question_answer 1)
The v-t graph for a particle is as shown. The distance travelled in the first four seconds is
A)
12 m
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B)
16 m
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C)
20 m
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D)
24 m
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question_answer 2) If a convex lens of focal length 75 cm and a concave lens of focal length 50 cm are combined together, what will be their resulting power?
A)
\[-6.6D\]
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B)
\[+0.66\text{ }D\]
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C)
\[+6.6D\]
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D)
\[-0.66D\]
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question_answer 3) When a ferromagnetic material is heated to temperature above its curie point, the material
A)
is permanently magnetized
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B)
remains ferromagnetic
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C)
behaves like a diamagnetic material
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D)
behaves like a paramagnetic material
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question_answer 4) Light of energy 2.0 eV falls on a metal of work function 1.4 eV. The stopping potential is
A)
0.6 V
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B)
2.0 V
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C)
3.4 V
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D)
1.4 V
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question_answer 5) During an isothermal expansion of an ideal gas
A)
its internal energy decreases
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B)
its internal energy does not change
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C)
the work done by the gas is equal to the quantity of heat absorbed by it
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D)
both (b) and (c) are correct
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question_answer 6) Find the dimensions of electric permittivity
A)
\[[{{A}^{2}}{{M}^{-1}}{{L}^{-3}}{{T}^{4}}]\]
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B)
\[[{{A}^{2}}{{M}^{-1}}{{L}^{3}}{{T}^{0}}]\]
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C)
\[[A{{M}^{-1}}{{L}^{-3}}{{T}^{4}}]\]
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D)
\[[{{A}^{2}}{{M}^{0}}{{L}^{-3}}{{T}^{4}}]\]
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question_answer 7) In Youngs double slit experiment, the slits are 3 mm apart. The wavelength of light used is \[5000\text{ }\overset{o}{\mathop{\text{A}}}\,\]and the distance between the slits and the screen is 90 cm. The fringe width in mm is
A)
1.5
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B)
0.015
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C)
2.0
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D)
0.15
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question_answer 8) A moving coil galvanometer has a resistance of\[10\text{ }\Omega \]. and full scale deflection of 0.01 A. It can be converted into voltmeter of 10 V full scale by connecting into resistance of
A)
\[\text{9}\text{.90 }\Omega \] in series
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B)
\[\text{10 }\Omega \] in series
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C)
\[\text{990 }\Omega \] in series
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D)
\[\text{0}\text{.10 }\Omega \] in series
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question_answer 9) A circular disc of radius R rolls without slipping along the horizontal surface with constant velocity vq. We consider a point A on the surface of the disc. Then the acceleration of the point A is
A)
constant in magnitude as well as direction
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B)
constant in direction
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C)
constant in magnitude
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D)
constant
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question_answer 10) The number of free electrons per 100 mm of ordinary Copper wire is\[2\times {{10}^{21}}\]. Average drift speed of electrons is 0.25 mm/s. The current flowing is
A)
5 A
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B)
80 A
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C)
8 A
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D)
0.8 A
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question_answer 11) A Carnot engine whose low temperature reservoir is at\[7{}^\circ C\] has an efficiency of 50%. It is desired to increase the efficiency to 70%. By how many degrees should the temperature of the high temperature reservoir be increased?
A)
840 K
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B)
280 K
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C)
560 K
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D)
380 K
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question_answer 12)
The current in the\[1\,\Omega \]. resistor shown in the circuit is
A)
\[\frac{2}{3}A\]
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B)
\[3A\]
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C)
\[6\text{ }A\]
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D)
\[\text{2 }A\]
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question_answer 13) Water is flowing through a pipe of constant cross-section. At some point the pipe becomes narrow and the cross-section is halved. The speed of water is
A)
reduced to zero
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B)
decreased by a factor of 2
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C)
increased by a factor of 2
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D)
unchanged
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question_answer 14) In Millikans oil drop experiment, an oil drop of mass\[16\times {{10}^{-6}}kg\]is balanced by an electric field of\[{{10}^{6}}V/m\]. The charge in coulomb on the drop is (assuming\[g=10m/{{s}^{2}}\])
A)
\[6.2\times {{10}^{-11}}\]
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B)
\[16\times {{10}^{-9}}\]
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C)
\[16\times {{10}^{-11}}\]
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D)
\[16\times {{10}^{-13}}\]
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question_answer 15) The minimum wavelength of X-ray emitted from X-ray machine operating at an accelerating potential of V volts is
A)
\[\frac{hc}{eV}\]
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B)
\[\frac{Vc}{eh}\]
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C)
\[\frac{eh}{Vc}\]
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D)
\[\frac{eV}{hc}\]
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question_answer 16)
Light wave is travelling alongy-direction. If the corresponding E vector at any time is along the \[x-\]axis, the direction of B vector at that time is along
A)
\[y-\]axis
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B)
\[x-\]axis
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C)
\[+z\]axis
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D)
\[-z-\]axis
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question_answer 17) Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror and parallel to the second is reflected from the second mirror parallel to the first mirror. The angle between the two mirrors is
A)
\[30{}^\circ \]
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B)
\[45{}^\circ \]
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C)
\[60{}^\circ \]
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D)
\[75{}^\circ \]
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question_answer 18) A radioactive material has a half-life of 8 yr. The activity of the material will decrease to about 1/8 of its original value in
A)
256 yr
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B)
128 yr
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C)
64 yr
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D)
24 yr
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question_answer 19) The number of beats produced per second by two vibrations\[{{x}_{1}}={{x}_{0}}\]and\[{{x}_{2}}={{x}_{0}}\sin 652\pi t\]is
A)
2
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B)
3
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C)
4
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D)
6
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question_answer 20) An engine is supposed to operate between two reservoirs at temperature\[727{}^\circ C\]and\[227{}^\circ C\]. The maximum possible efficiency of such an engine is
A)
1/2
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B)
¼
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C)
3/4
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D)
1
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question_answer 21) A string vibrates according to the equation\[y=5\sin \left( \frac{2\pi x}{3} \right)\cos 20\pi t\]where\[x\]and y are in cm and t in second. The distance between two adjacent nodes is
A)
3 cm
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B)
4.5 cm
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C)
6 cm
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D)
1.5 cm
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question_answer 22) On Centigrade scale the temperature of a body increases by\[30{}^\circ \]. The increase in temperature on Fahrenheit scale is
A)
\[50{}^\circ \]
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B)
\[40{}^\circ \]
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C)
\[30{}^\circ \]
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D)
\[54{}^\circ \]
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question_answer 23) A particle performs uniform circular motion with an angular momentum L. If the frequency of particles motion is doubled and its KE is halved. the angular momentum becomes
A)
\[\frac{L}{2}\]
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B)
\[2L\]
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C)
\[4L\]
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D)
\[\frac{L}{4}\]
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question_answer 24) An electron initially at rest is accelerated through a potential difference of\[1V\]. The energy acquired by electron is
A)
\[{{10}^{-19}}J\]
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B)
\[1.6\times {{10}^{-19}}erg\]
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C)
\[1.6\times {{10}^{-19}}J\]
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D)
\[1J\]
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question_answer 25) A nucleus decays by\[{{\beta }^{+}}-\] emission followed by a\[\gamma -\]emission. If the atomic and mass numbers of the parent nucleus are Z and A respectively, the corresponding numbers for the daughter nucleus are respectively
A)
\[Z-1\]and\[A-1\]
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B)
\[Z+1\] and A
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C)
\[Z-1\]and A
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D)
\[Z+1\]and\[A-1\]
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question_answer 26) An iron bar of length 10 m is heated from\[0{}^\circ C\] to\[100{}^\circ C\]. If the coefficient of linear thermal expansion of iron is\[10\times {{10}^{-6}}/{}^\circ C,\] the increase in the length of bar is
A)
0.5 cm
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B)
1.0 cm
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C)
1.5 cm
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D)
2:0 cm
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question_answer 27) A balloon going upward with a velocity of 12 m/s is at a height of 65 m from the earths surface at any instant. Exactly at this instant a ball drops from it. How much time will the ball take in reaching the surface of earth? \[(g=10m/{{s}^{2}})\]
A)
5s
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B)
5 s
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C)
10s
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D)
None of these
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question_answer 28) A block moving on a surface with velocity 20 m/s comes to rest because of surface friction over a distance of 40 m. Taking\[(g=10m/{{s}^{2}})\], the coefficient of dynamic friction is
A)
0.5
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B)
0.3
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C)
0.2
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D)
0.1
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question_answer 29) A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities remain unchanged?
