question_answer 1) The only mechanical quantity which has negative dimension of mass is
A)
angular momentum
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B)
torque
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C)
coefficient of thermal conductivity
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D)
gravitational constant
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question_answer 2) Two vectors are given by \[\vec{A}=3\hat{i}+\hat{j}+3\hat{k}\]and \[\vec{B}=3\hat{i}+5\hat{j}-2\hat{k}\]. Find the third vector \[\vec{C},\] if \[\vec{A}+3\vec{B}-\vec{C}=\vec{0}\].
A)
\[12\hat{i}+14\hat{j}+12\hat{k}\]
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B)
\[13\hat{i}+17\hat{j}+12\hat{k}\]
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C)
\[12\hat{i}+16\hat{j}-3\hat{k}\]
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D)
\[15\hat{i}+13\hat{j}+4\hat{k}\]
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question_answer 3) A particle moves from position \[3\hat{i}+2\hat{j}+6\hat{k}\] to \[14\hat{i}+13\hat{j}+9\hat{k}\] due to a uniform force of\[4\hat{i}+\hat{j}+3k\text{ }N\]. Find the work done, if the displacement is in metre.
A)
\[16\text{ }J\]
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B)
\[64\text{ }J\]
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C)
\[32\text{ }J\]
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D)
\[48\text{ }J\]
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question_answer 4) The coordinates of a moving particle at any time t are given by \[x=\alpha {{t}^{3}}\]and \[y=\beta {{t}^{3}}\]. The speed of the particle at time t is given by
A)
\[3t\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
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B)
\[3{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
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C)
\[{{t}^{2}}\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
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D)
\[\,\sqrt{{{\alpha }^{2}}+{{\beta }^{2}}}\]
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question_answer 5) A body is moving with uniform acceleration. covers \[200\text{ }m\]in the first \[2\text{ }s\]and \[220\text{ }m\]in the next\[4\text{ }s\] . Find the velocity in m/s after\[7\text{ }s\].
A)
\[10\]
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B)
\[15\]
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C)
\[20\]
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D)
\[30\]
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question_answer 6) From the top of a tower a body A is projected vertically up, another body B is horizontally thrown and a third body C is thrown vertically down with same velocity. Then
A)
B strikes the ground with more velocity
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B)
C strikes the ground with less velocity
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C)
A,B,C strike the ground with same velocity
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D)
A and C strike the ground with more velocity than B
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question_answer 7) A body is released from a great height falls freely towards the earth. Another body is released from the same height exactly a second latter. Then the separation between two bodies, 2 s after the release of the second body is, nearly
A)
\[15\,\,m\]
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B)
\[20\,\,m\]
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C)
\[25\,\,m\]
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D)
\[30\,\,m\]
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question_answer 8) A body of mass \[10\text{ }kg\]is acted upon by two forces each of magnitude \[10\,\,N\]making an angle of \[{{60}^{o}}\] with each other. Find the net acceleration of the body.
A)
\[2\sqrt{3}m/{{s}^{2}}\]
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B)
\[\sqrt{3}m/{{s}^{2}}\]
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C)
\[3\sqrt{3}m/{{s}^{2}}\]
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D)
\[4\sqrt{3}m/{{s}^{2}}\]
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question_answer 9) A body of mass \[{{m}_{1}}\] collides elastically with another body of mass \[{{m}_{2}}\] at rest. If the velocity of \[{{m}_{1}}\] after collision becomes \[2/3\] times its initial velocity, the ratio of their masses, is
A)
\[1:5\]
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B)
\[5:1\]
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C)
\[5:2\]
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D)
\[2:5\]
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question_answer 10) With increase of temperature, the frictional force acting between two surfaces
A)
increases
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B)
remains the same
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C)
decreases
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D)
becomes zero
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question_answer 11) The motion of the centre of mass is the result of
A)
internal forces
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B)
external forces
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C)
attractive forces
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D)
repulsive forces
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question_answer 12) A stationary bomb explodes into two parts of masses in the ratio of \[1:3\]. If the heavier mass moves with a velocity \[4\text{ }m/s,\] what is the velocity of lighter part?
A)
\[12\text{ }m{{s}^{-1}}\]opposite to heavier mass
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B)
\[12\text{ }m{{s}^{-1}}\] in the direction of heavier mass
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C)
\[\text{6 }m{{s}^{-1}}\] opposite to heavier mass
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D)
\[\text{6 }m{{s}^{-1}}\] in the direction of heavier mass
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question_answer 13) A body is tied to one end of the string and whirled in a vertical circle, the physical quantity which remains constant is
A)
momentum
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B)
speed
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C)
kinetic energy
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D)
total energy
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question_answer 14) A thin metal disc of radius of \[0.25\text{ }m\]and mass \[2\text{ }kg\]starts from rest and rolls down on an inclined plane. If its rotational kinetic energy is \[4\text{ }J\]at the foot of inclined plane, then the linear velocity at the same point, is in m/s
A)
\[2\]
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B)
\[2\sqrt{2}\]
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C)
\[2\sqrt{3}\]
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D)
\[3\sqrt{2}\]
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question_answer 15) A stone tied to one end of rope and rotated in a circular motion. If the string suddenly breaks, then the stone travels
A)
in perpendicular direction
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B)
in direction of centrifugal force
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C)
towards centripetal force
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D)
in tangential direction
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question_answer 16) The escape velocity of a body from the earth is \[{{v}_{e}}\]. If the radius of earth contracts to \[\frac{1}{4}th\] of its value, keeping the mass of the earth constant, the escape velocity will be
A)
doubled
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B)
halved
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C)
tripled
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D)
unaltered
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question_answer 17) The-radius of the earth is R. The height of a point vertically above the earth's surface at which acceleration due to gravity becomes \[1%\] of its value at the surface is
A)
\[8\,\,R\]
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B)
\[9\,\,R\]
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C)
\[10\,\,R\]
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D)
\[20\,\,R\]
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question_answer 18) A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is
A)
smallest at the top and gradually increases down the rod
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B)
largest at the top and gradually decreases down the rod
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C)
uniform everywhere
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D)
maximum in the middle
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question_answer 19) A particular force (F) applied on a wire increases its length by \[2\times {{10}^{-3}}\text{ }m\]. To increase the wire's length by \[4\times {{10}^{-3}}\text{ }m\]the applied force will be
A)
\[4\,\,F\]
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B)
\[3\,\,F\]
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C)
\[2\,\,F\]
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D)
\[F\]
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question_answer 20) The meniscus of mercury in a capillary glass tube, is
A)
concave
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B)
plane
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C)
cylindrical
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D)
convex
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question_answer 21) Two liquid drops have diameters of \[1\text{ }cm\]and \[1.5\text{ }cm\] The ratio of excess of pressures inside them is
A)
\[1:1\]
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B)
\[5:3\]
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C)
\[2:3\]
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D)
\[3:2\]
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question_answer 22) Temperature remaining constant, the pressure of gas is decreased by \[20%\]. The percentage change in volume
A)
increases by \[20%\]
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B)
decreases by \[20%\]
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C)
increases by \[25%\]
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D)
decreases by \[25%\]
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question_answer 23) Work done in converting one gram of ice at \[-{{10}^{o}}C\]into steam at \[{{100}^{o}}C\]is
A)
\[3045\text{ }J\]
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B)
\[6056\text{ }J\]
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C)
\[721\text{ }J\]
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D)
\[616\text{ }J\]
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question_answer 24) The temperature of the system decreases in the process of
A)
free expansion
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B)
adiabatic expansion
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C)
isothermal expansion
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D)
isothermal compression
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question_answer 25) The temperature at which a black body ceases to radiate energy, is
A)
\[0\,\,K\]
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B)
\[273\text{ }K\]
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C)
\[30\text{ }K\]
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D)
\[100\text{ }K\]
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question_answer 26) A particle executes SHM with a period of \[8\text{ }s\]and amplitude \[4\text{ }cm\]. Its maximum speed in cm/s, is
A)
\[\pi \]
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B)
\[\frac{\pi }{2}\]
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C)
\[\frac{\pi }{3}\]
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D)
\[\frac{\pi }{4}\]
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question_answer 27) The displacement of a particle of mass \[3\text{ }g\] executing simple harmonic motion is given by \[Y=3\text{ }sin\text{ (}0.2\text{ t)}\]in SI units. The KE of the particle at a point which is at a distance equal to \[1/3\] of its amplitude from its mean position is
A)
\[12\times {{10}^{-3}}\,J\]
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B)
\[25\times {{10}^{-3}}\,J\]
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C)
\[0.48\times {{10}^{-3}}\,J\]
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D)
\[0.24\times {{10}^{-3}}\,J\]
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question_answer 28) A uniform spring of force constant k is cut into two pieces whose lengths are in the ratio of \[1:2\]. What is the force constant of second piece in terms of k?
A)
\[\frac{k}{2}\]
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B)
\[\frac{2k}{2}\]
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C)
\[\frac{3k}{2}\]
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D)
\[\frac{4k}{2}\]
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question_answer 29) A girl swings on cradle in a sitting position. If she stands what happens to the time period of girl and cradle?
