Solved papers for Manipal Engineering Manipal Engineering Solved Paper-2010

done Manipal Engineering Solved Paper-2010

  • question_answer1) In the figure shown, the magnetic field induction at the point 0 will be

    A) \[\frac{{{\mu }_{0}}i}{2\pi r}\]

    B) \[\left( \frac{{{\mu }_{0}}}{4\pi } \right)\left( \frac{i}{r} \right)(\pi +2)\]

    C) \[\left( \frac{{{\mu }_{0}}}{4\pi } \right)\left( \frac{i}{r} \right)(\pi +1)\]

    D) \[\frac{{{\mu }_{0}}i}{4\pi r}(\pi +1)\]

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  • question_answer2) In the electrical network shown in the figure, the potential difference across \[3\,\Omega \] resistance will be

    A) 12V

    B) 2.4V

    C) 24V

    D) 36V

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  • question_answer3) Three identical thermal conductors are connected as shown in figure. Considering no heat loss due to radiation, temperature at the junction will be

    A) \[40{}^\circ C\]

    B) \[60{}^\circ C\]

    C) \[50{}^\circ C\]

    D) \[35{}^\circ C\]

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  • question_answer4) Surface tension vanishes at

    A) absolute zero temperature

    B) transition temperature

    C) critical temperature

    D) None of the above

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  • question_answer5) A transistor is working in common emitter mode. Its amplification factor (\[\beta \]) is 80. If the base current is 250\[\mu A\], the collector current will be

    A) 1.25\[\mu A\]

    B) \[\frac{250}{80}\mu A\]

    C) 430\[\mu A\]

    D) \[250\times 80\,\mu A\]

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  • question_answer6) From an inclined plane two particles are projected with same speed at same angle \[\theta ,\] one up and other down the plane as shown in figure, which of the following statements is/are correct?

    A) The time of flight of each particle is the same

    B) The particles will collide the plane with same speed

    C) Both the particles strike the plane perpendicularly

    D) The particles will collide in midair if projected simultaneously and time of flight of each parrick is less than the time of collision

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  • question_answer7) A battery of emf 10 V is connected to resistance as shown in figure. The potential difference \[{{V}_{A}}-{{V}_{B}}\]between the points A and B is

    A) -2V

    B) 2V

    C) 5V

    D) \[\frac{20}{11}V\]

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  • question_answer8) Solar radiation is

    A) transverse electromagnetic wave

    B) longitudinal electromagnetic wave

    C) stationary wave

    D) None of the above

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  • question_answer9) Fundamental frequency of an open pipe is \[{{f}_{0}},\]Fundamental frequency when it is half filled with water is

    A) \[{{f}_{0}}\]

    B) \[{{f}_{0}}/2\]

    C) \[2{{f}_{0}}\]

    D) \[3{{f}_{0}}\]

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  • question_answer10) If the rms velocity of a gas is v, then

    A) \[{{v}^{2}}T\] = constant

    B) \[{{v}^{2}}/T\] = constant

    C) \[v{{T}^{2}}\] = constant

    D) v is independent of T

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  • question_answer11) A sounding source of frequency 500 Hz moves towards a stationary observer with a velocity 30 m/s. If the velocity of sound in air is 330 m/s, find the frequency beared by the observer.

    A) 500 Hz

    B) 550 Hz

    C) 355 Hz

    D) 55.5 Hz

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  • question_answer12) At what height h above earth, the value of g becomes g/27 (.R = Radius of earth)

    A) 3R

    B) \[\sqrt{2}R\]

    C) \[(\sqrt{2}-1)R\]

    D) \[\frac{1}{\sqrt{2}}R\]

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  • question_answer13) A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. Calculate the minimum time after which it would be possible to work safely with this source.

    A) 12 h

    B) 24 h

    C) 6 h

    D) 130 h

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  • question_answer14) The current in the circuit shown in the figure, considering ideal diode is

    A) 20 A

    B) \[2\times {{10}^{-3}}A\]

    C) 200 A

    D) \[2\times {{10}^{-4}}A\]

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  • question_answer15) The tension in the string in the pulley system shown in the figure is

    A) 75 N

    B) 80 N

    C) 7.5 N

    D) 30 N

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  • question_answer16) A glass flask having mass 390 g and an interior volume of \[500\,c{{m}^{3}}\] floats on water when it is less than half filled with water. The density of material of the flask is

    A) 0.8g/cc

    B) 2.8g/cc

    C) 1.8g/cc

    D) 0.28 g/cc

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  • question_answer17) The angle of minimum deviation \[{{\delta }_{m}}\] for an equilateral glass prism is 30?. Refractive index of the prism is

    A) \[1/\sqrt{2}\]

    B) \[\sqrt{2}\]

    C) \[2\sqrt{2}\]

    D) \[1/2\sqrt{2}\]

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  • question_answer18) When the wavelength of sound changes from 1 m to 1.01 m, the number of beats heard are 4. The velocity of sound is

    A) 404 m/s

    B) 4.04 m/s

    C) 414 m/s

    D) 400 m/s

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  • question_answer19) An ideal gas expands along the path AB as shown in the p-V diagram. The work done is

    A) \[4\times {{10}^{4}}J\]

    B) \[1.2\times {{10}^{5}}J\]

    C) \[2.4\times {{10}^{5}}J\]

    D) None of these

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  • question_answer20) If force is proportional to square of velocity, then the dimensions of proportionality constant is

    A) \[[M{{L}^{-1}}T]\]

    B) \[[M{{L}^{-1}}{{T}^{0}}]\]

    C) \[[ML{{T}^{0}}]\]

    D) \[[{{M}^{0}}L{{T}^{-1}}]\]

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  • question_answer21) Two bodies A and B having temperatures \[327{}^\circ C\] and \[427{}^\circ C\] are radiating heat to the surrounding. The surrounding temperature is \[27{}^\circ C\]. The ratio of rates of heat radiation of A to that of B is

    A) 0.52

    B) 0.31

    C) 0.81

    D) 0.42

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  • question_answer22) Two bulbs 40 W and 60 W and rated voltage 240 V are connected in series across a potential difference of 420 V. Which bulb will work at above its rated voltage?

    A) 60 W bulb

    B) 40 W bulb

    C) Both will work

    D) None of these

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  • question_answer23) Two cars A and B move along a concentric circular path of radius \[{{r}_{A}}\]and \[{{r}_{B}}\] with velocities \[{{v}_{A}}\]and \[{{v}_{B}}\] maintaining constant distance, then \[\frac{{{v}_{A}}}{{{v}_{B}}}\]is equal to

    A) \[\frac{{{r}_{B}}}{{{r}_{A}}}\]

    B) \[\frac{{{r}_{A}}}{{{r}_{B}}}\]

    C) \[\frac{r_{A}^{2}}{r_{B}^{2}}\]

    D) \[\frac{r_{B}^{2}}{r_{A}^{2}}\]

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  • question_answer24) A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 s on it, it moves with a velocity 2 m/s in the opposite direction. The acceleration produced in it is

    A) \[3\,m/{{s}^{2}}\]

    B) \[-3\,m/{{s}^{2}}\]

    C) \[0.3\,m/{{s}^{2}}\]

    D) \[0.03\,m/{{s}^{2}}\]

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  • question_answer25) A beam of light is incident at 60? to a plane surface. The reflected and refracted rays are perpendicular to each other than refractive index of the surface is

    A) \[\sqrt{3}\]

    B) \[\frac{1}{\sqrt{3}}\]

    C) \[\frac{1}{2\sqrt{3}}\]

    D) None of these

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  • question_answer26) Two wires of lengths \[l\] and \[2l,\] radii r and 2r respectively having same Youngs modulus are hung with a weight mg. Net elongation is

    A) \[\frac{3mgl}{\pi {{r}^{2}}Y}\]

    B) \[\frac{2mgl}{3\pi {{r}^{2}}Y}\]

    C) \[\frac{3mgl}{2\pi {{r}^{2}}Y}\]

    D) \[\frac{3mgl}{4\pi {{r}^{2}}Y}\]

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  • question_answer27) A ball rolls off the top of stairway with a horizontal velocity of magnitude 1.8 m/s. The steps are 0.20 m high and 0.20 m wide. Which step will the ball hit first?

    A) First

    B) Second

    C) Third

    D) Fourth

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  • question_answer28) The peak value of an alternating emf E given by \[E={{E}_{0}}\cos \omega t\] is 10 V and its frequency is 50 Hz. At a time \[t=\frac{1}{600}\]s, the instantaneous value of the emf is

    A) 10 V

    B) \[5\sqrt{3}v\]

    C) 5V

    D) 1V

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  • question_answer29) A circuit area \[0.01\,{{m}^{2}}\] is kept inside a magnetic field which is normal to its plane. The magnetic field changes from 2 T to 1 T in 1 ms. if the resistance of the circuit is 2\[\Omega \]. The amount of heat evolved is

    A) 0.05 J

    B) 50 J

    C) 0.50 J

    D) 500 J

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  • question_answer30) A convex lens is placed between object and a screen. The size of object is 3 cm and an image of height 9 cm is obtained on the screen. When the lens is displaced to a new position, what will be the size of image on the screen?

    A) 2 cm

    B) 6 cm

    C) 4 cm

    D) 1 cm

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  • question_answer31) A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is 2R, then the ratio of initial to final pressures is nearly equal to

    A) 5

    B) 6.5

    C) 7

    D) 3.5

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  • question_answer32) Two pendulums have time periods T and 5T/4. They start SHM at the same time from the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation?

    A) \[45{}^\circ \]

    B) \[90{}^\circ \]

    C) \[60{}^\circ \]

    D) \[30{}^\circ \]

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  • question_answer33) A body is coming with a velocity of 72 km/h on a rough horizontal surface of coefficient of friction 0.5. If the acceleration due to gravity is \[10\,m/{{s}^{2}},\] find the minimum distance it can be stopped.

