromate
done
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C)
formation of chromyl chloride
done
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D)
liberation of chlorine
done
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View Answer play_arrow
question_answer 118) The magnetic moment of a transition metal ion is \[\sqrt{15}\,BM\]. Therefore, the number of unpaired electrons present in it, is
A)
3
done
clear
B)
4
done
clear
C)
1
done
clear
D)
2
done
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View Answer play_arrow
question_answer 119) The IUPAC name of \[{{[Co{{(N{{H}_{3}})}_{5}}ONO]}^{2+}}\] ion is
A)
penta ammine nitrito cobalt (IV) ion
done
clear
B)
penta ammine nitrito cobalt (III) ion
done
clear
C)
penta ammine nitro cobalt (III) ion
done
clear
D)
penta ammine nitro cobalt (IV) ion
done
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View Answer play_arrow
question_answer 120) The oxidation state of Fe in the brown ring complex: \[[Fe{{({{H}_{2}}O)}_{5}}NO]S{{O}_{4}}\] is
A)
+3
done
clear
B)
0
done
clear
C)
+2
done
clear
D)
+1
done
clear
View Answer play_arrow
question_answer 121) The smallest positive integral value of n such that \[{{\left[ \frac{1+\sin \frac{\pi }{8}+i\,\cos \frac{\pi }{8}}{1+\sin \frac{\pi }{8}-i\,\cos \frac{\pi }{8}} \right]}^{n}}\] is purely imaginary is equal to
A)
\[4\]
done
clear
B)
\[3\]
done
clear
C)
\[2\]
done
clear
D)
\[8\]
done
clear
View Answer play_arrow
question_answer 122) Which one of the following is possible?
A)
\[\sin \theta =\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}},(a\ne b)\]
done
clear
B)
\[\sin \theta =\frac{4}{5}\]
done
clear
C)
\[\sin \theta =45\]
done
clear
D)
\[\cos \theta =\frac{7}{3}\]
done
clear
View Answer play_arrow
question_answer 123) If one side of a triangle is double the other and the angles opposite to these sides differ by \[{{60}^{o}},\]then the triangle is
A)
obtuse angled
done
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B)
acute angled
done
clear
C)
isosceles
done
clear
D)
right angled
done
clear
View Answer play_arrow
question_answer 124) \[3{{(\sin x-\cos x)}^{4}}+6{{(\sin \,x+\operatorname{cosx})}^{2}}\]\[+({{\sin }^{6}}x+{{\cos }^{6}}x)\] is equal to
A)
\[12\]
done
clear
B)
\[13\]
done
clear
C)
\[14\]
done
clear
D)
\[11\]
done
clear
View Answer play_arrow
question_answer 125) A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes \[44\text{ }m,\] when it has traced out \[{{72}^{o}}\]at the centre, the length of the rope is
A)
\[22\,\,m\]
done
clear
B)
\[56\,\,m\]
done
clear
C)
\[45\,\,m\]
done
clear
D)
\[35\,\,m\]
done
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View Answer play_arrow
question_answer 126) If \[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\,\sin \,2\theta \\ {{\sin }^{2}}\theta & 1+{{\cos }^{2}}\theta & 4\sin 2\theta \\ {{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\sin 2\theta -1 \\ \end{matrix} \right|=0\] and \[0<\theta <\frac{\pi }{2},\] then \[\cos \,\,4\theta \] is equal to
A)
\[\frac{\sqrt{3}}{2}\]
done
clear
B)
\[0\]
done
clear
C)
\[\frac{-1}{2}\]
done
clear
D)