A)
Time period decreases
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B)
Time period increases
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C)
Remains constant
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D)
First increases and then remains constant
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question_answer 30) The intensity ratio of two waves is \[1:9\]. The ratio of their amplitudes, is
A)
\[3:1\]
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B)
\[1:3\]
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C)
\[1:9\]
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D)
\[9:1\]
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question_answer 31) The speed of sound waves in a gas
A)
does not depend upon density of the gas
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B)
'does not depend upon changes in pressure
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C)
does not depend upon temperature
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D)
depends upon density of the gas
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question_answer 32) A segment of wire vibrates with fundamental frequency of \[450\text{ }Hz\]under a tension of\[9\text{ }kg-wt\]. Then tension at which the fundamental frequency of the same wire becomes \[900\text{ }Hz\]is
A)
\[36\text{ }kg-wt\]
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B)
\[27\text{ }kg-wt\]
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C)
\[18\text{ }kg-wt\]
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D)
\[72\text{ }kg-wt\]
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question_answer 33) Sound waves in air cannot be polarized because
A)
their speed is small
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B)
they require medium
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C)
these are longitudinal
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D)
their speed is temperature dependent
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question_answer 34) Electric potential at the centre of a charged hollow metal sphere is
A)
zero
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B)
twice as that on the surface
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C)
half of that on the surface
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D)
same as that on the surface
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question_answer 35) Three charges \[1\mu C,\] \[1\mu C\] and \[2\mu C\] are kept at vertices of A, B and C of an equilateral triangle ABC of \[10\text{ }cm\]side respectively. The resultant force on the charge at C is
A)
\[0.9\text{ }N\]
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B)
\[1.8\text{ }N\]
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C)
\[2.72\text{ }N\]
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D)
\[3.12\text{ }N\]
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question_answer 36) A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is
A)
\[2\,C\]
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B)
\[C/2\]
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C)
\[(1+K)C/2\]
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D)
\[2C(1+K)\]
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question_answer 37) The value equal to the velocity of light in vacuum is
A)
\[\frac{\sqrt{{{\mu }_{0}}}}{{{\varepsilon }_{0}}}\]
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B)
\[\frac{1}{\sqrt{{{\mu }_{0}}{{\varepsilon }_{0}}}}\]
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C)
\[\sqrt{{{\mu }_{0}}\,{{\varepsilon }_{0}}}\]
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D)
\[\sqrt{\frac{{{\mu }_{0}}}{\,{{\varepsilon }_{0}}}}\]
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question_answer 38) Two unlike charges of the same magnitude Q are placed at a distance d. The intensity of the electric field at the middle point in the line joining the two charges
A)
zero
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B)
\[\frac{8\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]
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C)
\[\frac{6\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]
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D)
\[\frac{4\,Q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}\]
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question_answer 39) In a meter bridge experiment, the ratio of the left gap resistance to right gap resistance is \[2:3,\] the balance point from left is
A)
\[60\text{ }cm\]
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B)
\[50\text{ }cm\]
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C)
\[40\text{ }cm\]
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D)
\[20\text{ }cm\]
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question_answer 40) The physical quantity in electrostatics analogous to temperature in heat is
A)
heat energy
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B)
capacity
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C)
resistance
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D)
potential
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question_answer 41) If the electric current through an electric bulb is \[3.2\text{ }A,\] the number of electrons flow through it in one second is
A)
\[2\times {{10}^{9}}\]
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B)
\[2\times {{10}^{19}}\]
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C)
\[3.2\times {{10}^{19}}\]
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D)
\[1.6\times {{10}^{18}}\]
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question_answer 42) A wire P has a resistance of \[20\,\Omega \]. Another wire Q of same material but length twice that of P has resistance of \[8\,\,\,\Omega \]. If r is the radius of cross-section of P, the radius of cross-section of Q is
A)
\[r\]
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B)
\[\frac{r}{\sqrt{2}}\]
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C)
\[\sqrt{5}\,r\]
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D)
\[2\,r\]
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question_answer 43) When a metal conductor connected to the left gap of a meter bridge is heated, the balancing point
A)
shifts towards right
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B)
shifts towards left
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C)
remains unchanged
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D)
remains at zero
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question_answer 44) The thermocouple among the following that can produce maximum thermo emf for the same temperature difference between the junction is
A)
\[Fe-Cu\]
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B)
\[Ag-Au\]
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C)
\[Sb-Bi\]
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D)
\[Cu-Pb\]
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question_answer 45) A bar magnet of magnetic moment At and moment of inertia I is freely suspended such that the magnetic axial line is in the direction of magnetic meridian. If the magnet is displaced by a very small angle \[\theta ,\] angular acceleration is (magnetic induction of earth's horizontal field \[={{B}_{H}}\])
A)
\[\frac{M{{B}_{H}}\theta }{I}\]
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B)
\[\frac{I{{B}_{H}}\theta }{M}\]
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C)
\[\frac{M\theta }{I{{B}_{H}}}\]
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D)
\[\frac{I\theta }{M{{B}_{H}}}\]
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question_answer 46) A long magnet is cut into two equal parts, such that the length of each half is same as that of original magnet. If the period of original magnet is T, the period of new magnet is
A)
\[T\]
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B)
\[\frac{T}{2}\]
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C)
\[\frac{T}{4}\]
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D)
\[2T\]
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question_answer 47) The time period of a freely suspended bar magnet in a field is 2 s. It is cut into two equal parts along its axis, (hen the time period is
A)
\[4\,\,s\]
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B)
\[0.5\,\,s\]
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C)
\[2\,\,s\]
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D)
\[0.25\,\,s\]
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question_answer 48) The angle between magnetic meridian and geographical meridian is known as
A)
magnetic dip
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B)
magnetic latitude
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C)
magnetic declination
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D)
magnetic longitude
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question_answer 49) The net magnetic flux through any closed surface, kept in a magnetic field is
A)
zero
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B)
\[\frac{{{\mu }_{0}}}{4\pi }\]
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C)
\[4\,\,\pi {{\mu }_{0}}\]
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D)
\[\frac{4\,\,{{\mu }_{0}}}{\pi }\]
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question_answer 50) A paramagnetic liquid is taken in a U-tube and arranged so that one of its limbs is kept between pole pieces of the magnet. The liquid level in the limb
A)
goes down
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B)
rises up
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C)
remains same
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D)
first goes down and then rises
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question_answer 51) Two wires A and B are of lengths \[40\text{ }cm\]and\[30\text{ }cm\]. A is bent into a circle of radius r and B into an arc of radius r. A current \[{{i}_{1}}\] is passed through A and 13 through B. To have the same magnetic inductions at the centre, the ratio of \[{{i}_{1}}:{{i}_{2}}\] is
A)
\[3:4\]
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B)
\[3:5\]
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C)
\[2:3\]
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D)
\[4:3\]
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question_answer 52) An electron and proton having same kinetic energy enter into magnetic field perpendicular to it. Then
A)
the path of electron is less curved
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B)
the path of proton is less curved
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C)
both have equal curved paths
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D)
both have straight line paths
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question_answer 53) Two free parallel wires carrying currents in the opposite directions
A)
attract each other
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B)
repel each other
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C)
do not effect each other
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D)
get rotated to be perpendicular to each other
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question_answer 54) A circular coil of diameter \[21\text{ }cm\]is placed in a magnetic field of induction\[{{10}^{-4}}\text{ }T\]. The magnitude of flux linked with coil when the plane of coil makes an angle \[{{30}^{o}}\] with the field is
A)
\[1.44\times {{10}^{-6}}\,Wb\]
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B)
\[1.732\times {{10}^{-6}}\,\,Wb\]
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C)
\[3.1\times {{10}^{-6}}\,\,Wb\]
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D)
\[4.2\times {{10}^{-6}}\,\,Wb\]
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question_answer 55) The cladding material of optical fibres has refractive index
A)
greater than that of core
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B)
infinity
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C)
equal to that of core
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D)
less than that of core
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question_answer 56) Red colour is used for danger signals because
A)
it causes fear
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B)
it undergoes least scattering
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C)
it undergoes maximum scattering
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D)
it is in accordance with international convention
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question_answer 57) The least angle of deviation for a glass prism is equal to its refracting angle. The refractive index of glass is \[1.5\]. Then the angle of prism is
A)
\[2\,{{\cos }^{-1}}\left( \frac{3}{4} \right)\]
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B)
\[si{{n}^{-1}}\left( \frac{3}{4} \right)\]
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C)
\[2\,\,si{{n}^{-1}}\left( \frac{3}{2} \right)\]
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D)
\[{{\cos }^{-1}}\left( \frac{3}{2} \right)\]
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question_answer 58) In a spectrometer experiment the prisms A, B, C with same angle but different refractive index \[{{\mu }_{A}}=1.33,\,\,{{\mu }_{B}}=1.5,\,\,{{\mu }_{C}}=1.44\]are used. The corresponding angles of minimum deviation \[{{D}_{A}},\,{{D}_{B}},\,{{D}_{C}}\] measured will be such that
A)
\[{{D}_{A}}>\,{{D}_{B}}>\,{{D}_{C}}\]
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B)
\[{{D}_{A}}<\,{{D}_{B}}<\,{{D}_{C}}\]
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C)
\[{{D}_{A}}<\,{{D}_{C}}<\,{{D}_{B}}\]
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D)
\[{{D}_{A}}>\,{{D}_{C}}>\,{{D}_{B}}\]
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question_answer 59) Young's double slit experiment arrangement is shifted from air to water medium, the fringe width
A)
increases
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B)
decreases
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C)
becomes infinite
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D)
remains the same
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question_answer 60) On introducing a thin film in the path of one of the two interfering beams, the central fringe will shift by one fringe width. If \[\mu =1.5,\] the thickness of the film is (wavelength of monochromatic light is \[\lambda \])
A)
\[4\,\lambda \]
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B)
\[3\,\lambda \]
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C)
\[2\,\lambda \]
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D)
\[\lambda \]
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question_answer 61) The critical angle of the medium with respect to vacuum is \[{{30}^{o}}\]. If the velocity of light in vacuum is \[3\times {{10}^{8}}\text{ }m{{s}^{-1}},\] the velocity of light in medium is
A)
\[2\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
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B)
\[1.5\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
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C)
\[3\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
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D)
\[\sqrt{2}\times {{10}^{8}}\text{ }m{{s}^{-1}}\]
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question_answer 62) The distance between the first dark and bright band formed in Young's double slit experiment with band width B is
A)
\[\frac{B}{4}\]
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B)
\[B\]
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C)
\[\frac{B}{2}\]
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D)
\[\frac{3B}{2}\]
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question_answer 63) The important conclusion given by Millikan's experiment about the charge is
A)
charge is never quantized
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B)
charge has no definite value
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C)
charge is quantized
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D)
charge on oil drop always increases
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question_answer 64) An electron is accelerated through a potential difference of V volts. The speed of electrons will be
A)
\[\sqrt{\frac{eV}{m}}\]
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B)
\[\sqrt{\frac{2eV}{m}}\]
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C)
\[\sqrt{\frac{eV}{2m}}\]
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D)
\[\sqrt{\frac{m}{2eV}}\]
done
clear
View Answer play_arrow
question_answer 65) How many photons are emitted by a laser source of \[5\times {{10}^{-3}}W\]operating at \[632.2\text{ }nm\]in \[2s\]?