    A) 400m

    B) 40m

    C) 0.40m

    D) 4m

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  • question_answer34) A bullet comes out of the barrel of gun of length 2 m with a speed 80 m/s. The average acceleration of the bullet is

    A) \[1.6\,m/{{s}^{2}}\]

    B) \[160\,\,m/{{s}^{2}}\]

    C) \[1600\,\,m/{{s}^{2}}\]

    D) \[16\,\,m/{{s}^{2}}\]

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  • question_answer35) A disc of radius 0.1 m is rotating with a frequency 10 rev/s in a normal magnetic field of strength 0.1 T. Net induced emf is

    A) \[2\pi \times {{10}^{-2}}v\]

    B) \[\pi \times {{10}^{-2}}v\]

    C) \[\frac{\pi }{2}{{10}^{-2}}V\]

    D) None of these

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  • question_answer36) 1 \[c{{m}^{3}}\] of water at its boiling point absorbs 540 cal of heat to becomes steam with a volume of 1671 \[c{{m}^{3}}\]. If the atmospheric pressure \[=1.013\times {{10}^{5}}\,N/{{m}^{2}}\]and the mechanical equivalent of heat =4.19 J/cal, the energy spent in this process in overcoming intermolecular forces is

    A) 540 cal

    B) 40 cal

    C) 500 cal

    D) zero

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  • question_answer37) A string fixed at both ends oscillaress in 5 segments, length 10 m and velocity of wave is 20 m/s. What is the frequency?

    A) 5 Hz

    B) 15 Hz

    C) 10 Hz

    D) 2 Hz

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  • question_answer38) When the amplitude of a body executing SHM becomes twice what happens?

    A) Maximum potential energy is doubled

    B) Maximum kinetic energy is doubled

    C) Total energy is doubled

    D) Maximum velocity is doubled

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  • question_answer39) The time period of a geostationary satellite at a height 36000 km is 24 h. A spy satellite orbits earth at a height 6400 km. What will be the time period of spy satellite? [Radius of the earth = 6400 km]

    A) 5 h

    B) 4 h

    C) 3h

    D) 12 h

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  • question_answer40) A bomb of mass 9 kg explodes into two parts. One part of mass 3 kg moves with velocity 16 m/s, then the KE of the other part is

    A) 162 J

    B) 150 J

    C) 192 J

    D) 200 J

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  • question_answer41) In the reaction \[_{7}{{N}^{14}}+\alpha {{\to }_{8}}{{X}^{17}}{{+}_{1}}{{p}^{1}}\] identify X.

    A) \[{{O}_{2}}\]

    B) \[{{N}_{2}}\]

    C) He

    D) Ar

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  • question_answer42) Current in a coil changes from 5 A to 10 A in 0.2 s. If the coefficient of self-induction is 10 H, then the inducedi emf is

    A) 112 V

    B) 250 V

    C) 125 V

    D) 230 V

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  • question_answer43) The force of interaction between two charges \[{{q}_{1}}=6\mu C\]and \[{{q}_{2}}=2\mu C\] N. If charge \[q=-2\mu C\] is added to each of the charges, then the new force of interaction is

    A) \[2\times {{10}^{-7}}N\]

    B) Zero

    C) 30 N

    D) \[2\times {{10}^{-3}}N\]

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  • question_answer44) The number of turns in primary coil of a transformer is 20 and the number of turns in the secondary is 10. If the voltage across the primary is 220 V, what is the voltage across the secondary?

    A) 110 V

    B) 130 V

    C) 190 V

    D) 310 V

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  • question_answer45) An electron of an atom transits from\[{{n}_{1}}\], to \[{{n}_{2}}\] . In which of the following, maximum frequency of photon will be emitted?

    A) \[{{n}_{1}}=1\,to\,{{n}_{2}}=2\]

    B) \[{{n}_{1}}=2\,\,to\,\,{{n}_{2}}=1\]

    C) \[{{n}_{1}}=2\,\,to\,\,{{n}_{2}}=6\]

    D) \[{{n}_{1}}=6\,\,to\,\,{{n}_{2}}=2\]

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  • question_answer46) A rod of length L and mass M is bent to form a semicircular ring as shown in figure. The moment of inertia about XY is

    A) \[\frac{1}{4}\frac{M{{L}^{2}}}{{{\pi }^{2}}}\]

    B) \[\frac{2M{{L}^{2}}}{3{{\pi }^{2}}}\]

    C) \[\frac{M{{L}^{2}}}{2}\]

    D) \[\frac{M{{L}^{2}}}{2}\]

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  • question_answer47) In the figure shown, \[{{m}_{1}}=10kg,\,{{m}_{2}}=6\,kg,\] \[{{m}_{4}}=4kg.\,\,\,\]If\[{{T}_{3}}=40N,\,{{T}_{2}}=?.\,\,\,\]

    A) 13 N

    B) 32 N

    C) 25 N

    D) 35 N

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  • question_answer48) A stone is thrown at an angle 9 to be horizontal reaches a maximum height H. Then the time of flight of stone will be

    A) \[\sqrt{\frac{2H}{g}}\]

    B) \[2\sqrt{\frac{2H}{g}}\]

    C) \[\frac{2\sqrt{2H\,\sin \theta }}{g}\]

    D) \[\frac{\sqrt{2H\,\sin \theta }}{g}\]

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  • question_answer49) Two parallel plates of area A are separated by two different dielectrics as shown in figure. The net capacitance is

    A) \[\frac{{{\varepsilon }_{0}}A}{2d}\]

    B) \[\frac{{{\varepsilon }_{0}}A}{d}\]

    C) \[\frac{3{{\varepsilon }_{0}}A}{d}\]

    D) \[\frac{4{{\varepsilon }_{0}}A}{3d}\]

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  • question_answer50) Two springs of force constants \[{{k}_{1}}\] and \[{{k}_{2}}\] are connected as shown. The effective spring constant k is

    A) \[{{k}_{1}}+{{k}_{2}}\]

    B) \[\frac{{{k}_{1}}}{{{k}_{2}}}\]

    C) \[{{k}_{1}}{{k}_{2}}\]

    D) \[2{{k}_{1}}{{k}_{2}}\]

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  • question_answer51) A body of weight 2 kg is suspended as shown in figure. The tension \[{{T}_{1}}\] in the horizontal string (in kg-wt) is

    A) \[2/\sqrt{3}\]

    B) \[\sqrt{3}/2\]

    C) \[2\sqrt{3}\]

    D) 2

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  • question_answer52) If the momentum of a body is increased by 100%, then the percentage increase in the kinetic energy is

    A) 150%

    B) 200%

    C) 225%

    D) 300%

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  • question_answer53) In Youngs double slit experiment, slit separation is 0.6 mm and the separation between slit and screen is 1.2 m. The angular width is (the wavelength of light used is \[4800\overset{\text{o}}{\mathop{\text{A}}}\,\])

    A) 30 rad

    B) \[8\times {{10}^{-4}}\] rad

    C) 12 rad

    D) 70.5 rad

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  • question_answer54) X-ray of wavelength \[\lambda =2\overset{0}{\mathop{A}}\,\]is emitted from the metal target. The potential difference applied across the cathode and the metal target is

    A) 5525 V

    B) 320 V

    C) 6200 V

    D) 3250 V

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  • question_answer55) Two identical masses m moving with velocities \[{{u}_{1}}\] and \[{{u}_{2}}\] collide perfectly inefasticatiy. Find the loss in energy.

    A) \[m({{u}_{1}}-u_{2}^{2})\]

    B) \[\frac{m}{4}{{({{u}_{1}}-{{u}_{2}})}^{2}}\]

    C) \[\frac{m}{2}{{({{u}_{1}}-{{u}_{2}})}^{2}}\]

    D) \[m{{({{u}_{1}}-{{u}_{2}})}^{3}}\]

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  • question_answer56) A constant torque acting on a uniform circular wheel changes its angular momentum from \[{{A}_{0}}\] to \[4{{A}_{0}}\] in 4s. The magnitude of this torque is

    A) \[\frac{3{{A}_{0}}}{4}\]

    B) \[{{A}_{0}}\]

    C) 4\[{{A}_{0}}\]

    D) 12\[{{A}_{0}}\]

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  • question_answer57) When a number of small droplets combines to form a large drop, then

    A) energy is absorbed

    B) energy is liberated

    C) energy is neither liberated nor absorbed

    D) process is independent of energy

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  • question_answer58) With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is \[\frac{2}{3}\]of the weight?

    A) \[\frac{2}{3}g\]

    B) g

    C) \[\frac{1}{3}g\]

    D) Zero

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  • question_answer59) If two waves represented by \[{{y}_{1}}=4\sin \,\omega t\] and \[{{y}_{2}}=3\sin \left( \omega t+\frac{\pi }{3} \right)\]interfere at a point. The amplitude of the resulting wave will be about

    A) 7

    B) 6

    C) 5

    D) 3.5

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  • question_answer60) Saturated vapor is compressed to half its volume without any change in temperature, then the pressure will be

    A) doubled

    B) halved

    C) the same

    D) Zero

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  • question_answer61) The root mean square velocity of a gas is doubled when the temperature is

    A) increased four times

    B) increased two times

    C) reduced to half

    D) reduced to one fourth

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  • question_answer62) Acidity of phenol is due to

    A) hydrogen bonding

    B) phenolic group

    C) benzene ring

    D) resonance stabilization of its anion

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  • question_answer63) In which one of the following pairs the radius of the second species is greater than that of the first?