A)
The charge on the capacitor
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B)
The stored energy in the capacitor
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C)
The potential difference between the plates
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D)
The electric field in the capacitor
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question_answer 30) In a medium of dielectric constant K, the electric field is\[\overrightarrow{E}\]. If\[{{\varepsilon }_{0}}\]is permittivity of the free space, the electric displacement vector is
A)
\[\frac{K\vec{E}}{{{\varepsilon }_{0}}}\]
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B)
\[\frac{{\vec{E}}}{K{{\varepsilon }_{0}}}\]
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C)
\[\frac{{{\varepsilon }_{0}}\vec{E}}{K}\]
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D)
\[K{{\varepsilon }_{0}}\vec{E}\]
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question_answer 31) The phenomenon of polarization of light indicates that
A)
light is a longitudinal wave
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B)
light is a transverse wave
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C)
light is not a wave
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D)
light travels with the velocity of\[3\times {{10}^{8}}m/s\]
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question_answer 32) A ray of light passes from vacuum into a medium of refractive index u., the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is
A)
\[2{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
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B)
\[{{\sin }^{-1}}\left( \mu \right)\]
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C)
\[{{\sin }^{-1}}\left( \frac{\mu }{2} \right)\]
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D)
\[{{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]
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question_answer 33) A body dropped from top of a tower fall through 60 m during the last two seconds of its fall. The height of tower is\[(g=10\text{ }m/{{s}^{2}})\]
A)
95 m
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B)
60 m
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C)
80 m
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D)
90 m
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question_answer 34) A compound microscope has an eyepiece of focal length 10 cm and an objective of focal length 4 cm. Calculate the magnification, if an object is kept at a distance of 5 cm from the objective, so that final image is formed at the least distance of distinct vision 20 cm.
A)
12
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B)
11
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C)
10
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D)
13
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question_answer 35) The ratio of the velocity of sound in oxygen to that in hydrogen at same temperature and pressure is approximately
A)
\[16:1\]
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B)
\[1:16\]
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C)
\[4:1\]
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D)
\[1:4\]
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question_answer 36) The ratio\[\frac{g}{{{g}_{h}}},\]where g and\[{{g}_{h}}\]are the accelerations due to gravity at the surface of the earth and at a height h above the earths surface respectively, is
A)
\[{{\left( 1+\frac{h}{R} \right)}^{2}}\]
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B)
\[{{\left( 1+\frac{R}{h} \right)}^{2}}\]
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C)
\[{{\left( \frac{R}{h} \right)}^{2}}\]
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D)
\[{{\left( \frac{h}{R} \right)}^{2}}\]
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question_answer 37) In order that the light reflected from the surface of a medium of refractive index a is plane polarized, the angle of incidence should be
A)
\[{{\sin }^{-1}}(\mu )\]
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B)
\[{{\tan }^{-1}}(\mu )\]
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C)
\[{{\cot }^{-1}}(\mu )\]
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D)
\[{{\tan }^{-1}}\left( \frac{1}{\mu } \right)\]
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question_answer 38) The magnetic field at the centre of a current carrying circular loop is B. If the radius of the loop is doubled, keeping the current same, the magnetic field at the centre of the loop would be
A)
\[\frac{B}{4}\]
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B)
\[\frac{B}{2}\]
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C)
2B
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D)
4B
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question_answer 39) Let V be the electric potential at a given point. Then the electric field\[{{E}_{x}}\]along\[x-\]direction at that point is given by
A)
\[\int_{0}^{\infty }{V}dx\]
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B)
\[\frac{dV}{dx}\]
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C)
\[-\frac{dV}{dx}\]
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D)
\[-V\frac{dV}{dx}\]
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question_answer 40) Potential at any point inside a charged hollow, sphere
A)
increases with distance
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B)
is a constant
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C)
decreases with distance from centre
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D)
is zero
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question_answer 41) The length of a simple pendulum is increased by 44 %. What is the percentage increase in its time period?
A)
10%
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B)
20%
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C)
40 %
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D)
44 %
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question_answer 42) Four charges\[{{q}_{1}}=2\times {{10}^{-8}}C,{{q}_{2}}=-2\times {{10}^{-8}}C,\]\[{{q}_{3}}=-3\times {{10}^{-8}}C\]and\[{{q}_{4}}=6\times {{10}^{-8}}C\]are placed at four comers of a square of side\[\sqrt{2}m\]. What is the potential at the centre of the square?
A)
270V
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B)
300V
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C)
Zero
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D)
100 V
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question_answer 43) A point charge + q is placed at the midpoint of a cube of side L. The electric flux emerging from the cube is
A)
\[\frac{q}{{{\varepsilon }_{0}}}\]
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B)
\[\frac{q}{6{{L}^{2}}{{\varepsilon }_{0}}}\]
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C)
\[\frac{6q{{L}^{2}}}{{{\varepsilon }_{0}}}\]
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D)
zero
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question_answer 44) In which of the following is the interference due to the division of wavefront?