A)
\[3.2\times {{10}^{16}}\]
done
clear
B)
\[1.6\times {{10}^{16}}\]
done
clear
C)
\[4\times {{10}^{16}}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 66) If a is radius of first Bohr orbit in hydrogen atom, the radius of the third orbit is
A)
\[3a\]
done
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B)
\[9a\]
done
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C)
\[27a\]
done
clear
D)
\[81a\]
done
clear
View Answer play_arrow
question_answer 67) Nuclear fission can be explained based on
A)
Millikan's oil drop method
done
clear
B)
Liquid drop model
done
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C)
Shell model
done
clear
D)
Buffs model
done
clear
View Answer play_arrow
question_answer 68) The radius of a nucleus with atomic mass number 7 is 2 Fermi. Find the radius of nucleus with atomic number 189.
A)
3 Fermi
done
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B)
4 Fermi
done
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C)
5 Fermi
done
clear
D)
6 Fermi
done
clear
View Answer play_arrow
question_answer 69) As mass number increases, surface area
A)
decreases
done
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B)
increases
done
clear
C)
remains the same
done
clear
D)
remains the same and increases
done
clear
View Answer play_arrow
question_answer 70) All nucleons in an atom are held by
A)
nuclear forces
done
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B)
van der Waals' forces
done
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C)
tensor forces
done
clear
D)
Coulomb forces
done
clear
View Answer play_arrow
question_answer 71) The temperature of germanium is decreased from room temperature to \[100\text{ }K,\]the resistance of germanium
A)
decreases
done
clear
B)
increases
done
clear
C)
unaffected
done
clear
D)
depends on external conditions
done
clear
View Answer play_arrow
question_answer 72) The potential in depletion layer is due to
A)
electrons
done
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B)
holes
done
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C)
ions
done
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D)
forbidden band
done
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View Answer play_arrow
question_answer 73) In breakdown region, a zener diode behaves as a
A)
constant current source
done
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B)
constant voltage source
done
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C)
constant resistance source
done
clear
D)
constant power source
done
clear
View Answer play_arrow
question_answer 74) When boron is added as an impurity to silicon, the resulting material is
A)
n-type semiconductor
done
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B)
n-type conductor
done
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C)
p -type conductor
done
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D)
p -type semiconductor
done
clear
View Answer play_arrow
question_answer 75)
The diode used in the circuit shown in the figure has a constant voltage drop of \[0.5\text{ }V\]at all currents and a maximum power rating of 100 milli-watt. What should be the value of the resistance R, connected in series with the diode, for obtaining maximum current?
A)
\[1.5\,\Omega \]
done
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B)
\[5\,\Omega \]
done
clear
C)
\[6.67\,\,\Omega \]
done
clear
D)
\[200\]
done
clear
View Answer play_arrow
question_answer 76) The presence of electric charge on colloidal particles is indicated by the property, called
A)
dialysis
done
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B)
solubility
done
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C)
electrophoresis
done
clear
D)
osmosis
done
clear
View Answer play_arrow
question_answer 77) The protective action of different lyophilic colloids is expressed in terms of
A)
oxidation number
done
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B)
atomic number
done
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C)
Avogadro number
done
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D)
gold number
done
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View Answer play_arrow
question_answer 78) The group of elements in which the differentiating electrons enters in the antipenultimate shell of atoms are called
A)
\[f-\]block elements
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B)
\[p-\]block elements
done
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C)
\[s-\]block elements
done
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D)
\[d-\]block elements
done
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View Answer play_arrow
question_answer 79) Lanthanides and actinides are also called as
A)
short periods
done
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B)
inner-transition elements
done
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C)
long periods
done
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D)
main transition elements
done
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View Answer play_arrow
question_answer 80) The geometrical shape of \[s{{p}^{3}}d\]hybridisation is
A)
linear
done
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B)
trigonal bipyramid
done
clear
C)
square planar
done
clear
D)
tetrahedral
done
clear
View Answer play_arrow
question_answer 81) Intermolecular hydrogen bonding exists in
A)
\[~o-\] nitrophenol
done
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B)
\[~o-\]chlorophenol
done
clear
C)
water
done
clear
D)
ammonium chloride
done
clear
View Answer play_arrow
question_answer 82) Which one of the following examples exhibit transient existence?
A)
H
done
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B)
\[H_{2}^{+}\]
done
clear
C)
\[{{H}^{+}}\]
done
clear
D)
He
done
clear
View Answer play_arrow
question_answer 83) The number of covalent bonds in fluorine molecule is
A)
2
done
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B)
3
done
clear
C)
1
done
clear
D)
5
done
clear
View Answer play_arrow
question_answer 84) Carbon shows the following oxidation state a its hydrides
A)
+ 1
done
clear
B)
+ 4
done
clear
C)
+ 2
done
clear
D)
+ 3
done
clear
View Answer play_arrow
question_answer 85) The following is not an example of oxyacids of sulphur
A)
\[{{H}_{2}}S{{O}_{3}}\]
done
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B)
\[{{H}_{2}}{{S}_{2}}{{O}_{3}}\]
done
clear
C)
\[{{H}_{2}}S{{O}_{4}}\]
done
clear
D)
\[S{{O}_{3}}\]
done
clear
View Answer play_arrow
question_answer 86) Calcium sulphate is sparingly soluble in
A)
water
done
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B)
alcohol
done
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C)
acetic acid
done
clear
D)
benzene
done
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View Answer play_arrow
question_answer 87) The bleaching action of chlorine is due to the liberation of the following
A)
\[HOCl\]
done
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B)
\[HCl\]
done
clear
C)
\[[O]\]
done
clear
D)
\[{{O}_{2}}\]
done
clear
View Answer play_arrow
question_answer 88) The colour of transition metal ions is due to presence of unpaired electron transitions in available empty electron in
A)
\[d-\]orbitals
done
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B)
\[p-\]orbitals
done
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C)
\[s-\]orbitals
done
clear
D)
s and p-orbitals
done
clear
View Answer play_arrow
question_answer 89) The oxidation state of Cr in chromium trioxide is
A)
+ 3
done
clear
B)
+ 4
done
clear
C)
+ 5
done
clear
D)
+ 6
done
clear
View Answer play_arrow
question_answer 90) Monel metal is an alloy of
A)
\[Cu,Ni,Fe,Mn\]
done
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B)
\[Cu,Sn,Zn\]
done
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C)
\[Cu,Sn,P\]
done
clear
D)
\[Cu,Zn\]
done
clear
View Answer play_arrow
question_answer 91) The catalyst used in the manufacture of \[{{H}_{2}}S{{O}_{4}}\]by contact process is
A)
\[{{V}_{2}}{{O}_{3}}\]
done
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B)
\[{{V}_{2}}{{O}_{5}}\]
done
clear
C)
\[FeO\]
done
clear
D)
\[Cu\]
done
clear
View Answer play_arrow
question_answer 92) The tetrahedral complexes have coordination number
A)
3
done
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B)
6
done
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C)
4
done
clear
D)
8
done
clear
View Answer play_arrow
question_answer 93) Potassium ferrocyanide is an example of
A)
tetrahedral
done
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B)
octahedral
done
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C)
square planar
done
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D)
linear
done
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View Answer play_arrow
question_answer 94) Which one amongst the following, exhibit geometrical isomerism?
A)
\[\text{ }\!\![\!\!\text{ C}{{\text{o}}^{\text{III}}}{{\text{(N}{{\text{H}}_{\text{3}}}\text{)}}_{\text{5}}}\text{Br }\!\!]\!\!\text{ S}{{\text{O}}_{\text{4}}}\]
done
clear
B)
\[C{{o}^{\text{III}}}{{[EDTA]}^{-1}}\]
done
clear
C)
\[{{\text{ }\!\![\!\!\text{ C}{{\text{r}}^{\text{III}}}{{(SCN)}_{6}}]}^{3-}}\]
done
clear
D)
\[[P{{t}^{\text{III}}}{{(N{{H}_{3}})}_{2}}C{{l}_{2}}]\]
done
clear
View Answer play_arrow
question_answer 95) Benzoylacetonato beryllium exhibit isomerism of the type
A)
structural
done
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B)
geometrical
done
clear
C)
optical
done
clear
D)
conformational
done
clear
View Answer play_arrow
question_answer 96) The composition of malachite is
A)
\[CuFe{{S}_{2}}\]
done
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B)
\[CuC{{O}_{3}}\]
done
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C)
\[CuCO3.Cu{{(OH)}_{2}}\]
done
clear
D)
\[Cu{{(OH)}_{2}}\]
done
clear
View Answer play_arrow
question_answer 97) Which one of the following metals, is extracted on smelting of its ore in blast furnace?