    A) \[Na,\,\,Mg\]

    B) \[{{O}^{2-}},\,\,{{N}^{3-}}\]

    C) \[L{{i}^{+}},\,\,B{{e}^{2+}}\]

    D) \[B{{a}^{2+}},\,\,S{{r}^{2+}}\]

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  • question_answer64) The radius of the first Bohr orbit of hydrogen atom is\[0.529\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]. The radius of the third orbit of\[{{H}^{+}}\]will be

    A) \[8.46\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    B) \[0.705\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    C) \[1.59\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

    D) \[4.79\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]

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  • question_answer65) Both\[C{{o}^{3+}}\]and\[P{{t}^{4+}}\]have a coordination number of six. Which of the following pairs of complexes will show approximately the same electrical conductance for their\[~0.001\,\,M\]aqueous solutions?

    A) \[CoC{{l}_{3}}\cdot 4N{{H}_{3}}\]and\[PtC{{l}_{4}}\cdot 4N{{H}_{3}}\]

    B) \[CoC{{l}_{3}}\cdot 3N{{H}_{3}}\]and\[PtC{{l}_{4}}\cdot 5N{{H}_{3}}\]

    C) \[CoC{{l}_{3}}\cdot 6N{{H}_{3}}\]and\[PtC{{l}_{4}}\cdot 5N{{H}_{3}}\]

    D) \[CoC{{l}_{3}}\cdot 6N{{H}_{3}}\]and\[PtC{{l}_{4}}\cdot 3N{{H}_{3}}\]

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  • question_answer66) When ice melts into water, the entropy

    A) becomes zero

    B) remains same

    C) decreases

    D) increases

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  • question_answer67) Reduction of nitrobenzene in the presence of\[Zn/N{{H}_{4}}Cl\]gives

    A) azobenzene

    B) hydrazobenzene

    C) N-phenyl hydroxyl amine

    D) aniline

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  • question_answer68) Which one of the following is not a protein?

    A) Wool

    B) Nail

    C) Hair

    D) DNA

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  • question_answer69) Which of the following hexoses will form the same osazone when treated with excess phenyl hydrazine?

    A) D-glucose, D-fructose and D-galactose

    B) D-glucose, D-fructose and D-mannose

    C) D-glucose, D-mannose and D-galactose

    D) D-fructose, D-mannose and D-galactose

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  • question_answer70) A silver cup is plated with silver by passing 965C of electricity. The amount of\[Ag\]deposited is

    A) 107.89 g

    B) 9.89 g

    C) 1.0002 g

    D) 1.08 g

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  • question_answer71) The standard emf of a cell involving one electron change is found to be\[0.591V\]at\[{{25}^{o}}C\]. The equilibrium constant of the reaction is \[(F=96,500\,\,C\,\,mo{{l}^{-1}})\]

    A) \[1.0\times {{10}^{1}}\]

    B) \[1.0\times {{10}^{5}}\]

    C) \[1.0\times {{10}^{10}}\]

    D) \[1.0\times {{10}^{30}}\]

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  • question_answer72) \[E{}^\circ \]values of\[M{{g}^{2+}}/Mg\]is\[-2.37\,\,V\]of\[Z{{n}^{2+}}/Zn\]is\[-0.76\,\,V\] and\[F{{e}^{2+}}/Fe\]is\[-0.44\,\,V\]. Which of the statements is correct?

    A) \[Zn\]will reduce\[F{{e}^{2+}}\]

    B) \[Zn\]will reduce\[M{{g}^{2+}}\]

    C) \[Mg\]oxidizes\[Fe\]

    D) \[Zn\]oxidizes\[Fe\]

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  • question_answer73) The maximum proportion of available volume that can be filled by hard spheres in diamond is

    A) 0.52

    B) 0.34

    C) 0.32

    D) 0.68

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  • question_answer74) If we mix a pentavalent impurity in a crystal lattice of germanium, what type of semiconductor formation will occur?

    A) \[p-\]type

    B) \[n-\]type

    C) Both (a) and (b)

    D) None of the two

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  • question_answer75) Which one of the following complexes is an outer orbital complex? (Atomic numbers\[Mn=25,\,\,Fe=26,\,\,Co=27,\] \[Ni=28\])

    A) \[{{[Fe{{(CN)}_{6}}]}^{4-}}\]

    B) \[{{[Mn{{(CN)}_{6}}]}^{4-}}\]

    C) \[{{[Co{{(N{{H}_{3}})}_{6}}]}^{3+}}\]

    D) \[{{[Ni{{(N{{H}_{3}})}_{6}}]}^{2+}}\]

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  • question_answer76) The product of reaction between alcoholic silver nitrite with ethyl bromide is

    A) ethene

    B) ethane

    C) ethyl nitrile

    D) nitro ethane

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  • question_answer77) \[Iso-\]propyl chloride undergoes hydrolysis by

    A) \[{{S}_{N}}1\] mechanism

    B) \[{{S}_{N}}2\]mechanisms

    C) \[{{S}_{N}}1\]and\[{{S}_{N}}2\]mechanisms

    D) Neither\[{{S}_{N}}1\]nor\[{{S}_{N}}2\]mechanism

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  • question_answer78) \[o-\]toluic acid on reaction with\[B{{r}_{2}}+Fe\]gives

    A)

    B)

    C)

    D)

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  • question_answer79) Consider the acidity of the carboxylic acids

    I.\[PhCOOH\]
    II.\[o-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\]
    III.\[p-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\]
    IV.\[m-N{{O}_{2}}{{C}_{6}}{{H}_{4}}COOH\]
    Which of the following order is correct?

    A) \[I>II>III>IV\]

    B) \[II>IV>III>I\]

    C) \[II>IV>I>III\]

    D) \[II>III>IV>I\]

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  • question_answer80) Which of the following does not answer iodoform test?

    A) \[n-\]butyl alcohol

    B) Acetophenone

    C) Acetaldehyde

    D) Ethylmethyl ketone

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  • question_answer81) Which one of the following undergoes reaction with 50% sodium hydroxide solution to give the corresponding alcohol and acid?

    A) Phenol

    B) Benzaldehyde

    C) Butanal

    D) Benzoic acid

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  • question_answer82) The\[IUPAC\]name of \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-CH=\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,-CHO\]is

    A) 4-hydroxy-1-methylpentanal

    B) 4-hydroxy-2-methylpent-2-en-1 -al

    C) 2-hydroxy-4-methylpent-3-en-5 -al

    D) 2-hydroxy-3-methylpent-2-en-5-al

    View Answer play_arrow
  • question_answer83) The activation energy of exothermic reaction \[A\to B\]is\[80\,\,kJ\,\,mo{{l}^{-1}}\]. The heat of reaction is\[200\,\,kJ\,\,mo{{l}^{-1}}\]. The activation energy for the reaction\[B\to A\]\[(in\,\,kJ\,\,mo{{l}^{-1}})\]will be

    A) 80

    B) 120

    C) 40

    D) 280

    View Answer play_arrow
  • question_answer84) Which of the following electrolytes is least effective in coagulating ferric hydroxide solution?

    A) \[KBr\]

    B) \[{{K}_{2}}S{{O}_{4}}\]

    C) \[{{K}_{2}}Cr{{O}_{4}}\]

    D) \[{{K}_{4}}[Fe{{(CN)}_{6}}]\]

    View Answer play_arrow
  • question_answer85) Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

    A) \[(n-1){{d}^{8}},\,\,n{{s}^{2}}\]

    B) \[(n-1){{d}^{5}},\,\,n{{s}^{1}}\]

    C) \[(n-1){{d}^{3}},\,\,n{{s}^{2}}\]

    D) \[(n-1){{d}^{5}},\,\,n{{s}^{2}}\]

    View Answer play_arrow
  • question_answer86) The relative lowering of vapour pressure of a dilute aqueous solution containing nonvolatile solute is 0.0125. The molality of the solution is about

    A) 0.70

    B) 0.50

    C) 0.90

    D) 0.80

    View Answer play_arrow
  • question_answer87) When hydrogen peroxide is added to acidified potassium dichromate, a blue colour is produced due to formation of

    A) \[CrC{{O}_{3}}\]

    B) \[C{{r}_{2}}{{O}_{3}}\]

    C) \[Cr{{O}_{5}}\]

    D) \[CrO_{4}^{2-}\]

    View Answer play_arrow
  • question_answer88) In the following reaction, \[NaOH+S\xrightarrow{{}}A+N{{a}_{2}}S+{{H}_{2}}O;A\]is

    A) \[N{{a}_{2}}S{{O}_{4}}\]

    B) \[N{{a}_{2}}S{{O}_{3}}\]

    C) \[N{{a}_{2}}S\]

    D) \[N{{a}_{2}}{{S}_{2}}{{O}_{3}}\]

    View Answer play_arrow
  • question_answer89) On igniting\[F{{e}_{2}}{{O}_{3}}\]at\[{{1400}^{o}}C\], the product obtained is

    A) \[F{{e}_{2}}{{O}_{3}}\,\,melt\]

    B) \[FeO\]

    C) \[F{{e}_{3}}{{O}_{4}}\]

    D) metallic iron

    View Answer play_arrow
  • question_answer90) Sulphuric acid has great affinity for water because

    A) it hydrolyses the acid

    B) it decomposes the acid

    C) acid forms hydrates with water

    D) acid decomposes water

    View Answer play_arrow
  • question_answer91) Helium-oxygen mixture is used by deep sea divers in preference to nitrogen-oxygen mixture because

    A) helium is much less soluble in blood than nitrogen

    B) nitrogen is much less soluble in blood than helium

    C) due to high pressure deep under the sea nitrogen and oxygen react to give poisonous nitric oxide

    D) nitrogen is highly soluble in water

    View Answer play_arrow
  • question_answer92) One mole of\[C{{O}_{2}}\]contains

    A) \[3\,\,g\]atoms of\[C{{O}_{2}}\]

    B) \[18.1\times {{10}^{23}}\]molecules of\[C{{O}_{2}}\]

    C) \[6.02\times {{10}^{23}}\]atoms of\[O\]

    D) \[6.02\times {{10}^{23}}\]atoms of\[C\]

    View Answer play_arrow
  • question_answer93) The equivalent weight of \[KMn{{O}_{4}}\] for acid solution is

    A) 79

    B) 52.16

    C) 158

    D) 31.6

    View Answer play_arrow
  • question_answer94) Which has the highest weight?