\[\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 127) The locus of the mid points of the chords of the circle \[{{x}^{2}}+{{y}^{2}}=4\]which subtend a right angle at the origin is
A)
\[{{x}^{2}}+{{y}^{2}}=1\]
done
clear
B)
\[{{x}^{2}}+{{y}^{2}}=2\]
done
clear
C)
\[x+y=1\]
done
clear
D)
\[x+y=2\]
done
clear
View Answer play_arrow
question_answer 128) The length of the chord joining the points\[(4\,\cos \theta ,4sin\theta )\] and \[(4\,\cos (\theta +{{60}^{o}}),\] \[4sin(\theta +{{60}^{o}}))\]of the circle \[{{x}^{2}}+{{y}^{2}}=16\]is
A)
\[4\]
done
clear
B)
\[8\]
done
clear
C)
\[16\]
done
clear
D)
\[2\]
done
clear
View Answer play_arrow
question_answer 129) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-y=0\] and \[{{x}^{2}}+{{y}^{2}}+y=0\] and \[{{x}^{2}}+{{y}^{2}}+y=0\]is
A)
\[2\]
done
clear
B)
\[3\]
done
clear
C)
\[0\]
done
clear
D)
\[1\]
done
clear
View Answer play_arrow
question_answer 130) The coordinates of the centre of the smallest circle passing through the origin and having \[y=x+1\] as a diameter are
A)
\[\left( \frac{1}{2},\frac{-1}{2} \right)\]
done
clear
B)
\[\left( \frac{1}{2},\frac{1}{3} \right)\]
done
clear
C)
\[(-1,0)\]
done
clear
D)
\[\left( -\frac{1}{2},\frac{1}{2} \right)\]
done
clear
View Answer play_arrow
question_answer 131) The length of the diameter of the circle which cuts three circles \[{{x}^{2}}+{{y}^{2}}-x-y-14=0\] \[{{x}^{2}}+{{y}^{2}}+3x-5y-10=0\] \[{{x}^{2}}+{{y}^{2}}-2x+3y-27=0\] orthogonally, is
A)
\[8\]
done
clear
B)
\[6\]
done
clear
C)
\[4\]
done
clear
D)
\[2\]
done
clear
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question_answer 132) For the parabola \[{{y}^{2}}=4x,\]the point P whose focal distance is 17, is
A)
\[(8,8)\] or \[(8,-8)\]
done
clear
B)
\[(4,8)\] or \[(4,-8)\]
done
clear
C)
\[(2,8)\] or \[(2,-8)\]
done
clear
D)
\[(16,8)\] or \[(16,-8)\]
done
clear
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question_answer 133) The angle between the tangents drawn to the parabola \[{{y}^{2}}=12x\]from the point \[(-3,2)\]is
A)
\[{{90}^{o}}\]
done
clear
B)
\[{{60}^{o}}\]
done
clear
C)
\[{{30}^{o}}\]
done
clear
D)
\[{{45}^{o}}\]
done
clear
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question_answer 134) The number of values of c such that the line \[y=4x+c\]touches the curve \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\] is
A)
\[1\]
done
clear
B)
\[2\]
done
clear
C)
\[\infty \]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 135) If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] intersects the hyperbola \[xy={{c}^{2}}\]four points \[P({{x}_{1}},{{y}_{1}}),\] \[Q({{x}_{2}},{{y}_{2}}),\] \[R({{x}_{3}},{{y}_{3}})\] and \[S({{x}_{4}},{{y}_{4}})\] then,
A)
\[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}=2\]
done
clear
B)
\[{{x}_{1}}{{x}_{2}}{{x}_{3}}{{x}_{4}}=2{{c}^{4}}\]
done
clear
C)
\[{{y}_{1}}{{y}_{2}}{{y}_{3}}{{y}_{4}}=2{{c}^{4}}\]
done
clear
D)
\[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}=0\]
done
clear
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question_answer 136) The foot of the perpendicular from the point\[(2,4)\] upon \[x+y=4\]is
A)
\[(2,2)\]
done
clear
B)