A)
Iron
done
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B)
Sodium
done
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C)
Potassium
done
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D)
Magnesium
done
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View Answer play_arrow
question_answer 98) Prussian blue is obtained by mixing together aqueous solution of \[\text{F}{{\text{e}}^{\text{3+}}}\]salt with
A)
ferricyanide
done
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B)
ferrocyanide
done
clear
C)
hydrogen cyanide
done
clear
D)
sodium cyanide
done
clear
View Answer play_arrow
question_answer 99) The reaction intermediate produced, by homolytic cleavage of a bond is called
A)
carbene
done
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B)
carbocation
done
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C)
carbanion
done
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D)
free radical
done
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View Answer play_arrow
question_answer 100) The formation of cyanohydrin from a ketone is an example of
A)
electrophilic addition
done
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B)
nucleophilic Substitution
done
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C)
nucleophilic addition
done
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D)
electrophilic substitution
done
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question_answer 101) According to Huckel?s rule an aromatic compound must possess
A)
\[(4n+1)\pi \] electrons
done
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B)
\[(4n+2)\pi \] electrons
done
clear
C)
\[4n\,\pi \] electrons
done
clear
D)
\[(4n+3)\pi \] electrons
done
clear
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question_answer 102) Identify the substitute group, that acts as ortho-para director, during electrophilic substitution in aromatic compounds.
A)
\[-N{{H}_{2}}\]
done
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B)
\[-N{{O}_{2}}\]
done
clear
C)
\[-S{{O}_{3}}H\]
done
clear
D)
\[{{N}_{2}}\]
done
clear
View Answer play_arrow
question_answer 103) In a group of isomeric alkyl halides, the order of boiling points is
A)
primary < secondary < tertiary
done
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B)
primary > secondary < tertiary
done
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C)
primary < secondary > tertiary
done
clear
D)
primary > secondary > tertiary
done
clear
View Answer play_arrow
question_answer 104) On reacting with neutral ferric chloride, phenol gives
A)
red colour
done
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B)
blue colour
done
clear
C)
violet colour
done
clear
D)
green colour
done
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View Answer play_arrow
question_answer 105) The hybridisation of the ipso-carbon in chlorobenzene is
A)
\[sp\]hybridised
done
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B)
\[~s{{p}^{2}}\] hybridised
done
clear
C)
\[~s{{p}^{2}}\] hybridised
done
clear
D)
\[~s{{p}^{3}}\] hybridised
done
clear
View Answer play_arrow
question_answer 106) Which one of the following alcohol is used as an antifreeze reagent for making explosives?
A)
Glycerol
done
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B)
Glycol
done
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C)
Ethanol
done
clear
D)
Phenol
done
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View Answer play_arrow
question_answer 107) \[n-\]pentane, \[iso-\]pentane, and neo-pentane are examples for isomers of the type
A)
geometrical
done
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B)
optical
done
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C)
chain
done
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D)
positional
done
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View Answer play_arrow
question_answer 108) One of the following compounds exhibit geometrical isomerism
A)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}\]
done
clear
B)
\[C{{H}_{3}}-HC(C{{H}_{3}})-H(C)C{{H}_{3}}-C{{H}_{3}}\]
done
clear
C)
\[C{{H}_{3}}-HC(C{{H}_{3}})-C{{H}_{3}}\]
done
clear
D)
\[C{{H}_{3}}CH=CH-C{{H}_{3}}\]
done
clear
View Answer play_arrow
question_answer 109) Different structures generated due to rotation about, C-C axis, of an organic molecule, are examples of
A)
geometrical isomerism
done
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B)
conformational isomerism
done
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C)
optical isomerism
done
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D)
structural isomerism
done
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View Answer play_arrow
question_answer 110) The number of isomeric halopropanes produced, when propane gets halogenated, is
A)
1
done
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B)
2
done
clear
C)
4
done
clear
D)
3
done
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View Answer play_arrow
question_answer 111) The acid strength obeys the order. Arrange the following carboxylic acids in the decreasing order of their reactivities
A)
\[C{{H}_{3}}COOH\]
done
clear
B)
\[ClC{{H}_{2}}COOH\]
done
clear
C)
\[C{{l}_{2}}CHCOOH\]
done
clear
D)
\[C{{l}_{3}}CCOOH\]
done
clear
View Answer play_arrow
question_answer 112) Mohocarboxylic acids react with alcohols in the presence of an acid catalyst to form
A)
acid chlorides
done
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B)
acid amides
done
clear
C)
esters
done
clear
D)
ethers
done
clear
View Answer play_arrow
question_answer 113) On reaction with hydroxylamine, aldehydes produce
A)
ketoxime
done
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B)
hydrazone
done
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C)
semicarbazone
done
clear
D)
aldoxime
done
clear
View Answer play_arrow
question_answer 114) Amides are formed by the reaction of acid chloride with
A)
\[N{{H}_{2}}N{{H}_{2}}\]
done
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B)
\[N{{H}_{3}}\]
done
clear
C)
\[N{{H}_{2}}OH\]
done
clear
D)
\[{{C}_{6}}{{H}_{5}}NHN{{H}_{2}}\]
done
clear
View Answer play_arrow
question_answer 115) Which one of the following, is more acidic?
A)
done
clear
B)
done
clear
C)
done
clear
D)
done
clear
View Answer play_arrow
question_answer 116) Aliphatic nitriles are prepared by the treatment of alkyl halides with
A)
sodium cyanide
done
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B)
sodium isocyanide
done
clear
C)
sodium isocyanate
done
clear
D)
cyanamide
done
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View Answer play_arrow
question_answer 117) Among the following compounds, the most basic is
A)
aniline
done
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B)
acetanilide
done
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C)
\[p-\]nitroaniline
done
clear
D)
benzylamine
done
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View Answer play_arrow
question_answer 118) Reduction of alkyl nitriles, produces
A)
secondary amine
done
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B)
primary amine
done
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C)
tertiary amine
done
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D)
amide
done
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View Answer play_arrow
question_answer 119) Polypeptides having, molecular weights, above 10,000 are known as
A)
amino acids
done
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B)
harmones
done
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C)
proteins
done
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D)
terminal amino acids
done
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View Answer play_arrow
question_answer 120) Which one of the following is an example of a non-reducing sugar?
A)
Sucrose
done
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B)
Lactose
done
clear
C)
Maltose
done
clear
D)
Cellobiose
done
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View Answer play_arrow
question_answer 121) The value of Rydberg constant is
A)
\[10,9678\,\text{c}{{\text{m}}^{-1}}\]
done
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B)
\[10,9876\,\text{c}{{\text{m}}^{-1}}\]
done
clear
C)
\[10,8769\,\text{c}{{\text{m}}^{-1}}\]
done
clear
D)
\[10,8976\,\text{c}{{\text{m}}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 122) The wavelength of a spectral line in Lyman series, when electron jumps back from 2nd orbit, is
A)
\[\text{1162 }\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
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B)
\[1216\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
C)
\[1362\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
D)
\[1176\overset{\text{o}}{\mathop{\text{A}}}\,\]
done
clear
View Answer play_arrow
question_answer 123) The number of electrons accommodated in an orbit with principal quantum number 2, is
A)
2
done
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B)
6
done
clear
C)
10
done
clear
D)
8
done
clear
View Answer play_arrow
question_answer 124) Uranium with a mass number 237 and atomic number 92, changes to a nucleus with atomic number 90 and mass number 233 on emission of
A)
\[\beta -\]particle
done
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B)
\[\gamma -\]particle
done
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C)
\[\alpha -\]particle
done
clear
D)
positron
done
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View Answer play_arrow
question_answer 125) The only, most stable nucleus formed by bombarding, either \[_{\text{13}}\text{A}{{\text{l}}^{\text{27}}}\]by neutrons or \[_{\text{11}}\text{N}{{\text{a}}^{\text{23}}}\]by deuterons, is
A)
\[_{15}{{P}^{30}}\]
done
clear
B)
\[_{14}S{{i}^{30}}\]
done
clear
C)
\[_{12}M{{g}^{24}}\]
done
clear
D)
\[_{56}B{{a}^{137}}\]
done
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View Answer play_arrow
question_answer 126) The stable electronic configuration of chromium is
A)
\[3{{d}^{6}},4{{s}^{1}}\]
done
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B)
\[3{{d}^{5}},4{{s}^{2}}\]
done
clear
C)
\[3{{d}^{5}},4{{s}^{1}}\]
done
clear
D)
\[3{{d}^{6}},4{{s}^{0}}\]
done
clear
View Answer play_arrow
question_answer 127) The half-life of \[\text{R}{{\text{a}}^{\text{226}}}\]is \[1620\text{ }yr,\] the decay constant (k) is
A)
0.000452
done
clear
B)
0.0004278
done
clear
C)
0.04278
done
clear
D)
0.004278
done
clear
View Answer play_arrow
question_answer 128) According to Lowry and Bronsted, the strength of an acid depends upon
A)
the tendency to gain electrons
done
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B)
the tendency to loss protons
done
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C)
the tendency to accept protons
done
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D)
the tendency to loss electrons
done
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View Answer play_arrow
question_answer 129) By applying law of mass action, the equilibrium constant,\[K\] for the reaction \[HA+{{H}_{2}}O\rightleftharpoons {{H}_{3}}{{O}^{+}}+\bar{A},\]is given as
A)
\[K=\frac{[HA][{{H}_{2}}O]}{[{{H}_{3}}{{O}^{+}}][\bar{A}]}\]
done
clear
B)
\[K=\frac{[{{H}_{3}}{{O}^{+}}][\bar{A}]}{[HA][{{H}_{2}}O]}\]
done
clear
C)
\[K=\frac{[{{H}_{3}}{{O}^{+}}][{{H}_{2}}O]}{[\bar{A}][HA]}\]
done
clear
D)
\[K=\frac{[HA][\bar{A}]}{[\bar{A}][HA]}\]
done
clear
View Answer play_arrow
question_answer 130) The ionisation of strong electrolytes in acetic. acid, compared to in water, is
A)
weak, low
done
clear
B)
strong, more
done
clear
C)
medium, the same
done
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D)
no ionisation, 100%
done
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View Answer play_arrow
question_answer 131) Calculate the pH of a solution in which hydrogen ion concentration is 0.005 g-equi/L?