    A) \[1\,\,{{m}^{3}}\]of water

    B) A normal adult man

    C) \[10\,\,L\]of\[Hg\]

    D) All have same weight

    View Answer play_arrow
  • question_answer95) Which has the highest\[e/m\]ratio?

    A) \[H{{e}^{2+}}\]

    B) \[{{H}^{+}}\]

    C) \[H{{e}^{+}}\]

    D) \[{{D}^{+}}\]

    View Answer play_arrow
  • question_answer96) The ionization potential order for which set is correct?

    A) \[Cs<Li<K\]

    B) \[Cs>Li>B\]

    C) \[Li>K>Cs\]

    D) \[B>Li<K\]

    View Answer play_arrow
  • question_answer97) The oxidation state of\[Fe\]in\[F{{e}_{3}}{{O}_{4}}\]is

    A) \[+3\]

    B) \[8/3\]

    C) \[+6\]

    D) \[+2\]

    View Answer play_arrow
  • question_answer98) For a first order reaction, the concentration changes from 0.8 to 0.4 in 15 min. The time taken for the concentration to change from \[0.01\,\,M\]to\[0.025\,\,M\] is

    A) 30 min

    B) 15 min

    C) 7.5 min

    D) 60 min

    View Answer play_arrow
  • question_answer99) When phenol is treated with excess of bromine water, it gives

    A) \[m-\]bromophenol

    B) \[o-\]and prbromophenols

    C) \[2,\,\,4-\]dibromophenol

    D) \[2,\,\,4,\,\,6-\]tribromophenol

    View Answer play_arrow
  • question_answer100) Which reaction is suitable for the preparation of \[\alpha -\]chloroacetic acid?

    A) Hell-Volhard Zelinsky reaction

    B) Nef reaction

    C) Stephens reaction

    D) Perkin condensation

    View Answer play_arrow
  • question_answer101) Which one of the following compounds will dissolve in an alkali solution after it has undergone reaction with Hinsberg reagent?

    A) \[C{{H}_{3}}N{{H}_{2}}\]

    B) \[{{(C{{H}_{3}})}_{3}}N\]

    C) \[{{({{C}_{2}}{{H}_{5}})}_{2}}NH\]

    D) \[{{C}_{6}}{{H}_{5}}NH{{C}_{6}}{{H}_{5}}\]

    View Answer play_arrow
  • question_answer102) Angle strain in cyclopropane is

    A) \[24{}^\circ 44\]

    B) \[9{}^\circ 44\]

    C) \[44\]

    D) \[-5{}^\circ 16\]

    View Answer play_arrow
  • question_answer103) A group of atoms can function as a ligand only when

    A) it is a small molecule

    B) it has an unshared electron pair

    C) it is a negatively charged ion

    D) it is a positively charged ion

    View Answer play_arrow
  • question_answer104) The bond order in\[NO\]is 2.5 while that in\[N{{O}^{+}}\]is 3. Which of the following statements is true for these two species?

    A) Bond length in\[N{{O}^{+}}\]is greater than in\[NO\]

    B) Bond length in\[NO\]is greater than In\[N{{O}^{+}}\]

    C) Bond length in\[N{{O}^{+}}\]is equal to that in\[NO\]

    D) Bond length is unpredictable

    View Answer play_arrow
  • question_answer105) In a homonuclear molecule which of the following set of orbitals is degenerate?

    A) \[\sigma 2s\]and\[\sigma 1s\]

    B) \[\pi 2{{p}_{x}}\]and\[\pi 2{{p}_{y}}\]

    C) \[\pi 2{{p}_{x}}\]and\[\sigma 2{{p}_{z}}\]

    D) \[\sigma 2{{p}_{z}}\]and\[\pi 2{{p}_{x}}\]

    View Answer play_arrow
  • question_answer106) The pH of a neutral water sample is 6.5. Then the temperature of water

    A) is\[{{25}^{o}}C\]

    B) is more than\[{{25}^{o}}C\]

    C) is less than \[{{25}^{o}}C\]

    D) can be more or less than\[{{25}^{o}}C\]

    View Answer play_arrow
  • question_answer107) Which is Lewis acid?

    A) \[B{{F}_{3}}\]

    B) \[N{{F}_{3}}\]

    C) \[C{{l}^{-}}\]

    D) \[{{H}_{2}}O\]

    View Answer play_arrow
  • question_answer108) The\[pH\]of\[{{10}^{-10}}M\,\,NaOH\]solution is nearest to

    A) 4

    B) -10

    C) 4

    D) 7

    View Answer play_arrow
  • question_answer109) Which of the following is not true for carbanions?

    A) The carbon carrying the charge has eight valence electrons

    B) They are formed by heterolytic fission

    C) They are paramagnetic

    D) The carbon carrying the charge is \[s{{p}^{3}}\] hybridized

    View Answer play_arrow
  • question_answer110) Which among the following statements is correct with respect to the optical isomers?

    A) Enantiomers are non-superimposable mirror images

    B) Diastereomers are superimposable mirror images

    C) Enantiomers are superimposable mirror images

    D) Meso forms have no plane of symmetry

    View Answer play_arrow
  • question_answer111) Inductive effect involves

    A) delocalisation of\[\sigma -\]electrons

    B) displacement of\[\sigma -\]electrons

    C) delocalisation of \[n-\]electrons

    D) displacement of\[\pi -\]electrons

    View Answer play_arrow
  • question_answer112) The solubility of\[AgCl\]in\[0.2\,\,M\,\,NaCl\]solution is\[({{K}_{sp}}\,\,of\,\,AgCl=1.20\times {{10}^{-10}})\]

    A) \[6.0\times {{10}^{-10}}M\]

    B) \[0.2M\]

    C) \[1.2\times {{10}^{-10}}M\]

    D) \[0.2\times {{10}^{-10}}M\]

    View Answer play_arrow
  • question_answer113) Lipids are

    A) nucleic acids occurring in plants

    B) proteins occurring in animals

    C) carbohydrates occurring in plants

    D) fats of natural origin

    View Answer play_arrow
  • question_answer114) The enzyme pepsin hydrolyses

    A) proteins to amino acids

    B) fats to fatty acids

    C) glucose to ethyl alcohol

    D) polysaccharides to monosaccharides

    View Answer play_arrow
  • question_answer115) Carboy cannot be used in the reduction of\[A{{l}_{2}}{{O}_{3}}\]because

    A) it is an expensive proposition

    B) the enthalpy of formation of\[C{{O}_{2}}\]is more than that of\[A{{l}_{2}}{{O}_{3}}\]

    C) pure carbon is not easily available

    D) the enthalpy of formation of\[A{{l}_{2}}{{O}_{3}}\]is too high

    View Answer play_arrow
  • question_answer116) Oxalic acid when heated with cone\[{{H}_{2}}S{{O}_{4}}\], gives

    A) \[{{H}_{2}}{{O}_{2}}\]and\[C{{O}_{2}}\]

    B) \[CO\]and\[C{{O}_{2}}\]

    C) \[{{H}_{2}}{{O}_{2}}\]and\[CO\]

    D) \[CaC{{l}_{2}}\]

    View Answer play_arrow
  • question_answer117) At\[{{25}^{o}}C\], the highest osmotic pressure is exhibited by\[0.1\,\,M\]solution of

    A) urea

    B) glucose

    C) \[KCl\]

    D) \[CaC{{l}_{2}}\]

    View Answer play_arrow
  • question_answer118) Ammonia is dried over

    A) slaked lime

    B) calcium chloride

    C) phosphorus pentoxide

    D) quicklime

    View Answer play_arrow
  • question_answer119) \[{{C}_{6}}{{H}_{6}}\xrightarrow[350\,\,K]{{{H}_{2}}S{{O}_{4}}}A\xrightarrow[Fusion]{Alkali}B\xrightarrow[{{H}_{2}}O]{B{{r}_{2}}}C\] In the above sequence, C is

    A) \[o-\]bromophenol

    B) \[p-\]bromophenol

    C) \[m-\]bromophenol

    D) \[2,\,\,4,\,\,6-\]tribromophenol

    View Answer play_arrow
  • question_answer120) Collins reagent is used to convert

    A) \[\rangle C=O\xrightarrow{{}}\rangle CHOH\]

    B) \[-C{{H}_{2}}OH\xrightarrow{{}}-CHO\]

    C) \[-CHO\xrightarrow{{}}COOH\]

    D) \[-CHO\xrightarrow{{}}-C{{H}_{2}}OH\]

    View Answer play_arrow
  • question_answer121) The range of the function\[f(x)={{\log }_{e}}(3{{x}^{2}}-4x+5)\]is

    A) \[\left( -\infty ,\,\,{{\log }_{e}}\frac{11}{3} \right]\]

    B) \[\left[ {{\log }_{e}}\frac{11}{3},\,\,\infty \right)\]

    C) \[\left[ -{{\log }_{e}}\frac{11}{3},\,\,{{\log }_{e}}\frac{11}{3} \right]\]

    D) None of the above

    View Answer play_arrow
  • question_answer122) The domain of the function \[f(x)=\frac{\sqrt{9-{{x}^{2}}}}{{{\sin }^{-1}}(3-x)}\]

    A) \[(2,\,\,3)\]

    B) \[[2,\,\,3)\]

    C) \[(2,\,\,3]\]