\[(4,0)\]
done
clear
C)
\[(1,3)\]
done
clear
D)
\[(3,-1)\]
done
clear
View Answer play_arrow
question_answer 137) The vertices of a triangle are \[(6,0),(0,6)\] and \[(6,6)\]. The distance between its circumventer and centroid is
A)
\[2\]
done
clear
B)
\[\sqrt{2}\]
done
clear
C)
\[1\]
done
clear
D)
\[2\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 138) The angle between the pair of lines \[{{x}^{2}}+2xy-{{y}^{2}}=0\] is
A)
\[\frac{\pi }{6}\]
done
clear
B)
\[\frac{\pi }{2}\]
done
clear
C)
\[0\]
done
clear
D)
\[\frac{\pi }{3}\]
done
clear
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question_answer 139) \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{3.2}^{n+1}}-{{4.5}^{n+1}}}{{{5.2}^{n}}+{{7.5}^{n}}}\] is equal to
A)
\[\frac{3}{5}\]
done
clear
B)
\[-\frac{4}{7}\]
done
clear
C)
\[-\frac{20}{7}\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 140) The function \[f(x)=\frac{\log (1+ax)-\log (1-bx)}{x}\] is not defined at \[x=0\]. The value which should be assigned to f at \[x=0\] so that it is continuous at \[x=0\] is
A)
\[a-b\]
done
clear
B)
\[a+b\]
done
clear
C)
\[\log a+\log b\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 141) If \[f(x)=1+nx+\frac{n(n-1)}{2}{{x}^{2}}\]\[+\frac{n(n-1)(n-2)}{6}{{x}^{3}}+.....+{{x}^{n}},\]then \[f''\] (1) is equal to
A)
\[n(n-1){{2}^{n-1}}\]
done
clear
B)
\[(n-1){{2}^{n-1}}\]
done
clear
C)
\[n(n-1){{2}^{n-2}}\]
done
clear
D)
\[n(n-1){{2}^{n}}\]
done
clear
View Answer play_arrow
question_answer 142) If \[f(x)={{\log }_{{{x}^{2}}}}({{\log }_{e}}x),\] then \[f'(x)\] at \[x=e\] is
A)
\[1\]
done
clear
B)
\[\frac{1}{e}\]
done
clear
C)
\[\frac{1}{2e}\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 143) If \[y={{\sin }^{2}}x\,\cos \,nx,\]then \[\frac{dy}{dx}\] is
A)
\[n\,\,{{\sin }^{n-1}}x\,\sin (n+1)x\]
done
clear
B)
\[n\,\,{{\sin }^{n-1}}x\,\cos (n-1)x\]
done
clear
C)
\[n\,\,{{\sin }^{n-1}}\,x\,\cos nx\]
done
clear
D)
\[n{{\sin }^{n-1}}x\,\cos (n+1)x\]
done
clear
View Answer play_arrow
question_answer 144) If \[f(x)=\frac{g(x)+g(-x)}{2}+\frac{2}{{{[h(x)+h(-x)]}^{-1}}}\]where g and h are differentiable function, then \[f'(0)\]
A)
\[1\]
done
clear
B)
\[\frac{1}{2}\]
done
clear
C)
\[\frac{3}{2}\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 145) The tangent to a given curve \[y=f(x)\]is perpendicular to the x-axis, if
A)
\[\frac{dy}{dx}=1\]
done
clear
B)
\[\frac{dx}{dy}=0\]
done
clear
C)
\[\frac{dx}{dy}=1\]
done
clear
D)
\[\frac{dy}{dx}=0\]
done
clear
View Answer play_arrow
question_answer 146) The minimum value of s
A)
\[-5\]
done
clear
B)
\[\frac{1}{5}\]
done
clear
C)
\[\frac{1}{243}\]
done
clear
D)
\[\frac{1}{27}\]
done
clear
View Answer play_arrow
question_answer 147) A stone is thrown vertically upwards from the top of a tower \[64\text{ }m\]high according to the law \[s=48t-16{{t}^{2}}.\]The greatest height attained by the stone above ground is
A)
\[36\,m\]
done
clear
B)
\[32\,m\]
done
clear
C)
\[100\,\,m\]
done
clear
D)
\[64\,\,m\]
done
clear
View Answer play_arrow
question_answer 148) The length of the subtangent at t on the curve\[x=a(t+\sin t),\] \[y=a(1-\cos t)\] is
A)
\[a\,\,\sin \,t\]