A)
2.3
done
clear
B)
2.8
done
clear
C)
2.9
done
clear
D)
2.6
done
clear
View Answer play_arrow
question_answer 132) Inversion of cane-sugar in dilute acid is a
A)
bimolecular reaction
done
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B)
Pseudo-unimolecular reaction
done
clear
C)
unimolecular reaction
done
clear
D)
trimolecular reaction
done
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View Answer play_arrow
question_answer 133) The units of the rate constant of a second order reaction are
A)
\[mo{{l}^{-1}}L{{\,}^{-1}}{{s}^{-1}}\]
done
clear
B)
\[mo{{l}^{-1}}L\,{{s}^{-1}}\]
done
clear
C)
\[mo{{l}^{-1}}L\,s\]
done
clear
D)
\[mol\,{{L}^{-1}}{{s}^{-1}}\]
done
clear
View Answer play_arrow
question_answer 134) For the first order reaction half-life is 14 s, the time required for the initial concentration to reduce to 1/8 of its value is
A)
\[{{(14)}^{3}}s\]
done
clear
B)
28 s
done
clear
C)
42 s
done
clear
D)
\[{{(14)}^{2}}s\]
done
clear
View Answer play_arrow
question_answer 135) One part of solute in one million parts of solvent is expressed as
A)
ppm
done
clear
B)
mg/100 cc
done
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C)
g/L
done
clear
D)
g/100cc
done
clear
View Answer play_arrow
question_answer 136) The molarity of the solution obtained by dissolving 2.5 g of NaCI in 100 mL of water is
A)
0.00428 moles
done
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B)
428 moles
done
clear
C)
0.428 moles
done
clear
D)
0.0428 moles
done
clear
View Answer play_arrow
question_answer 137) The osmotic pressure is expressed in the units of
A)
MeV
done
clear
B)
cat
done
clear
C)
cm/s
done
clear
D)
atm
done
clear
View Answer play_arrow
question_answer 138) Fractional distillation is a process by which the separation of different fractions from mixture of solution is carried by making use of the following property of the fractions.
A)
freezing point
done
clear
B)
boiling point.
done
clear
C)
melting point
done
clear
D)
solubility
done
clear
View Answer play_arrow
question_answer 139) The quantity of heat measured for a reaction in a bomb calorimeter is equal to
A)
\[\Delta G\]
done
clear
B)
\[\Delta H\]
done
clear
C)
\[p\Delta V\]
done
clear
D)
\[\Delta E\]
done
clear
View Answer play_arrow
question_answer 140) All naturally occurring process, proceed in a direction, which leads to
A)
increase of enthalpy
done
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B)
increase of free energy
done
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C)
decrease of free energy
done
clear
D)
decrease of entropy
done
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View Answer play_arrow
question_answer 141) Heat of combustion of carbon monoxide at constant volume and at \[17{{\,}^{o}}C\]is \[-67,710\,\text{cal}\text{.}\]The heat of combustion at constant pressure is
A)
\[~-68,000\text{ cal}\]
done
clear
B)
\[~-67,800\text{ cal}\]
done
clear
C)
\[~-67,050\text{ cal}\]
done
clear
D)
\[~+\,68,500\text{ cal}\]
done
clear
View Answer play_arrow
question_answer 142) The free energy change \[\Delta G=0\] when
A)
the reactants are completely consumed
done
clear
B)
a catalyst is added
done
clear
C)
the system is at equilibrium
done
clear
D)
the reactants are initially mixed
done
clear
View Answer play_arrow
question_answer 143) The units of equivalent conductance, are
A)
ohm \[\text{c}{{\text{m}}^{\text{2}}}\text{equivalen}{{\text{t}}^{-1}}\]
done
clear
B)
ohm \[\text{c}{{\text{m}}^{\text{2}}}\,\text{equivalent}\]
done
clear
C)
\[\text{oh}{{\text{m}}^{-1}}\,c{{m}^{2}}\,\text{equivalen}{{\text{t}}^{-1}}\]
done
clear
D)
\[\text{mho c}{{\text{m}}^{\text{2}}}\text{ equivalent}\]
done
clear
View Answer play_arrow
question_answer 144) The specific conductance \[(\kappa )\] of an electrolyte of 0.1 N concentration is related to equivalent \[(\Lambda )\]by the following formula
A)
\[A=\kappa \]
done
clear
B)
\[A=10\,\kappa \]
done
clear
C)
\[A=100\,\kappa \]
done
clear
D)
\[A=10,000\,\kappa \]
done
clear
View Answer play_arrow
question_answer 145) The standard electrode potential of hydrogen electrode at 1 M concentration and hydrogen gas at 1 atm pressure is
A)
\[1\,V\]
done
clear
B)
\[~6\,V\]
done
clear
C)
\[~8\,V\]
done
clear
D)
\[~0\,V\]
done
clear
View Answer play_arrow
question_answer 146) Pure water does not conduct electricity because it is
A)
basic
done
clear
B)
almost not ionized
done
clear
C)
decomposed easily
done
clear
D)
acidic
done
clear
View Answer play_arrow
question_answer 147) The crystalline structure of \[\text{NaCl}\]is
A)
hexagonal close packing
done
clear
B)
face centred cubic
done
clear
C)
square planar
done
clear
D)
body centred cubic
done
clear
View Answer play_arrow
question_answer 148) Which one, among the following, is the van der Waals' equation, describing the behaviour of one mole of a real gas over wide ranges. temperature and pressure?
A)
\[\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V-b)=RT\]
done
clear
B)
\[\left( p-\frac{a}{^{{{V}^{2}}}} \right)(V-b)=RT\]
done
clear
C)
\[\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V-b)=\frac{R}{T}\]
done
clear
D)
\[\left( p+\frac{a}{^{{{V}^{2}}}} \right)(V+b)=RT\]
done
clear
View Answer play_arrow
question_answer 149) The following is a method to determine surface tension of liquids
A)
single capillary method
done
clear
B)
refractometric method
done
clear
C)
polarimetric method
done
clear
D)
boiling point method
done
clear
View Answer play_arrow
question_answer 150) The colloidal system of a solid dispersed in liquid medium, is called
A)
aerosol
done
clear
B)
sol
done
clear
C)
gel
done
clear
D)
foam
done
clear
View Answer play_arrow
question_answer 151) If \[2\hat{i}+4\hat{j}-5\hat{k}\] and \[\hat{i}+2\hat{j}+3\hat{k}\] are adjacent sides of a parallelogram, then the lengths of its diagonals are
A)
\[7,\,\sqrt{69}\]
done
clear
B)
\[6,\,\sqrt{59}\]
done
clear
C)
\[5,\,\sqrt{65}\]
done
clear
D)
\[5,\,\sqrt{55}\]
done
clear
View Answer play_arrow
question_answer 152) If the points \[\hat{i}-\hat{j}+\hat{k},\,\,\,2\hat{i}+3\hat{j}+4\hat{k}\]and \[3\hat{i}++7\hat{j}+p\hat{k}\]are collinear, then the value of p is
A)
\[6\]
done
clear
B)
\[5\]
done
clear
C)
\[4\]
done
clear
D)
\[7\]
done
clear
View Answer play_arrow
question_answer 153) If \[\hat{i}+2\hat{j}+3\hat{k}\] and \[2\hat{i}-\hat{j}+4\hat{k}\] are the position vectors of the points A and B, then the position vector of the points of trisection of AB are
A)
\[\frac{4}{3}\hat{i}+\hat{j}+\frac{10}{3}\hat{k},\,\frac{5}{3}\hat{i}+\frac{11}{3}\hat{k}\]
done
clear
B)
\[-\frac{4}{3}\hat{i}-\hat{j}-\frac{10}{3}\hat{k},-\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}\]
done
clear
C)
\[\frac{4}{3}\hat{i}-\hat{j}-\frac{10}{3}\hat{k},-\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}\]
done
clear
D)
\[-\frac{4}{3}\hat{i}+\hat{j}-\frac{10}{3}\hat{k},\,\frac{5}{3}\hat{i}-\frac{11}{3}\hat{k}\]
done
clear
View Answer play_arrow
question_answer 154) If \[\vec{a},\,\,\vec{b},\,\,\vec{c}\] are three vectors such that \[|\vec{a}|=3,|\,\,\vec{b}|=4,|\,\,\vec{c}|=5\] and \[\vec{a},\,\,\vec{b},\,\,\vec{c}\] are perpendicular to \[\vec{b}+\vec{c},\,\vec{c}+\vec{a},\,\,\vec{a}+\vec{b}\]respectively, then \[|\vec{a}\,+\,\vec{b}\,+\vec{c}|\] is equal to
A)
\[4\sqrt{2}\]
done
clear
B)
\[5\sqrt{2}\]
done
clear
C)
\[6\sqrt{2}\]
done
clear
D)
\[3\sqrt{2}\]
done
clear
View Answer play_arrow
question_answer 155) The area of a parallelogram having diagonals \[\vec{a}=3\hat{i}+\hat{j}-2\hat{k}\] and \[\vec{b}=\hat{i}-3\hat{j}+4\hat{k}\] is
A)
\[10\sqrt{3}\]
done
clear
B)
\[5\sqrt{3}\]
done
clear
C)
\[8\]
done
clear
D)
\[4\]
done
clear
View Answer play_arrow
question_answer 156) If \[|\vec{a}|=10,\,\,|\vec{b}|=2\] and \[\vec{a}.\vec{b}=12,\]then \[|\vec{a}\times \vec{b}|\] is equal to
A)
\[12\]
done
clear
B)
\[14\]
done
clear
C)
\[16\]
done
clear
D)
\[18\]
done
clear
View Answer play_arrow