    D) None of these

    View Answer play_arrow
  • question_answer123) The numbers\[a{{}_{n}}s\]are defined by \[{{a}_{0}}=1,\,\,{{a}_{n+1}}=3{{n}^{2}}+n+{{a}_{n}},\,\,(n\ge 0)\] Then,\[{{a}_{n}}\]is equal to

    A) \[{{n}^{3}}+{{n}^{2}}+1\]

    B) \[{{n}^{3}}-{{n}^{2}}+1\]

    C) \[{{n}^{3}}-{{n}^{2}}\]

    D) \[{{n}^{3}}+{{n}^{2}}\]

    View Answer play_arrow
  • question_answer124) Nishi has 5 coins each of the different denomination. The number different sums of money she conform

    A) 32

    B) 25

    C) 31

    D) None of these

    View Answer play_arrow
  • question_answer125) There are P copies of n-different books. The number of different ways in which a non-empty selection can be made from them, is

    A) \[{{(P+1)}^{n}}-1\]

    B) \[{{P}^{n}}-1\]

    C) \[{{(P+1)}^{n-1}}-1\]

    D) None of these

    View Answer play_arrow
  • question_answer126) Out of 18 points in a plane no three are in the same straight line except five points which are collinear. The number of straight lines that can be formed joining them, is

    A) 143

    B) 144

    C) 153

    D) None of these

    View Answer play_arrow
  • question_answer127) The term independent of\[x\]in \[{{\left[ \sqrt{\left( \frac{x}{3} \right)+}\sqrt{\left( \frac{3}{2{{x}^{2}}} \right)} \right]}^{10}}\]

    A) \[1\]

    B) \[^{10}{{C}_{1}}\]

    C) \[\frac{5}{12}\]

    D) None of these

    View Answer play_arrow
  • question_answer128) The greatest coefficient in the expansion of \[{{(1+x)}^{2n}}\] is

    A) \[^{2n}{{C}_{n}}\]

    B) \[^{2n}{{C}_{n-1}}\]

    C) \[^{2n}{{C}_{n-2}}\]

    D) None of these

    View Answer play_arrow
  • question_answer129) The number of terms in the expansion of\[{{(\sqrt{5}+\sqrt[4]{11})}^{124}}\]which are integers, is equal to

    A) 0

    B) 30

    C) 31

    D) 32

    View Answer play_arrow
  • question_answer130) The constant term in the expansion of\[{{(1+x)}^{m}}{{\left( 1+\frac{1}{x} \right)}^{n}}\]

    A) \[^{m+n}{{C}_{m-1}}\]

    B) \[^{m+n}{{C}_{n}}\]

    C) \[^{m+n}{{C}_{m-n}}\]

    D) None of these

    View Answer play_arrow
  • question_answer131) If\[a>1\], roots of the equation\[(1-a){{x}^{2}}+3ax-1=0\]are

    A) one positive and one negative

    B) both negative

    C) both positive

    D) both non-real complex

    View Answer play_arrow
  • question_answer132) The number of values of the triplet\[(a,\,\,b,\,\,c)\]for which\[a\cos 2x+b{{\sin }^{2}}x+c=0\]is satisfied by all real\[x\], is

    A) 0

    B) 2

    C) 3

    D) infinite

    View Answer play_arrow
  • question_answer133) If\[\alpha ,\,\,\beta ,\,\,\gamma \]are such that\[\alpha +\beta +\gamma =2,\]\[{{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}=6\],\[{{\alpha }^{3}}+{{\beta }^{3}}+{{\gamma }^{3}}=8\], then\[{{\alpha }^{4}}+{{\beta }^{4}}+{{\gamma }^{4}}\]is

    A) 5

    B) 18

    C) 12

    D) 36

    View Answer play_arrow
  • question_answer134) If\[a,\,\,b,\,\,c\]are three distinct positive real numbers of real roots of\[a{{x}^{2}}+2b|x|-c=0\]is

    A) 4

    B) 2

    C) 0

    D) None of these

    View Answer play_arrow
  • question_answer135) If\[A\]is a skew-symmetric matrix, then trace of\[A\]is

    A) 1

    B) -1

    C) 0

    D) None of these

    View Answer play_arrow
  • question_answer136) If the matrix\[A=\left[ \begin{matrix} y+a & b & c \\ a & y+b & c \\ a & b & y+c \\ \end{matrix} \right]\]has rank 3, then

    A) \[y\ne (a-b+c)\]

    B) \[y\ne 1\]

    C) \[y=0\]

    D) \[y\ne -(a+b+c)\]and\[y\ne 0\]

    View Answer play_arrow
  • question_answer137) For positive numbers\[x,\,\,y,\,\,z\]the numerical value of the determinant \[\left| \begin{matrix} 1 & {{\log }_{x}}y & {{\log }_{x}}z \\ {{\log }_{y}}x & 1 & {{\log }_{y}}z \\ {{\log }_{z}}x & {{\log }_{z}}y & 1 \\ \end{matrix} \right|\]

    A) 0

    B) 1

    C) 2

    D) None of these

    View Answer play_arrow
  • question_answer138) If\[A\]is an orthogonal matrix, then

    A) \[\det \,\,A=not\,\,exist\]

    B) \[\det \,\,A=0\]

    C) \[\det \,\,A=\pm 1\]

    D) None of these

    View Answer play_arrow
  • question_answer139) Let\[a,\,\,b,\,\,c\]be real numbers with\[a\ne 0\]and let \[\alpha ,\,\,\beta \]be the roots of the equation\[a{{x}^{2}}+bx+c=0\], then\[{{a}^{3}}{{x}^{2}}+abcx+{{c}^{3}}=0\]has roots

    A) \[{{\alpha }^{2}}\beta ,{{\beta }^{2}}\alpha \]

    B) \[\alpha ,{{\beta }^{2}}\]

    C) \[{{\alpha }^{2}}\beta ,\beta \alpha \]

    D) \[{{\alpha }^{3}}\beta ,{{\beta }^{3}}\alpha \]

    View Answer play_arrow
  • question_answer140) If\[{{n}_{1}},\,\,{{n}_{2}}\]are positive integers, then\[{{(1+i)}^{{{n}_{1}}}}+{{(1+{{i}^{3}})}^{{{n}_{1}}}}+{{(1+{{i}^{5}})}^{{{n}_{2}}}}+{{(1+{{i}^{7}})}^{{{n}_{2}}}}\]is a real number if and only if

    A) \[{{n}_{1}}={{n}_{2}}+1\]

    B) \[{{n}_{1}}={{n}_{2}}\]

    C) \[{{n}_{1}},\,\,{{n}_{2}}\]are any two negative integers

    D) \[{{n}_{1}},\,\,{{n}_{2}}\]are both any positive integers

    View Answer play_arrow
  • question_answer141) The equation\[|z+i|-|z-i|\,\,=k\]represent a hyperbola, if

    A) \[-2<k<2\]

    B) \[k>2\]

    C) \[0<k<2\]

    D) None of these

    View Answer play_arrow
  • question_answer142) The period of the function\[f(x)=|\sin 4x|+|\cos 4x|\]is

    A) \[\pi /2\]

    B) \[\pi /8\]

    C) \[\pi /4\]

    D) None of these

    View Answer play_arrow
  • question_answer143) If\[\cos x=\frac{2\cos y-1}{2-\cos y}\], where\[x,\,\,y\in (0,\,\,\pi )\], then\[\tan \frac{x}{2}\cdot \cot \frac{y}{2}\]is equal to

    A) \[\sqrt{2}\]

    B) \[\sqrt{3}\]

    C) \[\frac{1}{\sqrt{2}}\]

    D) \[\frac{1}{\sqrt{3}}\]

    View Answer play_arrow
  • question_answer144) The value of\[\cos \frac{2\pi }{15}\cdot \cos \frac{4\pi }{15}\cdot \cos \frac{8}{15}\cdot \cos \frac{16\pi }{15}\]is equal to

    A) \[\frac{1}{16}\]

    B) \[\frac{1}{32}\]

    C) \[\frac{1}{64}\]

    D) \[\frac{1}{8}\]

    View Answer play_arrow
  • question_answer145) The sum of all the solutions of the equation\[\cos x\cdot \cos \left( \frac{\pi }{3}+x \right)\cdot \cos \left( \frac{\pi }{3}-x \right)=\frac{1}{4}\],\[x\in [0,\,\,6\pi ]\]is

    A) \[15\pi \]

    B) \[30\pi \]

    C) \[\frac{110\pi }{3}\]

    D) None of these

    View Answer play_arrow
  • question_answer146) \[2{{\tan }^{-1}}(\cos ec{{\tan }^{-1}}x-\tan \,\,{{\cot }^{-1}}x)\]is equal to

    A) \[{{\cot }^{-1}}x\]

    B) \[{{\cot }^{-1}}\frac{1}{x}\]

    C) \[{{\tan }^{-1}}x\]

    D) None of these

    View Answer play_arrow
  • question_answer147) The value of\[{{\sin }^{-1}}\left[ \cos \left( {{\sin }^{-1}}\sqrt{\frac{2-\sqrt{3}}{4}} \right. \right.\]\[\left. \left. +{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} \right) \right]\]is

    A) 0

    B) \[\frac{\pi }{4}\]

    C) \[\frac{\pi }{6}\]

    D) \[\frac{\pi }{2}\]

    View Answer play_arrow
  • question_answer148) In a\[\Delta \,\,ABC,\,\,\angle B={{90}^{o}}\],then\[{{\tan }^{2}}\left( \frac{A}{2} \right)\]is

    A) \[\frac{b-c}{b+c}\]

    B) \[\frac{b+c}{b-c}\]

    C) \[\frac{b-2c}{b+c}\]

    D) None of these

    View Answer play_arrow
  • question_answer149) In a triangle, if\[{{r}_{1}}>{{r}_{2}}>{{r}_{3}}\], then

    A) \[a>b>c\]

    B) \[a<b<c\]