A)
Youngs double slit experiment
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B)
Fresnels biprism experiment
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C)
Llyods mirror experiment
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D)
Demonstration colours of thin film
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question_answer 45) A source of sound of frequency 500 Hz is moving towards a stationary observer with velocity 30 m/s. The speed of sound is 330 m/s. The frequency heard by the observer will be
A)
545 Hz
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B)
580 Hz
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C)
458.3 Hz
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D)
550 Hz
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question_answer 46) A ball is hit at\[45{}^\circ \]to the horizontal with a kinetic energy\[{{E}_{k}}\]. The kinetic energy at the highest point is
A)
\[{{E}_{k}}\]
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B)
\[\frac{{{E}_{k}}}{2}\]
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C)
\[\frac{{{E}_{k}}}{\sqrt{2}}\]
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D)
zero
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question_answer 47) In stream line flow of liquid, the total energy of liquid is constant at
A)
all points
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B)
inner points
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C)
outer points
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D)
none of these
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question_answer 48) The magnetic field at the point of intersection of diagonals of a square loop of side L carrying a current\[I\]is
A)
\[\frac{{{\mu }_{0}}I}{\pi L}\]
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B)
\[\frac{2{{\mu }_{0}}I}{\pi L}\]
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C)
\[\frac{\sqrt{2}{{\mu }_{0}}I}{\pi L}\]
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D)
\[\frac{2\sqrt{2}{{\mu }_{0}}I}{\pi L}\]
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question_answer 49) Two thin lenses of focal lengths\[{{f}_{1}}\]and\[{{f}_{2}}\]are placed in contact with each other. The focal length of the combination is
A)
\[\frac{{{f}_{1}}+{{f}_{2}}}{2}\]
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B)
\[\sqrt{{{f}_{1}}}{{f}_{2}}\]
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C)
\[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}+{{f}_{2}}}\]
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D)
\[\frac{{{f}_{1}}{{f}_{2}}}{{{f}_{1}}-{{f}_{2}}}\]
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question_answer 50) For ionising an excited hydrogen atom, the energy required (in eV) will be
A)
a little less than 13.6
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B)
13.6
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C)
more than 13.6
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D)
3.4 or less
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question_answer 51) A hollow sphere of charge does not produce an electric field at any
A)
interior point
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B)
outer point
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C)
beyond 2 m
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D)
beyond 10 m
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question_answer 52) When a force of 0.1 N is applied, the spring is stretched by 1.5 cm. The spring is cut into three parts and one part is stretched by 3 cm. Find the force required for doing so
A)
0.2 N
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B)
0.3 N
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C)
0.4 N
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D)
0.6 N
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question_answer 53) A bomb at rest explodes into 3 parts of the same mass. The momentum of the 2 parts is \[-2p\hat{i}\]and\[p\hat{j}\]. The momentum of the third part will have a magnitude of
A)
\[P\]
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B)
\[\sqrt{3p}\]
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C)
\[p\sqrt{5}\]
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D)
zero
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question_answer 54) A couple produces a
A)
pure linear motion
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B)
pure rotational
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C)
no motion
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D)
both linear (a) and (b)
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question_answer 55) If the external forces acting on a system have zero resultant, the centre of mass
A)
may move but not accelerate
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B)
may accelerate
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C)
must not move
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D)
none of the above
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question_answer 56) In the reaction \[R-C\equiv N+4(H)\xrightarrow[{}]{X}RC{{H}_{2}}N{{H}_{2}}\]\[X\]can be
A)
\[LiAl{{H}_{4}}\]
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B)
\[{{H}_{2}}S{{O}_{4}}\]
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C)
\[Ni\]
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D)
\[2KBr\]
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question_answer 57) At a given temperature the equilibrium constant for the reaction of\[PC{{l}_{5}}PC{{l}_{3}}+C{{l}_{2}}\]is\[2.4\times {{10}^{-3}}\]. At the same temperature, the equilibrium constant for the reaction\[PC{{l}_{3}}(g)+C{{l}_{2}}(g)PC{{l}_{5}}(g)\]is
A)
\[2.4\times {{10}^{-3}}\]
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B)
\[-2.4\times {{10}^{-3}}\]
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C)
\[4.2\times {{10}^{2}}\]
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D)
\[4.8\times {{10}^{-2}}\]
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question_answer 58) Which of the following is called polyamide?
A)
Terylene
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B)
Rayon
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C)
Nylon
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D)
Orion
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question_answer 59) The number of electrons in the valence shell of sulphur in\[S{{F}_{6}}\]is
A)
12
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B)
10
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C)
8
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D)
11
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question_answer 60) The minimum energy required for the reacting molecules to undergo reaction is
A)
potential energy
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B)
kinetic energy
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C)
thermal energy
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D)
activation energy
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question_answer 61) Which of the following is correct for the reaction? \[{{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)\]
A)
\[{{K}_{p}}={{K}_{c}}\]
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B)
\[{{K}_{p}}<{{K}_{c}}\]
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C)
\[{{K}_{p}}>{{K}_{c}}\]
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D)
Pressure is required to predict the correlation
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question_answer 62) The rate constant of a first order reaction is\[6.9\times {{10}^{-3}}{{s}^{-1}}\]. How much time will it take to reduce the initial concentration to its 1/8th value?
A)
100s
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B)
200s
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C)
300s
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D)
400s
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question_answer 63) Which has the minimum freezing point?
A)
One molal\[NaCl\]aqueous solution
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B)
One molal\[CaCla\]aqueous solution
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C)
One molal\[KCl\]aqueous solution
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D)
One molal urea aqueous solution
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question_answer 64) Among the following, the most acidic is
A)
\[C{{H}_{3}}COOH\]
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B)
\[ClC{{H}_{2}}COOH\]
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C)
\[C{{l}_{2}}CHCOOH\]
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D)
\[C{{l}_{2}}CHC{{H}_{2}}COOH\]
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question_answer 65) For a Bohr atom angular momentum M of the electron is: (n = 0, 1, 2, ......)
A)
\[\frac{n{{h}^{2}}}{4\pi }\]
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B)
\[\frac{{{n}^{2}}{{h}^{2}}}{4\pi }\]
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C)
\[\frac{\sqrt{n{{h}^{2}}}}{4\pi }\]
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D)
\[\frac{nh}{2\pi }\]
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question_answer 66) Which of the following combination will form an electrovalent bond?
A)
P and\[Cl\]
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B)
\[N{{H}_{3}}\]and\[B{{F}_{3}}\]
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C)
H and \[Ca\]
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D)
H and \[S\]
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question_answer 67) How many moles of\[A{{l}_{2}}{{(S{{O}_{4}})}_{3}}\]would be in 50 g of the substance?
A)
0.083 mol
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B)
0.952 mol
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C)
0.481 mol
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D)
0.140 mol
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question_answer 68) The IUPAC name of the compound \[C{{H}_{3}}CONHBr\]is
A)
1-bromoacetamide
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B)
ethanoylbromide
done
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C)
N-bromoethanamide
done
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D)
none of the above
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question_answer 69) Which of the following is a condensation polymer?