question_answer 157) If \[\vec{a}\] and \[\vec{b}\] are unit vectors and a is the angle between them, then \[\vec{a}\,\,.\,\,\vec{b}\] will be a unit vector, if a is equal to
A)
\[\frac{\pi }{4}\]
done
clear
B)
\[\frac{\pi }{3}\]
done
clear
C)
\[\frac{2\pi }{3}\]
done
clear
D)
\[\frac{\pi }{2}\]
done
clear
View Answer play_arrow
question_answer 158) The angle between the lines with direction ratios \[(4,-3,5)\] and \[(3,4,5)\] is
A)
\[\frac{\pi }{2}\]
done
clear
B)
\[\frac{\pi }{4}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{\pi }{6}\]
done
clear
View Answer play_arrow
question_answer 159) If the extremities of a diagonal of a square are \[(1,-2,3)\] and \[(2,-3,5)\] then the length of the side is
A)
\[\sqrt{6}\]
done
clear
B)
\[\sqrt{3}\]
done
clear
C)
\[\sqrt{5}\]
done
clear
D)
\[\sqrt{7}\]
done
clear
View Answer play_arrow
question_answer 160) If the foot of the perpendicular from \[(0,0,0)\]to a plane is \[(1,2,2),\] then the equation of the plane is
A)
\[-x+2y+8y-9=0\]
done
clear
B)
\[x+2y+2z-9=0\]
done
clear
C)
\[x+y+z-5=0\]
done
clear
D)
\[x+2y-3z+1=0\]
done
clear
View Answer play_arrow
question_answer 161) If a line makes angles \[\frac{\pi }{3}\] and \[\frac{\pi }{4}\] with the X and Y-axes respectively, then the angle made by the line and Z-axis is
A)
\[\frac{\pi }{2}\]
done
clear
B)
\[\frac{\pi }{3}\]
done
clear
C)
\[\frac{\pi }{4}\]
done
clear
D)
\[\frac{5\pi }{12}\]
done
clear
View Answer play_arrow
question_answer 162) If \[P=(0,1,2),\,\,Q=(4,-2,1),O=(0,0,0),\] then \[\angle POQ\] is equal to
A)
\[\frac{\pi }{6}\]
done
clear
B)
\[\frac{\pi }{4}\]
done
clear
C)
\[\frac{\pi }{3}\]
done
clear
D)
\[\frac{\pi }{2}\]
done
clear
View Answer play_arrow
question_answer 163) The direction cosines of two rays \[\overrightarrow{AB}\] and \[\overrightarrow{AC}\] are \[\left( \frac{1}{2},\frac{1}{2},-1 \right)\] and \[\left( \frac{2}{7},\frac{-3}{7},\frac{6}{7} \right).\] The direction ratios of one of the bisectors of angle \[\left( \overrightarrow{AB},\overrightarrow{AC} \right)\]are
A)
\[(13,\,-5,\,\,4)\]
done
clear
B)
\[(13,\,5,\,\,-5)\]
done
clear
C)
\[(13,\,5,4)\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 164) The equation of the plane passing through the points \[(a,0,0),(0,b,0)\] and \[(0,0,c)\] is
A)
\[ax+by+cz=0\]
done
clear
B)
\[ax+by+cz=1\]
done
clear
C)
\[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\]
done
clear
D)
\[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=0\]
done
clear
View Answer play_arrow
question_answer 165) Through the point \[P(\alpha ,\,\beta ,\,\,\gamma )\] a plane is drawn at right angles to OP to meet the coordinate axes are A, B,. C respectively. If \[OP=p,\]then equation of plane \[\underset{ABC}{\longleftrightarrow}\] is
A)
\[\alpha x+\beta y+\gamma z=p\]
done
clear
B)
\[\frac{x}{\alpha }+\frac{x}{\beta }+\frac{z}{\gamma }=p\]
done
clear
C)
\[2\alpha x+2\beta y+2\gamma z={{p}^{2}}\]
done
clear
D)
\[\alpha x+\beta y+\gamma z={{p}^{2}}\]
done
clear
View Answer play_arrow
question_answer 166) The solution of the equation \[2{{x}^{3}}-{{x}^{2}}-22x-24=0\]when two of the roots are in the ratio \[3:4,\] is
A)
\[3,\,4,\frac{1}{2}\]
done
clear
B)
\[-\frac{3}{2},-2,4\]
done
clear
C)
\[-\frac{1}{2},\frac{3}{2},2\]
done
clear
D)
\[\frac{3}{2},2,\frac{5}{2}\]
done
clear
View Answer play_arrow
question_answer 167) The condition that the roots of the equation \[{{x}^{3}}+3p{{x}^{2}}+3qx+r=0\] satisfied, is
A)
\[2{{p}^{3}}-3pq+r=0\]
done
clear
B)
\[2{{p}^{3}}+3pq+r=0\]
done
clear
C)
\[2{{p}^{3}}-3pq-r=0\]
done
clear
D)
\[{{p}^{3}}+3pq-r=0\]
done
clear
View Answer play_arrow
question_answer 168) If \[\alpha ,\beta ,\gamma \] are the roots of the equation \[{{x}^{3}}-7x+7=0,\] then \[\frac{1}{{{\alpha }^{4}}}+\frac{1}{{{\beta }^{4}}}+\frac{1}{{{\gamma }^{4}}}\] is
A)
\[\frac{7}{3}\]
done
clear
B)
\[\frac{3}{7}\]
done
clear
C)
\[\frac{4}{7}\]
done
clear
D)
\[\frac{7}{4}\]
done
clear
View Answer play_arrow
question_answer 169) At \[x=\frac{3}{2}\] the function \[f(x)=\frac{|2x-3|}{2x-3}\] is
A)
continuous
done
clear
B)
discontinuous
done
clear
C)
differentiable
done
clear
D)
non-zero
done
clear
View Answer play_arrow
question_answer 170) \[\underset{x\to -1}{\mathop{\lim }}\,\frac{1+\sqrt[3]{x}}{1+\sqrt[5]{x}}\]is equal to
A)
\[\frac{5}{3}\]
done
clear
B)
\[\frac{3}{7}\]
done
clear
C)
\[\frac{4}{7}\]
done
clear
D)
\[\frac{-3}{5}\]
done
clear
View Answer play_arrow
question_answer 171) \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{2}^{-n}}({{n}^{2}}+5n+6)}{(n+4)\,(n+5)}\] is equal to
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[\infty \]
done
clear
D)
\[-\infty \]
done
clear
View Answer play_arrow
question_answer 172) \[\underset{x\to \pi /4}{\mathop{\lim }}\,\frac{\sqrt{2}\cos \,x-1}{\cot \,x-1}\] is equal to
A)
\[1\]
done
clear
B)
\[-\frac{1}{2}\]
done
clear
C)
\[\frac{1}{2\sqrt{2}}\]
done
clear
D)
\[\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 173) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\]is equal to
A)
\[-2\]
done
clear
B)
\[0\]
done
clear
C)
\[2\]
done
clear
D)
\[\infty \]
done
clear
View Answer play_arrow
question_answer 174) If n is an integer, then \[\underset{x\to n}{\mathop{\lim }}\,[x]\]
A)
\[n-1\]
done
clear
B)
\[n\]
done
clear
C)
does not exist
done
clear
D)
\[n+1\]
done
clear
View Answer play_arrow
question_answer 175) If \[f(x)=\frac{{{e}^{1/x}}}{1+{{e}^{1/x}}}\]for \[x\ne 0\] and \[f(0)=0,\] then at \[x=0\] the function \[f(x)\] is
A)
continuous
done
clear
B)
discontinuous
done
clear
C)
increasing
done
clear
D)
differentiable
done
clear
View Answer play_arrow
question_answer 176) Derivative of \[{{\log }_{10}}\,x\] with respect to \[{{x}^{2}}\]is
A)
\[2{{x}^{2}}\,{{\log }_{e}}\,10\]
done
clear
B)
\[\frac{{{\log }_{10}}\,e}{2{{x}^{2}}}\]
done
clear
C)
\[\frac{{{\log }_{e}}\,10}{2{{x}^{2}}}\]
done
clear
D)
\[{{x}^{2}}\,{{\log }_{e}}\,10\]
done
clear
View Answer play_arrow
question_answer 177) The greatest value of \[si{{n}^{3}}x+co{{s}^{3}}x\]is
A)
\[1\]
done
clear
B)
\[2\]
done
clear
C)
\[\sqrt{2}\]
done
clear
D)
\[\sqrt{3}\]
done
clear
View Answer play_arrow
question_answer 178) The function \[f(x)=1-{{x}^{3}}\]
A)
increases everywhere
done
clear
B)
decrease in \[(0,\infty )\]
done
clear
C)
increases is \[(0,\infty )\]
done
clear
D)
None of the above
done
clear
View Answer play_arrow
question_answer 179) The equation of the normal line to the curve \[y=x\,{{\log }_{e}}x\] parallel to\[2x-2y+3=0\] is
A)
\[x+y=3{{e}^{-2}}\]
done
clear
B)
\[x-y=6{{e}^{-2}}\]
done
clear
C)
\[x-y=3{{e}^{-2}}\]
done
clear
D)
\[x-y=6{{e}^{2}}\]
done
clear
View Answer play_arrow
question_answer 180) If \[f(x)=\sin \,x/{{e}^{x}}\] in \[[0,\pi ],\] then \[f(x)\]
A)
satisfies Rollers theorem and \[c=\frac{\pi }{4},\] so that \[f'\left( \frac{\pi }{4} \right)=4\]
done
clear
B)
does not satisfy Rolle's theorem but \[f'\left( \frac{\pi }{4} \right)>0\]
done
clear
C)
satisfies Rolle's theorem but \[f'\left( \frac{\pi }{4} \right)=0\]
done
clear
D)
satisfies Lagranges Mean value theorem but \[f'\left( \frac{\pi }{4} \right)\ne 0\]
done
clear
View Answer play_arrow
question_answer 181) \[\int{\frac{1}{1+\cos \,\,ax}}\,\,dx\] is equal to
A)
\[\cot \,\frac{ax}{2}+c\]
done
clear
B)
\[\frac{1}{a}\,\tan \,\frac{ax}{2}+c\]
done
clear
C)
\[\frac{1}{a}(\text{cosec ax - cot ax)+c}\]
done
clear
D)
\[\frac{1}{a}(\text{cosec ax + cot ax)+c}\]
done
clear
View Answer play_arrow
question_answer 182) \[\int{\frac{{{\log }_{e}}\,(\tan x)}{sin\,x\,\cos \,x}}\,\,dx\] is equal to
A)
\[{{[{{\log }_{e}}\,(tan\,x)]}^{2}}+c\]
done
clear
B)
\[\frac{1}{2}{{({{\log }_{e}}\,\tan x)}^{2}}+c\]
done
clear
C)
\[{{\log }_{e}}\,\,({{\log }_{e}}\,\,\tan \,x)+c\]
done
clear
D)
\[{{\log }_{e}}\,\,\tan \,x+c\]
done
clear
View Answer play_arrow
question_answer 183) \[\int_{0}^{\pi }{{{\cos }^{3}}\,x\,\,dx}\]is equal to
A)
\[0\]
done
clear
B)
\[1\]
done
clear
C)
\[-1\]
done
clear
D)
\[\frac{1}{2\sqrt{2}}\]
done
clear
View Answer play_arrow
question_answer 184) \[\int_{0}^{a}{\sqrt{{{a}^{2}}-{{x}^{2}}}}\,\,\,dx\] is equal to