    C) \[a>b\]and\[b<c\]

    D) \[a<b\]and\[b>c\]

    View Answer play_arrow
  • question_answer150) A and B are two points on one bank of a straight river and C, D are two other points on the other bank of river, if direction from A to B is same as that from C to D and\[AB=a\],\[\angle CAD=\alpha \],\[\angle DAB=\beta \],\[\angle CBA=\gamma \], then CD is equal to

    A) \[\frac{a\sin \beta \cdot \sin \gamma }{\sin \alpha \cdot \sin (\alpha +\beta +\gamma )}\]

    B) \[\frac{a\sin \alpha \cdot \sin \gamma }{\sin \beta \cdot \sin (\alpha +\beta +\gamma )}\]

    C) \[\frac{a\sin \alpha \cdot \sin \beta }{\sin \gamma \cdot \sin (\alpha +\beta +\gamma )}\]

    D) None of the above

    View Answer play_arrow
  • question_answer151) In a trapezoid of the vector\[\overset{\to }{\mathop{\mathbf{BC}}}\,=\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,\]. We will, then find that\[\overset{\to }{\mathop{\mathbf{P}}}\,=\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{BD}}}\,\]is collinear with\[\overset{\to }{\mathop{\mathbf{AD}}}\,\]. If\[\overset{\to }{\mathop{\mathbf{P}}}\,=\mu \overset{\to }{\mathop{\mathbf{AD}}}\,\], then

    A) \[\mu =\lambda +1\]

    B) \[\lambda =\mu +1\]

    C) \[\lambda +\mu =1\]

    D) \[\mu =2+\lambda \]

    View Answer play_arrow
  • question_answer152) If\[P(\overrightarrow{\mathbf{p}}),\text{ }Q(\overrightarrow{\mathbf{q}}),\text{ }R(\overrightarrow{\mathbf{r}})\]and\[S(\overrightarrow{\mathbf{s}})\]be four points such that\[3\overrightarrow{\mathbf{p}}+8\overrightarrow{\mathbf{q}}=6\overrightarrow{\mathbf{r}}+5\overrightarrow{\mathbf{s}}\], then the lines\[PQ\] and\[RS\]are

    A) skew

    B) intersecting

    C) parallel

    D) None of these

    View Answer play_arrow
  • question_answer153) Let\[\overrightarrow{\mathbf{a}}=2\widehat{\mathbf{i}}+\widehat{\mathbf{j}}-2\widehat{\mathbf{k}}\]and\[\overrightarrow{\mathbf{b}}=\mathbf{\hat{i}}+\widehat{\mathbf{j}}\], if\[\overrightarrow{\mathbf{c}}\]is a vector such that\[\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{c}}=|\overrightarrow{\mathbf{c}}|,\,\,|\overrightarrow{\mathbf{c}}-\overrightarrow{\mathbf{a}}|=2\sqrt{2}\]and the angle between\[\overrightarrow{\mathbf{a}}\times \overrightarrow{\mathbf{b}}\]and\[\overrightarrow{\mathbf{c}}\]is\[{{30}^{o}}\], then\[|(\overrightarrow{\mathbf{a}}\times \overrightarrow{\mathbf{b}})\times \overrightarrow{\mathbf{c}}|\]is equal to

    A) \[\frac{2}{3}\]

    B) \[\frac{3}{2}\]

    C) \[2\]

    D) \[3\]

    View Answer play_arrow
  • question_answer154) Consider a tetrahedron with faces\[{{F}_{1}},\,\,{{F}_{2}},\,\,{{F}_{3}},\,\,{{F}_{4}}\]. Let\[{{V}_{1}},\,\,{{V}_{2}},\,\,{{V}_{3}},\,\,{{V}_{4}}\]be the vectors whose magnitudes are respectively equal to areas of\[{{F}_{1}},\,\,{{F}_{2}},\,\,{{F}_{3}},\,\,{{F}_{4}}\] and whose directions are perpendicular to these faces in outward direction, then\[|{{\overset{\to }{\mathop{\mathbf{V}}}\,}_{\mathbf{1}}}\mathbf{+}{{\overset{\to }{\mathop{\mathbf{V}}}\,}_{\mathbf{2}}}\mathbf{+}{{\overset{\to }{\mathop{\mathbf{V}}}\,}_{\mathbf{3}}}\mathbf{+}{{\overset{\to }{\mathop{\mathbf{V}}}\,}_{\mathbf{4}}}|\]equals

    A) 1

    B) 4

    C) \[\vec{0}\]

    D) None of these

    View Answer play_arrow
  • question_answer155) If\[V\]is the volume of the parallelepiped having three coterminus edges as\[\overrightarrow{\mathbf{a}},\,\,\overrightarrow{\mathbf{b}}\]and\[\overrightarrow{\mathbf{c}}\], then the volume of the parallelepiped having three coterminus edge as \[\overrightarrow{\alpha }=(\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{a}})\overrightarrow{\mathbf{a}}+(\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}})\overrightarrow{\mathbf{b}}+(\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{c}})\overrightarrow{\mathbf{c}}\], \[\overrightarrow{\beta }=(\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{b}})\overrightarrow{\mathbf{a}}+(\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{b}})\overrightarrow{\mathbf{b}}+(\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{c}})\overrightarrow{\mathbf{c}}\] \[\overrightarrow{\gamma }=(\overrightarrow{\mathbf{a}}\cdot \overrightarrow{\mathbf{c}})\overrightarrow{\mathbf{a}}+(\overrightarrow{\mathbf{b}}\cdot \overrightarrow{\mathbf{c}})\overrightarrow{\mathbf{b}}+(\overrightarrow{\mathbf{c}}\cdot \overrightarrow{\mathbf{c}})\overrightarrow{\mathbf{c}}\]

    A) \[{{V}^{3}}\]

    B) \[3V\]

    C) \[{{V}^{2}}\]

    D) \[2V\]

    View Answer play_arrow
  • question_answer156) Let us define the length of a vector\[a\widehat{\mathbf{i}}+b\widehat{\mathbf{j}}+c\widehat{\mathbf{k}}\]as\[|a|+|b|+|c|\]. This definition coincides with the usual definition of length of a vector\[a\widehat{\mathbf{i}}+b\widehat{\mathbf{j}}+c\widehat{\mathbf{k}}\], if

    A) \[a=b=c=0\]

    B) any two of\[a,\,\,b\]and\[c\]are zero

    C) any one of\[a,\,\,b\]and\[c\]is zero

    D) \[a+b+c=0\]

    View Answer play_arrow
  • question_answer157) Let\[\overrightarrow{\mathbf{u}}=\widehat{\mathbf{i}}+\widehat{\mathbf{j}}\],\[\overrightarrow{\mathbf{v}}=\widehat{\mathbf{i}}-\widehat{\mathbf{j}}\]and\[\overset{\to }{\mathop{\mathbf{w}}}\,=\widehat{\mathbf{i}}+2\widehat{\mathbf{j}}+3\widehat{\mathbf{k}}\], if\[\widehat{\mathbf{n}}\]is a unit vector such that\[\mathbf{\vec{u}}\cdot \widehat{\mathbf{n}}=0\]and \[\overrightarrow{\mathbf{v}}\cdot \widehat{\mathbf{n}}=0\], then\[|\overset{\to }{\mathop{\mathbf{w}}}\,.\widehat{\mathbf{n}}|\]is equal to

    A) 3

    B) 0

    C) 1

    D) 2

    View Answer play_arrow
  • question_answer158) For two events A and B, it is given that\[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\]and\[P\left( \frac{B}{A} \right)=\frac{1}{2}\]. Then

    A) A and B are mutually exclusive events

    B) A and B are dependent events

    C) \[P\left( \frac{A}{B} \right)=\frac{3}{4}\]

    D) None of the above

    View Answer play_arrow
  • question_answer159) The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is

    A) 7

    B) 6

    C) 5

    D) 3

    View Answer play_arrow
  • question_answer160) If\[x\]follows a binomial distribution with parameters\[n=100\]and\[p=\frac{1}{3}\], then\[p(X=r)\]is maximum when r equals

    A) 16

    B) 32

    C) 33

    D) None of these

    View Answer play_arrow
  • question_answer161) If\[{{\bar{x}}_{1}}\]and\[{{\bar{x}}_{2}}\]are the means of two distributions such that\[{{\bar{x}}_{1}}<{{\bar{x}}_{2}}\]and\[\bar{x}\]is the mean of the combined distribution, then

    A) \[\bar{x}<{{\bar{x}}_{1}}\]

    B) \[\bar{x}>{{\bar{x}}_{2}}\]

    C) \[\bar{x}=\frac{{{{\bar{x}}}_{1}}+{{{\bar{x}}}_{2}}}{2}\]

    D) \[{{\bar{x}}_{1}}<\bar{x}<{{\bar{x}}_{2}}\]

    View Answer play_arrow
  • question_answer162) If the axes be turned through an angle\[{{\tan }^{-1}}2\]. What does the equation\[4xy-3{{x}^{2}}={{a}^{2}}\]become?