done
clear
B)
\[2a\,\,\sin \,\left( \frac{t}{2} \right)\tan \left( \frac{t}{2} \right)\]
done
clear
C)
\[2a\,\,\sin \,\frac{t}{2}\]
done
clear
D)
\[2a\,\,{{\sin }^{3}}\,\left( \frac{t}{2} \right)\sec \left( \frac{t}{2} \right)\]
done
clear
View Answer play_arrow
question_answer 149) \[\int{\text{cosec (x-a) cosec x dx}}\] is equal to
A)
\[x{{e}^{{{\tan }^{-1}}x}}+c\]
done
clear
B)
\[{{e}^{{{\tan }^{-1}}x}}+c\]
done
clear
C)
\[\frac{1}{2}{{e}^{{{\tan }^{-1}}x}}+c\]
done
clear
D)
\[\frac{1}{2}x{{e}^{{{\tan }^{-1}}x}}+c\]
done
clear
View Answer play_arrow
question_answer 150) \[\int{\text{cosec (x - a) cosec x dx}}\]is equal to
A)
\[\frac{-1}{\sin a}\log |\sin \,x\,\text{cosec(x-a) }\!\!|\!\!\text{ +c}\]
done
clear
B)
\[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)\sin x]+c\]
done
clear
C)
\[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)cosecx]+c\]
done
clear
D)
\[\frac{1}{\sin a}\log |\sin \,(\lambda -a)\sin x]+c\]
done
clear
View Answer play_arrow
question_answer 151) If \[f(x)=\int_{-1}^{x}{|t|\,\,dt,}\] then for any \[x\ge 0,\] \[f(x)\]equal to
A)
\[1-{{x}^{2}}\]
done
clear
B)
\[\frac{1}{2}(1+{{x}^{2}})\]
done
clear
C)
\[1+{{x}^{2}}\]
done
clear
D)
\[\frac{1}{2}(1-{{x}^{2}})\]
done
clear
View Answer play_arrow
question_answer 152) \[\int_{1}^{3}{\frac{\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}}dx\] is equal to
A)
\[1\]
done
clear
B)
\[3\]
done
clear
C)
\[2\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 153) The area bounded between the parabola\[{{y}^{2}}=4x\]and the line \[y=2x-4\]is equal to
A)
\[\frac{17}{3}sq\,unit\]
done
clear
B)
\[\frac{19}{3}sq\,unit\]
done
clear
C)
\[9\,sq\,unit\]
done
clear
D)
\[15\,sq\,unit\]
done
clear
View Answer play_arrow
question_answer 154) The differential equation of the family of circles passing through the orign and having their centres on the x-axis is
A)
\[{{y}^{2}}={{x}^{2}}+2xy\,\frac{dy}{dx}\]
done
clear
B)
\[{{y}^{2}}={{x}^{2}}-2xy\,\frac{dy}{dx}\]
done
clear
C)
\[{{x}^{2}}={{y}^{2}}+xy\,\frac{dy}{dx}\]
done
clear
D)
\[{{x}^{2}}={{y}^{2}}+3xy\,\frac{dy}{dx}\]
done
clear
View Answer play_arrow
question_answer 155) A population grows at the rate of 10% of the population per year. How long does it take for the population to double?
A)
\[20\text{ }log\text{ }2\text{ }yr\]
done
clear
B)
\[10\text{ }log\text{ }2\text{ y}r\]
done
clear
C)
\[5\text{ }log\text{ }2\text{ }yr\]
done
clear
D)
\[2\text{ }log\text{ }10\text{ }yr\]
done
clear
E)
None of these
done
clear
View Answer play_arrow
question_answer 156) On the set of all natural numbers N, which one of the following * is a binary operation?
A)
\[a*b=\sqrt{ab}\]
done
clear
B)
\[a*b=\frac{a-b}{a+b}\]
done
clear
C)
\[a*b=a+3b\]
done
clear
D)
\[a*b=3a-4b\]
done
clear
View Answer play_arrow
question_answer 157) If \[\int_{0}^{1}{f(x)\,dx=5,}\] then the value of \[....+100\int_{0}^{1}{{{x}^{9}}\,\,f({{x}^{10}})dx}\]is equal to
A)
\[125\]
done
clear
B)
\[625\]
done
clear
C)
\[275\]
done
clear
D)
\[55\]
done
clear
View Answer play_arrow
question_answer 158) If \[ax+by=1,\] where a, b, x and y are integers, then which one of the following is not true?