A)
\[\pi {{a}^{2}}\]
done
clear
B)
\[\frac{1}{2}\pi {{a}^{2}}\]
done
clear
C)
\[\frac{1}{3}\pi {{a}^{2}}\]
done
clear
D)
\[\frac{1}{4}\pi {{a}^{2}}\]
done
clear
View Answer play_arrow
question_answer 185) The area bounded by the curves \[y=3x\]and \[y={{x}^{2}}\]is (in square units)
A)
\[10\]
done
clear
B)
\[5\]
done
clear
C)
\[4.5\]
done
clear
D)
\[9\]
done
clear
View Answer play_arrow
question_answer 186) The order of the differential equation \[{{\left( \frac{dy}{dx} \right)}^{3}}+{{\left( \frac{dy}{dx} \right)}^{2}}+{{y}^{4}}=0\]is
A)
\[4\]
done
clear
B)
\[3\]
done
clear
C)
\[1\]
done
clear
D)
\[2\]
done
clear
View Answer play_arrow
question_answer 187) The solution \[\frac{dy}{dx}+y={{e}^{x}}\]is
A)
\[2y={{e}^{2x}}+c\]
done
clear
B)
s\[2y{{e}^{x}}={{e}^{2}}+c\]
done
clear
C)
\[2y{{e}^{x}}={{e}^{2x}}+c\]
done
clear
D)
\[2y{{e}^{2x}}=2{{e}^{x}}+c\]
done
clear
View Answer play_arrow
question_answer 188) When three dice are thrown the probability of getting a 4 or a 5 on each of the dice simultaneously is
A)
\[\frac{1}{72}\]
done
clear
B)
\[\frac{1}{108}\]
done
clear
C)
\[\frac{1}{24}\]
done
clear
D)
None of these
done
clear
View Answer play_arrow
question_answer 189) The probability of forming a three digit number with the same digits when three digit numbers are formed out of the digits \[0,2,4,6,8\]
A)
\[\frac{1}{16}\]
done
clear
B)
\[\frac{1}{12}\]
done
clear
C)
\[\frac{1}{645}\]
done
clear
D)
\[\frac{1}{25}\]
done
clear
View Answer play_arrow
question_answer 190) \[P(A\cup B)=\frac{1}{2},P(\bar{A})=\frac{2}{3},\] find \[P(\bar{A}\cap B)\]
A)
\[\frac{1}{3}\]
done
clear
B)
\[1\]
done
clear
C)
\[\frac{1}{5}\]
done
clear
D)
\[\frac{1}{6}\]
done
clear
View Answer play_arrow
question_answer 191)
A random variable X has the following probability distribution \[X(={{x}_{i}})\] \[1\] \[2\] \[3\] \[4\] \[P(X={{x}_{i}})\] \[k\] \[2k\] \[3k\] \[4k\]
Then, the mean of X is
A)
\[3\]
done
clear
B)
\[1\]
done
clear
C)
\[4\]
done
clear
D)
\[2\]
done
clear
View Answer play_arrow
question_answer 192) The mean and variance of a random variable X having a Binomial distribution are 4 and 2 respectively. Then, \[P(X>6)\] is equal to
A)
\[\frac{1}{256}\]
done
clear
B)
\[\frac{3}{256}\]
done
clear
C)
\[\frac{9}{256}\]
done
clear
D)
\[\frac{7}{256}\]
done
clear
View Answer play_arrow
question_answer 193) If A and B are mutually exclusive events with \[P(A)=\frac{1}{2}\times P(B)\] and \[A\cup B=S,\] (total sample space) then \[P(A)\] is equal to
A)
\[\frac{2}{3}\]
done
clear
B)
\[\frac{1}{3}\]
done
clear
C)
\[\frac{1}{4}\]
done
clear
D)
\[\frac{3}{4}\]
done
clear
View Answer play_arrow
question_answer 194) A coin is tossed three times. The probability of getting a head once and a tail twice is
A)
\[\frac{1}{8}\]
done
clear
B)
\[\frac{1}{3}\]
done
clear
C)
\[\frac{3}{8}\]
done
clear
D)
\[\frac{1}{2}\]
done
clear
View Answer play_arrow
question_answer 195) The probability of choosing a number divisible by 6 or 8 from among 1 to 90 is
A)
\[\frac{1}{6}\]
done
clear
B)
\[\frac{1}{90}\]
done
clear
C)
\[\frac{1}{30}\]
done
clear
D)
\[\frac{23}{90}\]
done
clear
View Answer play_arrow
question_answer 196) If the function \[f:R\to R\] denned by \[f(x)=[x]\]where \[[x]\] is the greatest integer not exceeding x, for \[x\in R\] then /is
A)
even
done
clear
B)
odd
done
clear
C)
neither even nor odd
done
clear
D)
strictly increasing
done
clear
View Answer play_arrow
question_answer 197) If \[f:R\to R\] is given by \[f(x)=\left\{ \begin{matrix} -1,\,when\,\,x\,\,is\,\,rational \\ 1,\,when\,\,x\,\,is\,\,irrational \\ \end{matrix} \right.\] then \[(fof)\,(1-\sqrt{3})\] is equal to
A)
\[1\]
done
clear
B)
\[-1\]
done
clear
C)
\[\sqrt{3}\]
done
clear
D)
\[0\]
done
clear
View Answer play_arrow
question_answer 198) If \[\frac{{{(1+i)}^{2}}}{2-i}=x+iy,\] then \[x+y\] is equal to
A)
\[-\frac{2}{5}\]
done
clear
B)
\[\frac{6}{5}\]
done
clear
C)
\[\frac{2}{5}\]
done
clear
D)
\[-\frac{6}{5}\]
done
clear
View Answer play_arrow
question_answer 199) If \[1,\,\omega ,\,{{\omega }^{2}}\] are the cube roots of unity, then \[(1-\omega +{{\omega }^{2}})(1-{{\omega }^{2}}+{{\omega }^{4}})(1-{{\omega }^{4}}+{{\omega }^{8}})\] \[(1-{{\omega }^{8}}+{{\omega }^{16}})....\] upto 2n factors is
A)
\[2n\]
done
clear
B)
\[{{2}^{2n}}\]
done
clear
C)
\[1\]
done
clear
D)
\[-{{2}^{2n}}\]
done
clear
View Answer play_arrow
question_answer 200) If \[\alpha \] and \[\beta \] are the roots of \[{{x}^{2}}+5x+4=0,\]then equation whose roots are \[\frac{\alpha +2}{3},\frac{\beta +2}{3}\]is
A)
\[9{{x}^{2}}+3x+2=0\]
done
clear
B)
\[9{{x}^{2}}-3x-2=0\]
done
clear
C)
\[9{{x}^{2}}+3x-2=0\]
done
clear
D)
\[9{{x}^{2}}-3x+2=0\]
done
clear
View Answer play_arrow
question_answer 201) If the difference between the roots of \[{{x}^{2}}+ax-b=0\]is equal to the difference between the roots of \[{{x}^{2}}-px+q=0,\]then \[{{a}^{2}}-{{p}^{2}}\]in terms of b and q is
A)
\[-4(b+q)\]
done
clear
B)
\[4(b+q)\]
done
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C)
\[4(b-q)\]
done
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D)
\[4(q-b)\]
done
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question_answer 202) In a geometric progression (GP) the ratio of the sum of the 1st three terms and first six terms is \[125:152\] the common ratio is
A)
\[\frac{1}{5}\]
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B)
\[\frac{2}{5}\]
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C)
\[\frac{4}{5}\]
done
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D)
\[\frac{3}{5}\]
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question_answer 203) The term independent of x in the expansion of \[\left( \frac{2\sqrt{x}}{x}-\frac{1}{2x\sqrt{x}} \right)\] is
A)
5th term
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B)
6th term
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C)
11 th term
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D)
no term
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question_answer 204) The mid points of the sides of a triangle are \[D(6,1),\,\,E(3,\,5)\] and \[F(-1,-2),\] then the vertex opposite to D is
A)
\[(-4,2)\]
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B)
\[(-4,5)\]
done
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C)
\[(2,\,5)\]
done
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D)
\[(10,\,8)\]
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question_answer 205) If the centroid of the triangle formed by the points \[(0,\,0),\,\,(\cos \theta ,\sin \theta )\] and \[(sin\theta ,-\cos \theta )\] lies on the line \[y=2x,\]then \[\theta \] is equal to
A)
\[{{\tan }^{-1}}\,\,2\]
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B)
\[{{\tan }^{-1}}\,\,3\]
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C)
\[{{\tan }^{-1}}\,\,(-3)\]
done
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D)
\[{{\tan }^{-1}}\,\,(-2)\]
done
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question_answer 206) The point of concurrence of the lines \[ax+by+c=0\]and \[a,b,c\]satisfy the relation \[3a+2b+4c=0\]is
A)
\[\left( \frac{3}{2},\frac{1}{4} \right)\]
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B)
\[\left( \frac{3}{4},\frac{1}{4} \right)\]
done
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C)
\[\left( \frac{3}{4},\frac{1}{2} \right)\]
done
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D)
\[\left( \frac{3}{2},\frac{1}{2} \right)\]
done
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question_answer 207) If 3, 4 are intercepts of a line \[L=0,\]then the distance of \[L=0\]from the origin is
A)
5 unit
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B)
12 unit
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C)
\[\frac{5}{12}\]unit
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D)
\[\frac{12}{5}\]unit