    A) \[{{X}^{2}}-4{{Y}^{2}}={{a}^{2}}\]

    B) \[{{X}^{2}}+4{{Y}^{2}}={{a}^{2}}\]

    C) \[{{X}^{2}}+4{{Y}^{2}}=-{{a}^{2}}\]

    D) None of these

    View Answer play_arrow
  • question_answer163) If\[{{t}_{1}},\,\,{{t}_{2}}\]and\[{{t}_{3}}\]are distinct, the points\[({{t}_{1}},\,\,2a{{t}_{1}},\,\,at_{1}^{3})\],\[({{t}_{2}},\,\,2a{{t}_{2}},\,\,at_{2}^{3})\]\[({{t}_{3}},\,\,2a{{t}_{3}},\,\,at_{3}^{3})\]are collinear, if

    A) \[{{t}_{1}}{{t}_{2}}{{t}_{3}}=1\]

    B) \[{{t}_{1}}+{{t}_{2}}+{{t}_{3}}={{t}_{1}}{{t}_{2}}{{t}_{3}}\]

    C) \[{{t}_{1}}+{{t}_{2}}+{{t}_{3}}=0\]

    D) \[{{t}_{1}}+{{t}_{2}}+{{t}_{3}}=-1\]

    View Answer play_arrow
  • question_answer164) The distance of the point (2, 3) from the line \[2x-3y+9=0\]measured along a line\[x-y+1=0\]is

    A) \[4\sqrt{2}\]

    B) \[2\sqrt{2}\]

    C) \[\sqrt{2}\]

    D) \[\frac{1}{\sqrt{2}}\]

    View Answer play_arrow
  • question_answer165) The equation of the straight line which passes through the intersection of the lines\[x-y-1=0\]and\[2x-3y+1=0\]and is parallel to x-axis, is

    A) \[y=3\]

    B) \[y=-3\]

    C) \[x+y=3\]

    D) None of these

    View Answer play_arrow
  • question_answer166) If the straight line\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\],\[{{a}_{1}}x+{{b}_{1}}y+{{c}_{2}}=0\], \[{{a}_{2}}x+{{b}_{2}}y+{{d}_{1}}=0\]and\[{{a}_{2}}x+{{b}_{2}}y+{{d}_{2}}=0\]are the sides of rhombus, then

    A) \[(a_{2}^{2}+b_{2}^{2}){{({{c}_{1}}-{{c}_{2}})}^{2}}=(a_{1}^{2}+b_{1}^{2}){{({{d}_{1}}-{{d}_{2}})}^{2}}\]

    B) \[(a_{1}^{2}+b_{1}^{2})|{{d}_{1}}-{{d}_{2}}|\,\,=(a_{2}^{2}+b_{2}^{2})|{{c}_{1}}-{{c}_{2}}|\]

    C) \[(a_{2}^{2}+b_{2}^{2}){{({{d}_{1}}-{{d}_{2}})}^{2}}=(a_{1}^{2}+b_{1}^{2}){{({{c}_{1}}-{{c}_{2}})}^{2}}\]

    D) \[(a_{1}^{2}+b_{1}^{2})|{{c}_{1}}-{{c}_{2}}|\,\,=(a_{2}^{2}+b_{2}^{2})|{{d}_{1}}-{{d}_{2}}\]

    View Answer play_arrow
  • question_answer167) The equation\[3{{x}^{2}}+7xy+2{{y}^{2}}+5x+5y+2=0\] represents

    A) a pair of straight lines

    B) a circle

    C) an ellipse

    D) a hyperbola

    View Answer play_arrow
  • question_answer168) To the lines\[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]the lines \[{{a}^{2}}{{x}^{2}}+2h(a+b)xy+{{b}^{2}}{{y}^{2}}=0\], are

    A) equally inclined

    B) perpendicular

    C) bisector of the angle

    D) None of the above

    View Answer play_arrow
  • question_answer169) Consider four circles\[{{(x\pm 1)}^{2}}+{{(y\pm 1)}^{2}}=1\], then the equation of smaller circle touching these four circle is

    A) \[{{x}^{2}}+{{y}^{2}}=3-\sqrt{2}\]

    B) \[{{x}^{2}}+{{y}^{2}}=6-3\sqrt{2}\]

    C) \[{{x}^{2}}+{{y}^{2}}=5-2\sqrt{2}\]

    D) \[{{x}^{2}}+{{y}^{2}}=3-2\sqrt{2}\]

    View Answer play_arrow
  • question_answer170) The locus of the point of intersection of tangents to the circle\[x=a\cos \theta ,\,\,y=a\sin \theta \]at the points, whose parametric angles differe by\[\frac{\pi }{2}\], is

    A) a straight line

    B) a circle

    C) a pair of straight line

    D) None of the above

    View Answer play_arrow
  • question_answer171) The equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius is

    A) \[{{x}^{2}}-{{y}^{2}}-x-y=0\]

    B) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]

    C) \[{{x}^{2}}+{{y}^{2}}+x+y=0\]

    D) \[{{x}^{2}}+{{y}^{2}}-2x-2y=0\]

    View Answer play_arrow
  • question_answer172) The length of the common chord of the two circles\[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\]and\[{{(x-b)}^{2}}+{{(y-a)}^{2}}={{c}^{2}}\]

    A) \[\sqrt{4{{c}^{2}}+2{{(a-b)}^{2}}}\]

    B) \[\sqrt{4{{c}^{2}}-{{(a-b)}^{2}}}\]

    C) \[\sqrt{4{{c}^{2}}-2{{(a-b)}^{2}}}\]

    D) \[\sqrt{2{{c}^{2}}-2{{(a-b)}^{2}}}\]

    View Answer play_arrow
  • question_answer173) If\[\left( {{m}_{i}},\,\,\frac{1}{{{m}_{i}}} \right)\]are four distinct points on a circle, then

    A) \[{{m}_{1}}{{m}_{2}}{{m}_{3}}{{m}_{4}}=1\]

    B) \[{{m}_{1}}{{m}_{2}}{{m}_{3}}{{m}_{4}}=-1\]

    C) \[{{m}_{1}}{{m}_{2}}{{m}_{3}}{{m}_{4}}=\frac{1}{2}\]

    D) \[\frac{1}{{{m}_{1}}}+\frac{1}{{{m}_{2}}}+\frac{1}{{{m}_{3}}}+\frac{1}{{{m}_{4}}}\]

    View Answer play_arrow
  • question_answer174) If the normal to the parabola\[{{y}^{2}}=4ax\]at the point\[(a{{t}^{2}},\,\,2aT)\]cuts the parabola again at

    A) \[-2\le T\le 2\]

    B) \[T\in (-\infty ,\,\,-8)\cup (8,\,\,\infty )\]

    C) \[{{T}^{2}}<8\]

    D) \[{{T}^{2}}\ge 8\]

    View Answer play_arrow
  • question_answer175) The number of real tangents that can be drawn to the ellipse\[3{{x}^{2}}+5{{y}^{2}}=32\]passing through (3, 5) is

    A) 0

    B) 1

    C) 2

    D) infinite

    View Answer play_arrow
  • question_answer176) If the equation \[l{{x}^{2}}+2mxy+n{{y}^{2}}=0\]represents a pair conjugate diameter of the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], then

    A) \[l{{a}^{2}}+n{{b}^{2}}=0\]

    B) \[l{{a}^{2}}=n{{b}^{2}}\]

    C) \[2l{{a}^{2}}=n{{b}^{2}}\]

    D) None of these

    View Answer play_arrow
  • question_answer177) If\[e\]is the eccentricity of the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]and\[\theta \]is the angle between the asymptotes, then\[\cos \left( \frac{\theta }{2} \right)\]is equal to

    A) \[\frac{1}{e}\]

    B) \[\frac{-1}{e}\]

    C) \[e\]

    D) \[\frac{2}{e}\]

    View Answer play_arrow
  • question_answer178) The tangent and normal to a rectangular hyperbola\[xy={{c}^{2}}\]at a point cuts off intercepts\[{{a}_{1}}\]and\[{{a}_{2}}\]on one axis and\[{{b}_{1}},\,\,{{b}_{2}}\]on the other, then\[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}\]is equal to

    A) 1

    B) 2

    C) 3

    D) 0

    View Answer play_arrow
  • question_answer179) The direction cosines of any normal to the\[xy-\]plane are

    A) 1, 0, 0

    B) 0, 1, 0

    C) 1, 1, 0

    D) 0, 0, 1

    View Answer play_arrow
  • question_answer180) The locus of the equation\[xy+yz=0\]is

    A) a pair of straight lines

    B) a pair of parallel lines

    C) a pair of perpendicular planes

    D) None of the above

    View Answer play_arrow
  • question_answer181) The reflection of the point (2, -1, 3) in the plane\[3x-2y-z=9\]is

    A) \[\left( \frac{26}{7},\,\,\frac{15}{7},\,\,\frac{17}{7} \right)\]

    B) \[\left( \frac{26}{7},\,\,\frac{-15}{7},\,\,\frac{17}{7} \right)\]

    C) \[\left( \frac{15}{7},\,\,\frac{26}{7},\,\,\frac{-17}{7} \right)\]

    D) \[\left( \frac{26}{7},\,\,\frac{17}{7},\,\,\frac{-15}{7} \right)\]

    View Answer play_arrow
  • question_answer182) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1-\cos 2x}}{\sqrt{2}\cdot x}\]is

    A) 1

    B) -1

    C) zero

    D) does not exist

    View Answer play_arrow
  • question_answer183) If\[f(x)\left\{ \begin{matrix} a{{x}^{2}}+b, & 0\le x\le 1 \\ x+3, & 1<x\le 2 \\ 4, & x=1 \\ \end{matrix} \right.\], then the value of \[(a,\,\,b)\]for which\[f(x)\]cannot be continuous at\[x=1\]is

    A) (2, 2)

    B) (3, 1)

    C) (4, 0)

    D) (5, 2)

    View Answer play_arrow
  • question_answer184) If\[f(x)={{\log }_{x}}(\log x)\], then\[f(x)\]at\[x=e\]is

    A) \[1/e\]

    B) \[e\]

    C) \[-1/e\]

    D) \[0\]

    View Answer play_arrow
  • question_answer185) Radius of the circle \[\overset{\to }{\mathop{{{\mathbf{r}}^{\mathbf{2}}}}}\,+\overrightarrow{\mathbf{r}}(2\widehat{\mathbf{i}}-\widehat{\mathbf{j}}-4\widehat{\mathbf{k}})-19=0\] \[\overrightarrow{\mathbf{r}}\cdot (\widehat{\mathbf{i}}-2\widehat{\mathbf{j}}+2\widehat{\mathbf{k}})+8=0\], is