A)
\[-\left[ N{{H}_{2}}-\overset{\begin{smallmatrix} O \\ |\,| \end{smallmatrix}}{\mathop{C}}\,-{{(C{{H}_{2}})}_{5}} \right]{{-}_{n}}\]
done
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B)
Rubber
done
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C)
Polyvinyl chloride
done
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D)
Polyethylene
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question_answer 70) The solubility of\[Ca{{F}_{2}}\]in pure water is\[2.3\times {{10}^{-4}}mol\text{ }d{{m}^{-3}}\]. Its solubility product will be
A)
\[4.6\times {{10}^{-4}}\]
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B)
\[4.6\times {{10}^{-8}}\]
done
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C)
\[6.9\times {{10}^{-12}}\]
done
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D)
\[4.9\times {{10}^{-11}}\]
done
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question_answer 71) Copper sulphate solution, when added to an excess of ammonium hydroxide, forms a complex compound due to
A)
\[{{[Cu{{(N{{H}_{3}})}_{2}}]}^{2+}}\]
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B)
\[{{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\]
done
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C)
\[{{[Cu{{(N{{H}_{3}})}_{6}}]}^{2+}}\]
done
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D)
\[C{{u}^{2+}}\]
done
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question_answer 72) If a solution containing 0.072 g atom of sulphur in 100 g of a solvent\[({{k}_{f}}=7.0)\]gave a freezing point depression of\[0.84{}^\circ C,\]the molecular formula of sulphur in the solutions is
A)
\[{{S}_{6}}\]
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B)
\[{{S}_{7}}\]
done
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C)
\[{{S}_{8}}\]
done
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D)
\[{{S}_{9}}\]
done
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question_answer 73) Which of the following is a dynamic isomerism?
A)
Metamerism
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B)
Geometrical isomerism
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C)
Tautomerism
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D)
Co-ordinate isomerism
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question_answer 74) When\[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]is converted into\[{{K}_{2}}Cr{{O}_{4}},\]the change in oxidation number of chromium is
A)
0
done
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B)
5
done
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C)
7
done
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D)
9
done
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question_answer 75) Which of the following will be the most effective in the coagulation of\[Fe{{(OH)}_{3}}\]Sol?
A)
\[KCN\]
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B)
\[BaC{{l}_{2}}\]
done
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C)
\[NaCl\]
done
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D)
\[M{{g}_{3}}{{(P{{O}_{4}})}_{2}}\]
done
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question_answer 76) For d-block elements the first ionization potential is of the order
A)
\[Zn>Fe>Cu>Cr\]
done
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B)
\[Sc=Ti<V=Cr\]
done
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C)
\[Zn<Cu<Ni<Co\]
done
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D)
\[V>Cr>Mn>Fe\]
done
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question_answer 77) High basicity of IV^NH relative to\[M{{e}_{3}}N\]is attributed to
A)
effect of solvent
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B)
inductive effect of Me
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C)
shape of \[M{{e}_{2}}NH\]
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D)
shape of\[M{{e}_{3}}N\]
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question_answer 78)
In the reaction
A)
\[SiC\]
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B)
\[{{H}_{2}}S{{O}_{4}}\]
done
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C)
\[KMn{{O}_{4}}\]
done
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D)
\[Fe/HCl\]
done
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question_answer 79) In Grignard reagent the carbon-magnesium bond is
A)
electrovalent
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B)
covalent
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C)
dative
done
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D)
hydrogen bonding
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question_answer 80) The radius of hydrogen atom in the ground state is\[0.53\text{ }\overset{o}{\mathop{\text{A}}}\,\]. The radius of\[L{{i}^{2+}}\]ion (atomic number = 3) in a similar state is
A)
\[0.176\text{ }\overset{o}{\mathop{\text{A}}}\,\]
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B)
\[\text{0}\text{.30 }\overset{o}{\mathop{\text{A}}}\,\]
done
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C)
\[\text{0}\text{.53 }\overset{o}{\mathop{\text{A}}}\,\]
done
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D)
\[\text{1}\text{.23 }\overset{o}{\mathop{\text{A}}}\,\]
done
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question_answer 81) Tyndall effect shown by colloids is due to
A)
scattering of light by the particles
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B)
movements of particles
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C)
reflection of light by the particles
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D)
coagulation of particles
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question_answer 82) Iodine is a
A)
electrovalent solid
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B)
atomic solid
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C)
molecular solid
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D)
covalent solid
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question_answer 83) \[F{{e}^{2+}}\]ion is distinguished from\[F{{e}^{3+}}\]ion by
A)
\[BaC{{l}_{2}}\]
done
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B)
\[KCN\]
done
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C)
\[NaN{{O}_{3}}\]
done
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D)
\[N{{H}_{4}}SCN\]
done
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question_answer 84) Lattice energy of a solid increases if
A)
size of ions is small
done
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B)
charges of ions are small
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C)
ions are neutral
done
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D)
none of the above
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question_answer 85) Which of the following will not give a positive iodoform test?
A)
\[C{{H}_{3}}C{{H}_{2}}CHOHC{{H}_{3}}\]
done
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B)
\[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COC{{H}_{3}}\]
done
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C)
\[C{{H}_{3}}C{{H}_{2}}COC{{H}_{2}}C{{H}_{3}}\]
done
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D)
\[C{{H}_{3}}CO{{C}_{6}}{{H}_{5}}\]
done
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question_answer 86) The reason for the loss of optical activity of lactic acid when\[-OH\]group is changed by H is that
A)
chiral centre of the molecule is destroyed
done
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B)
molecules acquires asymmetry
done
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C)
due to change in configuration
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D)
structural changes occurs
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question_answer 87) To distinguish between salicylic acid and phenol one can use
A)
\[NaHC{{O}_{3}}\]solution
done
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B)
\[5%\text{ }NaOH\]solution
done
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C)
neutral\[FeC{{l}_{3}}\]
done
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D)
bromine water
done
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question_answer 88) \[C-H\]bond energy is about 101 kcal/mol for methane, ethane and other alkanes but is only 77 kcal/mol for\[C-H\]bond of\[C{{H}_{3}}\]in toluene. This is because
A)
of inductive effect due to\[-C{{H}_{3}}\]in toluene
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B)
of the presence of benzene ring in toluene
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C)
of resonance among the structures of benzyl radical in toluene
done
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D)
aromaticity of toluene
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question_answer 89) Which of the following ions can be replaced by \[{{H}^{+}}\]ions when\[{{H}_{2}}\]gas is bubbled through the solutions containing these ions?