A)
\[(a,y)=1\]
done
clear
B)
\[(x,y)=1\]
done
clear
C)
\[(b,y)=1\]
done
clear
D)
\[(a,b)=1\]
done
clear
View Answer play_arrow
question_answer 159) The digit in the unit place of the number \[2009!+{{3}^{7886}}\]is
A)
\[7\]
done
clear
B)
\[3\]
done
clear
C)
\[1\]
done
clear
D)
\[9\]
done
clear
View Answer play_arrow
question_answer 160) If \[\left| \begin{matrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \\ \end{matrix} \right|=0,\] then a, b, c are
A)
in GP
done
clear
B)
in HP
done
clear
C)
equal
done
clear
D)
in AP
done
clear
View Answer play_arrow
question_answer 161) The value of \[\left| \begin{matrix} 1 & {{\log }_{x}}y & {{\log }_{x}}z \\ {{\log }_{y}}x & 1 & {{\log }_{y}}z \\ {{\log }_{z}}x & {{\log }_{e}}y & 1 \\ \end{matrix} \right|\] is equal to
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[xyz\]
done
clear
D)
\[\log \,xyz\]
done
clear
View Answer play_arrow
question_answer 162) If \[A=\left[ \begin{matrix} 2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2 \\ \end{matrix} \right],\]then \[|adj\,A|\]is equal to
A)
\[0\]
done
clear
B)
\[9\]
done
clear
C)
\[\frac{1}{9}\]
done
clear
D)
\[81\]
done
clear
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question_answer 163) If A and B are square matrices of the same order such that \[(A+B)\,(A-B)={{A}^{2}}-{{B}^{2}},\] then \[{{(AB{{A}^{-1}})}^{2}}\]is equal to
A)
\[{{B}^{2}}\]
done
clear
B)
\[I\]
done
clear
C)
\[{{A}^{2}}{{B}^{2}}\]
done
clear
D)
\[{{A}^{2}}\]
done
clear
View Answer play_arrow
question_answer 164) If \[\vec{a}.\vec{b}=-|\vec{a}||\vec{b}|,\]then the angle between \[\vec{a}\] and \[\vec{b}\] is
A)
\[{{45}^{o}}\]
done
clear
B)
\[{{180}^{o}}\]
done
clear
C)
\[{{90}^{o}}\]
done
clear
D)
\[{{60}^{o}}\]
done
clear
View Answer play_arrow
question_answer 165) If \[\vec{a}+2\vec{b}+3\vec{c}=\vec{0},\] then \[\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}\] is equal to
A)
\[2(\vec{b}\times \vec{c})\]
done
clear
B)
\[3(\vec{c}\times \vec{a})\]
done
clear
C)
\[\vec{0}\]
done
clear
D)
\[6(\vec{b}\times \vec{c})\]
done
clear
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question_answer 166) If the volume of the parallelepiped with \[\vec{a},\] \[\vec{b}\] and \[\vec{c}\]as coterminous edges is \[40\text{ }cu\]unit, then the volume of the parallelepiped having \[\vec{b}+\vec{c},\] \[\vec{c}+\vec{a}\] and \[\vec{a}+\vec{b}\] as coterminous edges in cubic unit is
A)
\[80\]
done
clear
B)
\[120\]
done
clear
C)
\[160\]
done
clear
D)
\[40\]
done
clear
View Answer play_arrow
question_answer 167) In the group \[G\{0,1,2,3,4,5\}\] under addition modulo \[6,{{(2{{+}_{6}}{{3}^{-1}}{{+}_{6}}4)}^{-1}}\] is equal to
A)
\[2\]
done
clear
B)
\[3\]
done
clear
C)
\[5\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 168) Which one of the following is not true?
A)
Inverse of an element in a group is unique.
done
clear
B)
Fourth roots of unity form an additive abelian group.
done
clear
C)
Cancellation laws hold in a group.
done
clear
D)
Identity element in a group is unique.