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question_answer 208) The angle between the pair of lines \[({{x}^{2}}+{{y}^{2}}){{\sin }^{2}}\alpha ={{(x\,\cos \theta -y\,\sin \theta )}^{2}}\] is
A)
\[\theta \]
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B)
\[2\,\theta \]
done
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C)
\[\alpha \]
done
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D)
\[2\,\alpha \]
done
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question_answer 209) The other end of the diameter through the point \[(-1,1)\] on the circle \[{{x}^{2}}+{{y}^{2}}-6x+4y-12=0\]'
A)
\[(-7,5)\]
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B)
\[(-7,-5)\]
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C)
\[(7,-5)\]
done
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D)
\[(7,5)\]
done
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question_answer 210) In the parabola \[{{y}^{2}}=4ax,\]the length of the chord passing through the vertex inclined to the axis at\[\frac{\pi }{4}\] is
A)
\[4a\sqrt{2}\]
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B)
\[2a\sqrt{2}\]
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C)
\[a\sqrt{2}\]
done
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D)
\[a\]
done
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question_answer 211) If \[\frac{1+\cos A}{1-\cos A}=\frac{{{m}^{2}}}{{{n}^{2}}},\] then tan A is equal to
A)
\[\pm \frac{2mn}{{{m}^{2}}+{{n}^{2}}}\]
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B)
\[\pm \frac{2mn}{{{m}^{2}}-{{n}^{2}}}\]
done
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C)
\[\frac{{{m}^{2}}+{{n}^{2}}}{{{m}^{2}}-{{n}^{2}}}\]
done
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D)
\[\frac{{{m}^{2}}-{{n}^{2}}}{{{m}^{2}}+{{n}^{2}}}\]
done
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question_answer 212) If \[\alpha +\beta =\frac{\pi }{4},\]then the value of \[(1+\tan \alpha )\] \[(1+\tan \beta )\]is equal to
A)
\[1\]
done
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B)
\[-1\]
done
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C)
\[2\]
done
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D)
\[-2\]
done
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question_answer 213) The value of \[{{\cos }^{2}}\left( \frac{\pi }{4}+\theta \right)-{{\sin }^{2}}\left( \frac{\pi }{4}-\theta \right)\]is
A)
\[0\]
done
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B)
\[\cos \,\,2\theta \]
done
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C)
\[sin\,\,2\theta \]
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D)
\[\cos \,\theta \]
done
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question_answer 214) The solutions of \[x+\sin \,5x=\sin 3x\] in \[\left( 0,\frac{\pi }{2} \right)\]
A)
\[\frac{\pi }{4},\frac{\pi }{10}\]
done
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B)
\[\frac{\pi }{6},\frac{\pi }{3}\]
done
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C)
\[\frac{\pi }{4},\frac{\pi }{2}\]
done
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D)
\[\frac{\pi }{8},\frac{\pi }{16}\]
done
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question_answer 215) If \[\cot \,x+\,\text{cosec x = }\sqrt{3},\] the principal value of \[\left( x-\frac{\pi }{6} \right)\]is
A)
\[\frac{\pi }{3}\]
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B)
\[\frac{\pi }{4}\]
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C)
\[\frac{\pi }{2}\]
done
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D)
\[\frac{\pi }{6}\]
done
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question_answer 216) The value of \[{{\cos }^{-1}}\left( -\frac{1}{2} \right)\] among the following, is
A)
\[\frac{9\pi }{3}\]
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B)
\[\frac{8\pi }{3}\]
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C)
\[\frac{5\pi }{3}\]
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D)
\[\frac{11\pi }{3}\]
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question_answer 217) The value of \[{{\cot }^{-1}}\,9+\text{cose}{{\text{c}}^{-1}}\frac{\sqrt{41}}{4}\]is
A)
\[\frac{\pi }{2}\]
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B)
\[\frac{\pi }{4}\]
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C)
\[\frac{\pi }{3}\]
done
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D)
\[\pi \]
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question_answer 218) If \[\left| \begin{matrix} 1 & 1 & 0 \\ 2 & 0 & 3 \\ 5 & -6 & x \\ \end{matrix} \right|=29,\] then x is
A)
\[1\]
done
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B)
\[2\]
done
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C)
\[3\]
done
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D)
\[4\]
done
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question_answer 219) If \[A=\left[ \begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],\] then \[{{A}^{-1}}\]is equal to
A)
\[2A\]
done
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B)
\[A\]
done
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C)
\[-A\]
done
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D)
\[I\]
done
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question_answer 220) If \[x\left[ \begin{matrix} -3 \\ 4 \\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\ 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\ -5 \\ \end{matrix} \right],\] then
A)
\[x=-2,\,y=1\]
done
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B)
\[x=-9,y=10\]
done
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C)
\[x=22,y=1\]
done
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D)
\[x=2,y=-1\]
done
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question_answer 221) Let A be a square matrix and \[{{A}^{T}}\] is its transpose, then \[A+{{A}^{T}}\]is
A)
a diagonal matrix
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B)
a symmetric matrix
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C)
the identity matrix
done
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D)
a skew-symmetric matrix
done
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question_answer 222) If \[\left| \begin{matrix} x & y & z \\ -x & y & z \\ x & -y & z \\ \end{matrix} \right|=kxyz,\] then k is equal to
A)
\[1\]
done
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B)
\[3\]
done
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C)
\[4\]
done
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D)
\[2\]
done
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question_answer 223) The system of equations \[3x-y+4z=3\] \[x+2y-3z=-2\] \[6x+5y+\lambda z=-3\] has at least one solution, if
A)
\[\lambda =-5\]
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B)
\[\lambda =5\]
done
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C)
\[\lambda =3\]
done
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D)
\[\lambda =-13\]
done
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question_answer 224) The inverse of \[\left[ \begin{matrix} 5 & 2 \\ 3 & 1 \\ \end{matrix} \right]\]is
A)
\[\left[ \begin{matrix} 1 & -2 \\ -3 & 5 \\ \end{matrix} \right]\]
done
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B)
\[\left[ \begin{matrix} -1 & 2 \\ 3 & -5 \\ \end{matrix} \right]\]
done
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C)
\[\left[ \begin{matrix} -1 & -2 \\ -3 & -5 \\ \end{matrix} \right]\]
done
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D)
\[\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]\]
done
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question_answer 225) \[A=\left[ \begin{matrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],\] then \[{{A}^{-1}}\] is
A)
\[A\]
done
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B)
\[-A\]
done
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C)
\[adj\,(A)\]
done
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D)
\[-adj\,(A)\]
done
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