A)
\[L{{i}^{+}}\]
done
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B)
\[B{{a}^{2+}}\]
done
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C)
\[C{{u}^{2+}}\]
done
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D)
\[B{{e}^{2+}}\]
done
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question_answer 90) Alum is added to muddy water because
A)
it acts as disinfectant
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B)
it results in coagulation of clay arid sand
done
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C)
clay is soluble in alum, hence removes it
done
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D)
it makes water alkaline which is good for health
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question_answer 91) \[N{{H}_{3}}\]gas is dried over
A)
\[CaO\]
done
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B)
\[HN{{O}_{3}}\]
done
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C)
\[{{P}_{2}}{{O}_{5}}\]
done
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D)
\[CuS{{O}_{4}}\]
done
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question_answer 92) Which one of the following is not correct for an ideal solution?
A)
It must obey Raoults law
done
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B)
\[\Delta H=0\]
done
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C)
\[\Delta U=0\]
done
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D)
\[\Delta H=\Delta V\ne 0\]
done
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question_answer 93) Borax bead test of Cr (chromium) is
A)
green
done
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B)
blue
done
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C)
violet
done
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D)
brown
done
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question_answer 94) A catalyst
A)
lowers the activation energy
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B)
changes the rate constant
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C)
changes the product
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D)
itself destroys in the reaction
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question_answer 95) Which of the following is cross-linked polymer?
A)
Teflon
done
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B)
Orion
done
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C)
Nylon
done
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D)
Bakelite
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question_answer 96) In the reaction sequence\[C{{H}_{3}}CH=C{{H}_{2}}\xrightarrow[(ii){{H}_{2}}O/Zn]{(i){{O}_{3}}}\Pr oducts\]Products will be
A)
\[C{{H}_{3}}COC{{H}_{3}}\]
done
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B)
\[C{{H}_{3}}COC{{H}_{2}}OH\]
done
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C)
\[C{{H}_{3}}COOH+HCOOH\]
done
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D)
\[C{{H}_{3}}CHO+HCHO\]
done
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question_answer 97) The conditions for aromaticity is
A)
molecule must have clouds of delocalized \[\pi -\]electrons
done
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B)
molecule must contain\[(4n+2)\pi -\]electrons
done
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C)
both (a) and (b)
done
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D)
none of the above
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question_answer 98) Which of the following increases the octane number?
A)
Branching of chain
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B)
Absence of double and triple bond
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C)
Non-cyclic alkanes
done
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D)
None of the above
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question_answer 99) Chlorobenzene gives aniline with
A)
\[N{{H}_{3}}/C{{u}_{2}}O\]
done
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B)
\[N{{H}_{3}}/{{H}_{2}}S{{O}_{4}}\]
done
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C)
\[NaN{{H}_{2}}\]
done
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D)
none of these
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question_answer 100) In\[CsCl\] type structure the co-ordination of\[C{{s}^{+}}\]and\[C{{l}^{-}}\]are
A)
6, 6
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B)
6, 8
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C)
8, 8
done
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D)
8, 6
done
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question_answer 101) Hesss law is used to calculate:
A)
enthalpy of reaction
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B)
entropy of reaction
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C)
work done in reaction
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D)
all of the above
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question_answer 102) Which of the following is not a Lewis base?
A)
\[N{{H}_{3}}\]
done
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B)
\[{{H}_{2}}O\]
done
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C)
\[AlC{{l}_{3}}\]
done
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D)
None of these
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question_answer 103) Active charcoal is a good catalyst because
A)
made up of carbon atoms
done
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B)
is very reactive
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C)
has more adsorption power
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D)
has inert nature toward reagent
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question_answer 104) \[{{H}_{2}}\]cannot be displaced by
A)
\[L{{i}^{+}}\]
done
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B)
\[S{{r}^{2+}}\]
done
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C)
\[A{{l}^{3+}}\]
done
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D)
\[A{{g}^{+}}\]
done
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question_answer 105) Which of the following is amphoteric?
A)
\[{{V}_{2}}{{O}_{3}}\]
done
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B)
\[CuO\]
done
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C)
\[{{V}_{2}}{{O}_{5}}\]
done
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D)
\[NiO\]
done
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question_answer 106) The emf of the cell,\[({{E}_{Z{{n}^{2+}}/Zn}}=-0.76\,V)\]\[Zn/Z{{n}^{2+}}(1M)||C{{u}^{2+}}(1M)Cu\]\[({{E}_{C{{u}^{2+}}/Cu}}=+0.34V)\]will be
A)
\[+1.10\text{ }V\]
done
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B)
\[-1.10\text{ }V\]
done
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C)
\[+\text{ }0.42V\]
done
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D)
\[-0.42V\]
done
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question_answer 107) Which of the following is correct number of carbon atom present as the constituent of kerosene oil?
A)
\[{{C}_{10}}-{{C}_{16}}\]
done
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B)
\[{{C}_{4}}-{{C}_{6}}\]
done
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C)
\[{{C}_{8}}-{{C}_{16}}\]
done
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D)
\[{{C}_{12}}-{{C}_{18}}\]
done
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question_answer 108) Water possesses a high dielectric constant, therefore
A)
it always contains ions
done
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B)
it is a universal solvent
done
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C)
can dissolve covalent compounds
done
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D)
can conduct electricity
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question_answer 109) Aldehydes can be oxidised by
A)