done
clear
View Answer play_arrow
question_answer 169) The number of subgroups of the group \[({{Z}_{5}},{{+}_{5}})\] is
A)
\[1\]
done
clear
B)
\[3\]
done
clear
C)
\[4\]
done
clear
D)
\[2\]
done
clear
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question_answer 170) The negation of \[p\wedge (q\to \tilde{\ }r)\] is
A)
\[\tilde{\ }p\wedge (q\wedge r)\]
done
clear
B)
\[p\vee (q\vee r)\]
done
clear
C)
\[p\vee (q\wedge r)\]
done
clear
D)
\[\tilde{\ }p\vee (q\wedge r)\]
done
clear
View Answer play_arrow
question_answer 171) If \[n=(2020)!\]then\[\frac{1}{{{\log }_{2}}n}+\frac{1}{{{\log }_{3}}n}+\frac{1}{{{\log }_{4}}n}+....+\frac{1}{{{\log }_{2020}}n}\]is equal to
A)
\[2020\]
done
clear
B)
\[1\]
done
clear
C)
\[(2020)!\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 172) If 'n' is a positive integer, then \[{{n}^{3}}+2n\]is divisible by
A)
\[2\]
done
clear
B)
\[6\]
done
clear
C)
\[15\]
done
clear
D)
\[3\]
done
clear
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question_answer 173) On the set of integers Z, define \[f:z\to z\] as \[f(n)=\left\{ \begin{matrix} \frac{n}{2}, & n\,is\,\,even \\ 0, & n\,\,\,is\,\,odd \\ \end{matrix} \right.\], then f is
A)
injective but not subjective
done
clear
B)
neither injective nor subjective
done
clear
C)
surjective but not injective
done
clear
D)
objective
done
clear
View Answer play_arrow
question_answer 174) If \[\alpha \] and \[\beta \] are the roots of then \[{{\alpha }^{16}}+{{\beta }^{16}}\] is equal to
A)
\[1\]
done
clear
B)
\[-1\]
done
clear
C)
\[2\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 175) The total number of terms in the expansion of \[{{(x+y)}^{100}}+{{(x-y)}^{100}}\] after simplification is
A)
\[51\]
done
clear
B)
\[202\]
done
clear
C)
\[100\]
done
clear
D)
\[50\]
done
clear
View Answer play_arrow
question_answer 176) \[{{\cot }^{-1}}({{2.1}^{2}})+co{{t}^{-1}}({{2.2}^{2}})+{{\cot }^{-1}}({{2.3}^{2}})+...\] upto \[\infty \] is equal to
A)
\[\frac{\pi }{4}\]
done
clear
B)
\[\frac{\pi }{3}\]
done
clear
C)
\[\frac{\pi }{2}\]
done
clear
D)
\[\frac{\pi }{5}\]
done
clear
View Answer play_arrow
question_answer 177) If 'x' takes negative permissible value, then \[{{\sin }^{-1}}x\] is equal to
A)
\[-{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]
done
clear
B)
\[{{\cos }^{-1}}\sqrt{{{x}^{2}}-1}\]
done
clear
C)
\[\pi -{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]
done
clear
D)
\[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]
done
clear
View Answer play_arrow
question_answer 178) If \[1+\sin +{{\sin }^{2}}x+...\] upto \[\infty =4+2\sqrt{3},\] \[0<x<\pi \]and \[x\ne \frac{\pi }{2},\] then x is equal to
A)
\[\frac{\pi }{3},\frac{5\pi }{6}\]
done
clear
B)
\[\frac{2\pi }{3},\frac{\pi }{6}\]
done
clear
C)
\[\frac{\pi }{3},\frac{2\pi }{3}\]
done
clear
D)
\[\frac{\pi }{6},\frac{\pi }{3}\]
done
clear
View Answer play_arrow
question_answer 179) The complex number \[\frac{1+2i}{1-i}\] lies in
A)
second quadrant
done
clear
B)
third quadrant
done
clear
C)
fourth quadrant
done
clear
D)
first quadrant
done
clear
View Answer play_arrow
question_answer 180) If P is the point in the Agrand diagram corresponding to the complex number \[\sqrt{3}+i\] and if OPQ is an isosceles right angled triangle, right angled at ?O?, then Q represents the complex number
A)
\[-1+i\sqrt{3}\] or \[1-i\sqrt{3}\]
done
clear
B)
\[1\pm i\sqrt{3}\]
done
clear
C)
\[\sqrt{3}-i\] or \[1-i\sqrt{3}\]
done
clear
D)
\[-1\pm i\sqrt{3}\]
done
clear
View Answer play_arrow