Tollens reagent
done
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B)
Fehling solution
done
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C)
Benedict solution
done
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D)
All of these
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question_answer 110) The\[\Delta H_{f}^{o}\]for\[C{{O}_{2}}(g),CO(g)\]and\[{{H}_{2}}O(g)\] are \[-393.5,-110.5\] and \[-241.8~kJ/mol\] respectively. The standard enthalpy change (in kJ) for the reaction\[C{{O}_{2}}(g)+{{H}_{2}}(g)\xrightarrow[{}]{{}}CO(g)+{{H}_{2}}O(g)\]is
A)
524.1
done
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B)
41.2
done
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C)
\[-262.5\]
done
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D)
\[-41.2\]
done
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question_answer 111) Of a total of 600 bolts, 20% are too large and 10% are too small. The remainder are considered to be suitable. If a bolt is selected at random, the probability that it will be suitable is
A)
\[\frac{1}{5}\]
done
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B)
\[\frac{7}{10}\]
done
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C)
\[\frac{1}{10}\]
done
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D)
\[\frac{3}{10}\]
done
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question_answer 112) The area enclosed within the curve\[|x|+|y|=1\]is
A)
1 sq unit
done
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B)
\[2\sqrt{2}\]sq unit
done
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C)
\[\sqrt{2}\]sq unit
done
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D)
2 sq unit
done
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question_answer 113) If\[P(B)=\frac{3}{4},P(A\cap B\cap \overline{C})=\frac{1}{3}\]and\[P(\overline{A}\cap B\cap \overline{C})=\frac{1}{3},\]then\[P(B\cap C)\]is
A)
1/12
done
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B)
1/6
done
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C)
1/15
done
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D)
1/9
done
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question_answer 114) The value of\[\sin \left( {{\sin }^{-1}}\frac{1}{3}+{{\sec }^{-1}}3 \right)+\]\[\cos \left( {{\tan }^{-1}}\frac{1}{2}+{{\tan }^{-1}}2 \right)\]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 115) \[\int_{0}^{\pi /2}{\frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}}}dx\]is equal to
A)
1
done
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B)
\[-1\]
done
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C)
\[\frac{\pi }{2}\]
done
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D)
\[\frac{\pi }{4}\]
done
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question_answer 116) Area bounded by the curve\[y={{\log }_{e}}x,x=0,y\le 0\]and\[x-\]axis is
A)
1 sq unit
done
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B)
1/2 sq unit
done
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C)
2 sq unit
done
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D)
none of these
done
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question_answer 117) If\[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=144\]and\[|\overrightarrow{a}|=4,\]Then\[|\overrightarrow{b}|\]is equal to
A)
12
done
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B)
3
done
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C)
8
done
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D)
4
done
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question_answer 118) Given that\[|\overrightarrow{a}|=3,|\overrightarrow{b}|=4,|\overrightarrow{a}\times \overrightarrow{b}|=10,\]then\[|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}\]equals
A)
88
done
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B)
44
done
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C)
22
done
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D)
none of these
done
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question_answer 119) \[\underset{x\to 0}{\mathop{\lim }}\,x\log \sin x\]is equal to
A)
zero
done
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B)
\[\infty \]
done
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C)
1
done
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D)
cannot be determined
done
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question_answer 120) If\[x=1+a+{{a}^{2}}+......\] to infinity and \[y=1+b+{{b}^{2}}+......\]to infinity, where a, bare proper fractions, then\[1+ab+{{a}^{2}}{{b}^{2}}+...\]to infinity is equal to
A)
\[\frac{xy}{x+y-1}\]
done
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B)
\[\frac{xy}{x-y-1}\]
done
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C)
\[\frac{xy}{x-y+1}\]
done
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D)
\[\frac{xy}{x+y+1}\]
done
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question_answer 121) \[{{\cos }^{4}}\theta -{{\sin }^{4}}\theta \]is equal to
A)
\[1+2{{\sin }^{2}}\left( \frac{\theta }{2} \right)\]
done
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B)
\[2{{\cos }^{2}}\theta -1\]
done
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C)
\[1-2{{\sin }^{2}}\left( \frac{\theta }{2} \right)\]
done
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D)
\[1+2{{\cos }^{2}}\theta \]
done
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question_answer 122) If\[y=f(x)=\frac{x+2}{x-1},\]then
A)
\[x=f(y)\]
done
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B)
\[f(1)=3\]
done
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C)
\[y\]increases with\[x\]for\[x<1\]
done
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D)
\[f\]is a rational function of\[x\]
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question_answer 123) A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is \[60{}^\circ \]. When he retreats 20 ft from the bank, he finds the angle to be\[30{}^\circ \]. The breadth of the river in feet is
A)
15
done
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B)
\[15\sqrt{3}\]
done
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C)
\[10\sqrt{3}\]
done
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D)
\[10\]
done
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question_answer 124) If\[\tan \alpha =\frac{m}{m+1}\]and\[\tan \beta =\frac{1}{2m+1},\]then\[\alpha +\beta \]is equal to
A)
\[\frac{\pi }{3}\]
done
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B)
\[\frac{\pi }{4}\]
done
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C)
zero
done
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D)
\[\frac{\pi }{2}\]
done
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View Answer play_arrow
question_answer 125) If\[f(x)=x[\sqrt{x}-\sqrt{x+1}],\]then
A)
\[f(x)\]is continuous but not differentiable at\[x=0\]
done
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B)
\[f(x)\]is not differentiable at \[x=0\]
done
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C)
\[f(x)\]is differentiable at\[x=0\]
done
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D)
none of the above
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question_answer 126) \[tan\alpha +2\text{ }tan\text{ }2\alpha +4\text{ }tan\text{ }4\alpha +8\text{ }cot\text{ }8\alpha \]is equal to
A)
\[tan\text{ }16\alpha \]
done
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B)
0
done
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C)
\[\cot \alpha \]
done
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D)
none of these
done
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question_answer 127) A book contains 1000 pages numbered consecutively. The probability that the sum of the digits of the number of a page is 9, is
A)
zero
done
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B)
\[\frac{55}{1000}\]
done
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C)
\[\frac{33}{1000}\]
done
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D)
\[\frac{44}{1000}\]
done
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question_answer 128) A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is
A)
\[\frac{1}{8}\]
done
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B)
\[\frac{1}{5}\]
done
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C)
\[\frac{1}{24}\]
done
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D)
\[\frac{1}{6}\]
done
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question_answer 129) If\[\overrightarrow{a}=2\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}-2\hat{j}-\hat{k},\]\[\overrightarrow{c}=\hat{i}+\hat{j}+\hat{k},\] then\[\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})\]equals
A)
\[5\hat{i}-7\hat{j}-3\hat{k}\]
done
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B)
\[5\hat{i}+7\hat{j}-3\hat{k}\]
done
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C)
\[5\hat{i}-7\hat{j}+3\hat{k}\]
done
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D)
zero
done
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question_answer 130) The coefficient of\[{{x}^{4}}\]in the expansion of\[{{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}\]is
A)
\[\frac{504}{259}\]
done
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B)
\[\frac{450}{263}\]
done
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C)
\[\frac{405}{256}\]
done
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D)
none of these
done
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question_answer 131) Equation of the ellipse whose foci are (2, 2) and (4, 2) and the major axis is of length 10, is
A)
\[\frac{{{(x+3)}^{2}}}{24}+\frac{{{(y+2)}^{2}}}{25}=1\]
done
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B)
\[\frac{{{(x-3)}^{2}}}{24}+\frac{{{(y-2)}^{2}}}{25}=1\]
done
clear
C)
\[\frac{{{(x+3)}^{2}}}{24}+\frac{{{(y+2)}^{2}}}{24}=1\]
done
clear
D)
\[\frac{{{(x-3)}^{2}}}{25}+\frac{{{(y-2)}^{2}}}{24}=1\]
done
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question_answer 132) The volume of the solid generated by the revolution of the curve\[y=\frac{{{a}^{3}}}{{{a}^{2}}+{{x}^{2}}}\]about\[x-\]axis is
A)
\[\frac{1}{2}{{\pi }^{3}}{{a}^{2}}\]
done
clear
B)
\[{{\pi }^{3}}{{a}^{2}}\]
done
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C)
\[\frac{1}{2}{{\pi }^{2}}{{a}^{3}}\]
done
clear
D)
\[{{\pi }^{2}}{{a}^{3}}\]
done
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question_answer 133) The radius of the circle\[\left| \frac{z-i}{z+i} \right|=5\]is given by
A)
\[\frac{13}{12}\]
done
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B)
\[\frac{5}{12}\]
done
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C)
5
done
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D)
625
done
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question_answer 134) If\[\overrightarrow{a}=(1,p,1),\overrightarrow{b}=(q,2,2),\overrightarrow{a}.\overrightarrow{b}=r\]and \[\overrightarrow{a}\times \overrightarrow{b}=(0,-3,3)\], then p, q, r are in that order
A)
1, 5, 9
done
clear
B)
9, 5, 1
done
clear
C)
5, 1, 9
done
clear
D)
none of these
done
clear
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question_answer 135) The foci of an ellipse are\[(0,\pm 4)\]and the equations for the directories are\[y=\pm 9\]. The equation for the ellipse is
A)
\[5{{x}^{2}}+9{{y}^{2}}=4\]
done
clear
B)
\[2{{x}^{2}}-6{{y}^{2}}=28\]
done
clear
C)
\[6{{x}^{2}}+3{{y}^{2}}=45\]
done
clear
D)
\[9{{x}^{2}}+5{{y}^{2}}=180\]
done
clear
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question_answer 136) The straight lines \[x+y=0,3x+y-4=0\] and \[x+3y-4=0\]form a triangle which is
A)
right angled
done
clear
B)
equilateral
done
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C)
isosceles
done
clear
D)
none of these
done
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question_answer 137) The eccentricity of the hyperbola \[9{{x}^{2}}-16{{y}^{2}}-18x-64y-199=0\]is
A)
\[\frac{16}{9}\]
done
clear
B)
\[\frac{5}{4}\]
done
clear
C)
\[\frac{25}{16}\]
done
clear
D)
zero
done
clear
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question_answer 138) A four-digit number is formed by the digits 1, 2, 3, 4 with no repetition. The probability that the number is odd, is
A)
zero
done
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B)
1/3
done
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C)
1/4
done
clear
D)
none of these
done
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question_answer 139) The coefficient of\[{{x}^{n}}\]in the expansion of\[\frac{(a-bx)}{{{e}^{x}}}\]is
A)
\[\frac{{{(-1)}^{n}}}{n!}(a+bn)\]
done
clear
B)
\[\frac{{{(-1)}^{n}}}{n!}(b+an)\]
done
clear
C)
\[\frac{{{(-1)}^{n+1}}}{n!}(a+bn)\]
done
clear
D)
none of these
done
clear
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question_answer 140) The value of \[{{\cot }^{-1}}9+\cos e{{c}^{-1}}\frac{\sqrt{41}}{4}\]is given by
A)
0
done
clear
B)
\[\frac{\pi }{4}\]
done
clear
C)
\[{{\tan }^{-1}}2\]
done
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D)
\[\frac{\pi }{2}\]
done
clear
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question_answer 141) The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{x}}+\log (1+x)-{{(1-x)}^{-2}}}{{{x}^{2}}}\]is equal to
A)
0
done
clear
B)
-3
done
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C)
\[-1\]
done
clear
D)
infinity
done
clear
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question_answer 142) The values of k for which the equations \[{{x}^{2}}-kx-21=0\]and\[{{x}^{2}}-3kx+35=0\]will have a common roots are
A)
\[k=\pm 4\]
done
clear
B)
\[k=\pm 1\]
done
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C)
\[k=\pm 3\]
done
clear
D)
\[k=0\]
done
clear
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question_answer 143) \[\overrightarrow{a}\]and\[\overrightarrow{b}\]are two non-zero vectors, then \[(\overrightarrow{a}+\overrightarrow{b})-(\overrightarrow{a}-\overrightarrow{b})\]is equal to
A)
\[a+b\]
done
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B)
\[{{(a-b)}^{2}}\]
done
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C)
\[{{(a+b)}^{2}}\]
done
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D)
\[({{a}^{2}}-{{b}^{2}})\]
done
clear
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question_answer 144) If\[sin\text{ }x+si{{n}^{2}}x=1,\]then \[co{{s}^{6}}x+co{{s}^{12}}x+3\text{ }co{{s}^{10}}x+3\text{ }co{{s}^{8}}x\] is equal to
A)
1
done
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B)
\[co{{s}^{3}}x\text{ }si{{n}^{3}}x\]
done
clear
C)
0
done
clear
D)
\[\infty \]
done
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question_answer 145) The integrating factor of the differential equation\[\frac{dy}{dx}+\frac{1}{x}y=3x\]is
A)
\[x\]
done
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B)
In \[x\]
done
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C)
0
done
clear
D)
\[\infty \]
done
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question_answer 146) \[\int_{0}^{\pi /2}{x{{\sin }^{2}}x{{\cos }^{2}}x}dx\]is equal to
A)
\[\frac{{{\pi }^{2}}}{32}\]
done
clear
B)
\[\frac{{{\pi }^{2}}}{16}\]
done
clear
C)
\[\frac{\pi }{32}\]
done
clear
D)
none of these
done
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question_answer 147) If H is harmonic mean between P and Q, then the value of\[\frac{H}{P}+\frac{H}{Q}\]is
A)
2
done
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B)
\[\frac{PQ}{(P+Q)}\]
done
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C)
\[\frac{(P+Q)}{PQ}\]
done
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D)
none of these
done
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question_answer 148) The value of y for which the equation \[{{x}^{2}}+pxy+{{y}^{2}}-5x-7y+6=0\]represents a pair of straight lines is
A)
5/2
done
clear
B)
5
done
clear
C)
2
done
clear
D)
2/5
done
clear
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question_answer 149) Angle between the vectors\[\sqrt{3}(\overrightarrow{a}\times \overrightarrow{b})\]and\[\overrightarrow{b}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{a}\]is
A)
\[\frac{\pi }{2}\]
done
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B)
0
done
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C)
\[\frac{\pi }{4}\]
done
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D)
\[\frac{\pi }{3}\]
done
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question_answer 150) The equation of the circle passing through (4,5) having the centre (2, 2) is
A)
\[{{x}^{2}}+{{y}^{2}}+4x+4y-5=0\]
done
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B)
\[{{x}^{2}}+{{y}^{2}}-4x-4y-5=0\]
done
clear
C)
\[{{x}^{2}}+{{y}^{2}}-4x=13\]
done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-4x-4y+5=0\]
done
clear
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question_answer 151) The smallest positive integer n for which\[{{\left( \frac{1+i}{1-i} \right)}^{n}}=1\]is
A)
\[n=8\]
done
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B)
\[n=12\]
done
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C)
\[n=16\]
done
clear
D)
none of these
done
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question_answer 152) The equation of tangents drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}-2rx-2hy+{{h}^{2}}=0\] are
A)
\[x=0,y=0\]
done
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B)
\[x=1,y=0\]
done
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C)
\[({{h}^{2}}-{{r}^{2}}))x-2rhy=0,y=0\]
done
clear
D)
\[({{h}^{2}}-{{r}^{2}})x-2rhy=0,x=0\]
done
clear
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question_answer 153) The value of\[{{9}^{1/3}}\times {{9}^{1/9}}\times {{9}^{1/27}}\times ....\infty \]is
A)
9
done
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B)
1
done
clear
C)
3
done
clear
D)
none of these
done
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question_answer 154) Let\[0<P(A)<1,0<P(B)<1\]and\[P(A\cup B)=P(A)+P(B)-P(A)\text{ }P(B),\]then
A)
\[P(B/A)=P(B)-P(A)\]
done
clear
B)
\[P(A\cup B)=P(A)+P(B)\]
done
clear
C)
\[P(A\cap B)=P(A)P(B)\]
done
clear
D)
none of the above
done
clear
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question_answer 155) The probability that in the toss of two dice we obtain the sum 7 or 11, is
A)
\[\frac{1}{6}\]
done
clear
B)
\[\frac{1}{18}\]
done
clear
C)
\[\frac{2}{9}\]
done
clear
D)
\[\frac{23}{108}\]
done
clear
View Answer play_arrow
question_answer 156) If\[{{2}^{x}}+{{2}^{y}}={{2}^{x+y}},\]then\[\frac{dy}{dx}\]is equal to
A)
\[\frac{({{2}^{x}}+{{2}^{y}})}{({{2}^{x}}-{{2}^{y}})}\]
done
clear
B)
\[\frac{({{2}^{x}}+{{2}^{y}})}{(1+{{2}^{x+y}})}\]
done
clear
C)
\[{{2}^{x-y}}\left( \frac{{{2}^{y}}-1}{1-{{2}^{x}}} \right)\]
done
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D)
\[\frac{{{2}^{x+y}}-{{2}^{x}}}{{{2}^{y}}}\]
done
clear
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question_answer 157) If the probability of A to fail in an examination is 0.2 and that for B is 0.3, then probability that either A or B is fail, is
A)
0.5
done
clear
B)
0.44
done
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C)
0.8
done
clear
D)
0.25
done
clear
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question_answer 158) If\[f(x)=\cos (\log x),\]then\[f(x)f(y)-\frac{1}{2}\left[ f\left( \frac{x}{y} \right)+f(xy) \right]\]has the value
A)
\[-1\]
done
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B)
\[\frac{1}{2}\]
done
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C)
\[-2\]
done
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D)
zero
done
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question_answer 159) If\[y={{3}^{x-1}}+{{3}^{-x-1}}\] (\[x\]real), then the least value of y is
A)
2
done
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B)
6
done
clear
C)
2/3
done
clear
D)
none of these
done
clear
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question_answer 160) The value of\[\theta \]lying between\[\theta =0\]and\[\frac{\pi }{2}\]and satisfying the equation\[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\sin 4\theta \\ {{\sin }^{2}}\theta & 1+{{\cos }^{2}}\theta & 4\sin 4\theta \\ {{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 1+4\sin 4\theta \\ \end{matrix} \right|=0\]is
A)
\[\frac{7\pi }{24}\]
done
clear
B)
\[\frac{5\pi }{24}\]
done
clear
C)
\[\frac{11\pi }{2}\]
done
clear
D)
\[\frac{\pi }{24}\]
done
clear
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question_answer 161) \[{{\left( \frac{-1+\sqrt{-3}}{2} \right)}^{100}}+{{\left( \frac{-1-\sqrt{-3}}{2} \right)}^{100}}\]is equal to
A)
2
done
clear
B)
zero
done
clear
C)
\[-1\]
done
clear
D)
1
done
clear
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question_answer 162) If\[\alpha ,\beta \]be the two roots of the equation \[{{x}^{2}}+x+1=0,\]then the equation whose roots are \[\frac{\alpha }{\beta }\]and \[\frac{\beta }{\alpha }\]is
A)
\[{{x}^{2}}+x+1=0\]
done
clear
B)
\[{{x}^{2}}-x+1=0\]
done
clear
C)
\[{{x}^{2}}-x-1=0\]
done
clear
D)
\[{{x}^{2}}+x-1=0\]
done
clear
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question_answer 163) In a binomial distribution, the mean is 4 and variance is 3. Then, its mode is
A)
5
done
clear
B)
6
done
clear
C)
4
done
clear
D)
none of these
done
clear
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question_answer 164) The equation of a line passing through\[(-2,-4)\] and perpendicular to the line\[3x-y+5=0\]is
A)
\[3y+x-8=0\]
done
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B)
\[3x+y+6=0\]
done
clear
C)
\[x+3y+14=0\]
done
clear
D)
none of these
done
clear
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question_answer 165) \[\underset{x\to 0}{\mathop{\lim }}\,{{(\cos ecx)}^{1/\log x}}\]is equal to
A)
0
done
clear
B)
1
done
clear
C)
1/e
done
clear
D)
none of these
done
clear
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question_answer 166) The minimum value of \[f(x)={{\sin }^{4}}x+{{\cos }^{4}}x,0\le x\le \frac{\pi }{2}\]is
A)
\[\frac{1}{2\sqrt{2}}\]
done
clear
B)
\[\frac{1}{4}\]
done
clear
C)
\[\frac{-1}{2}\]
done
clear
D)
\[\frac{1}{2}\]
done
clear
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question_answer 167) A vector of magnitude 5 and perpendicular to. \[(\hat{i}-2\hat{j}+\hat{k})\]and\[(2\hat{i}+\hat{j}-3\hat{k})\]is
A)
\[\frac{5\sqrt{3}}{3}(\hat{i}+\hat{j}+\hat{k})\]
done
clear
B)
\[\frac{5\sqrt{3}}{3}(\hat{i}+\hat{j}-\hat{k})\]
done
clear
C)
\[\frac{5\sqrt{3}}{3}(\hat{i}-\hat{j}+\hat{k})\]
done
clear
D)
\[\frac{5\sqrt{3}}{3}(-\hat{i}+\hat{j}+\hat{k})\]
done
clear
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question_answer 168) \[\int_{-\pi /3}^{\pi /3}{\frac{x\sin x}{{{\cos }^{2}}x}}dx\]is
A)
\[\frac{1}{3}(4\pi +1)\]
done
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B)
\[\frac{4\pi }{3}-2\log \tan \frac{5\pi }{12}\]
done
clear
C)
\[\frac{4\pi }{3}+\log \tan \frac{5}{12}\]
done
clear
D)
none of these
done
clear
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question_answer 169) \[\sum\limits_{r=0}^{m}{^{n+r}{{C}_{n}}}\]is equal to
A)
\[^{n+m+1}{{C}_{n+1}}\]
done
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B)
\[^{n+m+2}{{C}_{n}}\]
done
clear
C)
\[^{n+m+3}{{C}_{n-1}}\]
done
clear
D)
none of these
done
clear
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question_answer 170) The angle between the lines \[2x=3y=-\text{ }z\] and \[6x=-\text{ }y=-4z\]is
A)
\[90{}^\circ \]
done
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B)
\[0{}^\circ \]
done
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C)
\[30{}^\circ \]
done
clear
D)
\[45{}^\circ \]
done
clear
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\[X\]is