    A) 5

    B) 4

    C) 3

    D) 2

    View Answer play_arrow
  • question_answer186) If\[{{x}^{y}}={{e}^{x}}^{-y}\], then\[\frac{dy}{dx}\]is equal to

    A) \[\frac{\log x}{{{(1+\log x)}^{2}}}\]

    B) \[\frac{x-y}{(1+\log x)}\]

    C) \[\frac{x-y}{{{(1+\log x)}^{2}}}\]

    D) \[\frac{1}{(1+\log x)}\]

    View Answer play_arrow
  • question_answer187) If\[y=\sin (m{{\sin }^{-1}}x)\], then\[(1-{{x}^{2}})y-xy\]is equal to

    A) \[{{m}^{2}}y\]

    B) \[my\]

    C) \[-{{m}^{2}}y\]

    D) None of these

    View Answer play_arrow
  • question_answer188) If\[f(x)=(ax+b)\sin x+(cx+d)\cos x\], then the values of\[a,\,\,b,\,\,c\]and\[d\]such that\[f(x)=x\cos x\]for all\[x\], are

    A) \[b=c=0,\,\,a=d=1\]

    B) \[b=d=0,\,\,a=c=1\]

    C) \[c=d=0,\,\,a=b=1\]

    D) None of the above

    View Answer play_arrow
  • question_answer189) If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is

    A) a constant

    B) \[\propto {{s}^{2}}\]

    C) \[\propto \frac{1}{{{s}^{2}}}\]

    D) \[\propto \frac{1}{s}\]

    View Answer play_arrow
  • question_answer190) The point in the interval\[[0,\,\,2\pi ]\], where\[f(x)={{e}^{x}}\sin x\]has maximum slope, is

    A) \[\frac{\pi }{4}\]

    B) \[\frac{\pi }{2}\]

    C) \[\pi \]

    D) \[\frac{3\pi }{2}\]

    View Answer play_arrow
  • question_answer191) The function\[f(x)=\frac{ax+b}{(x-1)(x-4)}\]has a local maxima at\[(2,\,\,-1)\], then

    A) \[b=1,\,\,a=0\]

    B) \[b=1,\,\,a=0\]

    C) \[b=-1,\,\,a=0\]

    D) \[a=-1,\,\,b=0\]

    View Answer play_arrow
  • question_answer192) If\[z=\tan (y+ax)+\sqrt{y-ax}\], then\[{{z}_{xx}}-{{a}^{2}}{{z}_{yy}}\]is equal to

    A) \[0\]

    B) \[2\]

    C) \[{{z}_{x}}+{{z}_{y}}\]

    D) \[{{z}_{x}}{{z}_{y}}\]

    View Answer play_arrow
  • question_answer193) If\[\int{f(x)dx}=F(x)\], then\[\int{{{x}^{3}}}f{{(x)}^{2}}dx\]is equal to

    A) \[\frac{1}{2}[{{x}^{2}}{{\{F(x)\}}^{2}}-\int{{{\{F(x)\}}^{2}}dx]}\]

    B) \[\frac{1}{2}[{{x}^{2}}F{{(x)}^{2}}-\int{F{{(x)}^{2}}d{{(x)}^{2}}]}\]

    C) \[\frac{1}{2}[{{x}^{2}}F(x)-\frac{1}{2}\int{{{\{F(x)\}}^{2}}dx]}\]

    D) None of the above

    View Answer play_arrow
  • question_answer194) \[\int{\frac{{{x}^{2}}+4}{{{x}^{4}}+16}}\]is equal to

    A) \[\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}+4}{2x} \right)+c\]

    B) \[\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-4}{2\sqrt{2x}} \right)+c\]

    C) \[\frac{1}{2\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}+4}{2\sqrt{2x}} \right)+c\]

    D) \[\frac{1}{2}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-4}{2x} \right)+c\]

    View Answer play_arrow
  • question_answer195) Evaluate\[\int{\frac{1}{(x+1)\sqrt{{{x}^{2}}-1}}dx}\]

    A) \[\sqrt{\frac{x+1}{x-1}}+c\]

    B) \[\sqrt{\frac{x-1}{x+1}}+c\]

    C) \[\sqrt{\frac{1}{x+1}}+c\]

    D) None of these

    View Answer play_arrow
  • question_answer196) The value of the integral\[\int_{\pi /2}^{3\pi /2}{[\sin x]dx}\], where \[[\cdot ]\]denotes the greatest integer function, is

    A) \[\frac{\pi }{2}\]

    B) \[-\frac{\pi }{2}\]

    C) \[0\]

    D) \[\pi \]

    View Answer play_arrow
  • question_answer197) The area of the loop the curve \[a{{y}^{2}}={{x}^{2}}(a-x)\]is

    A) \[\frac{8{{a}^{2}}}{15}sq\,\,unit\]

    B) \[\frac{4{{a}^{2}}}{15}sq\,\,unit\]

    C) \[\frac{2{{a}^{2}}}{15}sq\,\,unit\]

    D) None of these

    View Answer play_arrow
  • question_answer198) Solution of the differential equation \[x=1+xy\frac{dy}{dx}+\frac{{{(xy)}^{2}}}{2!}{{\left( \frac{dy}{dx} \right)}^{2}}\]\[+\frac{{{(xy)}^{3}}}{3!}{{\left( \frac{dy}{dx} \right)}^{3}}+...\]is

    A) \[y={{\log }_{e}}(x)+c\]

    B) \[y={{({{\log }_{e}}x)}^{2}}+c\]

    C) \[y=\pm \sqrt{{{({{\log }_{e}}x)}^{2}}+2c}\]

    D) \[xy={{x}^{y}}=k\]

    View Answer play_arrow
  • question_answer199) If the solution of the differential equation\[\frac{dy}{dx}=\frac{ax+3}{2y+f}\]represents a circle, then the value of\[a\]is

    A) 2

    B) -2

    C) 3

    D) -4

    View Answer play_arrow
  • question_answer200) The approximate value of\[\int_{1}^{5}{{{x}^{2}}dx}\]using trapezoidal rule with n = 4 is

    A) 41

    B) 41.5

    C) 41.75

    D) 42

    View Answer play_arrow
  • question_answer201) MOSQUERADE

    A) to provide support

    B) to go in disguise

    C) to mesmerize

    D) marathon race

    View Answer play_arrow
  • question_answer202) PREPOSTEROUS

    A) careful

    B) casual

    C) absurd

    D) deterrent

    View Answer play_arrow
  • question_answer203) SOLITUDE

    A) musical composition

    B) aloneness

    C) true statement

    D) single mindedness

    View Answer play_arrow
  • question_answer204) PROPITIOUS

    A) favorable

    B) clean

    C) nearby

    D) patriotic

    View Answer play_arrow
  • question_answer205) RELENTLESS

    A) merciless

    B) yielding

    C) monotonous

    D) incisive

    View Answer play_arrow
  • question_answer206) FORBEARANCE

    A) patience

    B) self-control

    C) intolerance

    D) preference

    View Answer play_arrow
  • question_answer207) PALTRY

    A) absolete

    B) cautious

    C) random

    D) plentiful

    View Answer play_arrow
  • question_answer208) EXODUS

    A) influx

    B) return

    C) home coming

    D) restoration

    View Answer play_arrow
  • question_answer209) The........argument put forth for not disclosing the facts did not impress anybody.

    A) intemperate

    B) spurious

    C) specious

    D) convincing

    View Answer play_arrow
  • question_answer210) Director, he said, would.......the matter at once.

    A) invigilate

    B) explore

    C) investigate

    D) survey

    View Answer play_arrow
  • question_answer211) Everyone was.........by surprise when she announced her plan to marry that boy,

    A) moved

    B) shaken

    C) taken

    D) prevailed

    View Answer play_arrow
  • question_answer212) Your case is so unique that I am not getting any........to support it.

    A) reason

    B) help

    C) happening

    D) precedent

    View Answer play_arrow
  • question_answer213) The writing or compiling of dictionaries

    A) Lexicography

    B) Numismatics

    C) Cytology

    D) Demography

    View Answer play_arrow
  • question_answer214) The study of Insects

    A) Chromatics

    B) Dactylology

    C) Calligraphy

    D) Entomology

    View Answer play_arrow
  • question_answer215) Murder of ones brother

    A) Regiside

    B) Foeticide

    C) Fratricide

    D) Uxoricide

    View Answer play_arrow
  • question_answer216) Government by one person

    A) Autonomy

    B) Autocracy

    C) Plutocracy

    D) Theocracy

    View Answer play_arrow
  • question_answer217) She cut a sad figure in her first performance on the stage.

    A) made a sorry figure

    B) cut a sorry face

    C) cut a sorry figure

    D) no improvement

    View Answer play_arrow
  • question_answer218) No sooner I saw the tiger, than I ran away.

    A) as soon as I saw

    B) no sooner 1 had seen

    C) no sooner did I see

    D) no improvement

    View Answer play_arrow
  • question_answer219) If he had time he will call you.

    A) would have

    B) would have had

    C) has

    D) no improvement

    View Answer play_arrow
  • question_answer220) AH his answers were correct.

    A) his nil answers

    B) his every answers

    C) all of his answers

    D) no improvement

    View Answer play_arrow
  • question_answer221) Jam : Jelly : Pickles

    A) Butter : Marmalade : Grapes

    B) Granite : Basalt : Coke

    C) Cow : Dry : Draft

    D) Bleat : Bray : Grunt

    View Answer play_arrow
  • question_answer222) Mountain : Height : Climber

    A) River : Length : Water

    B) Land : Farmer : Crop

    C) College : Building : Student

    D) Sea : Depth : Diver

    View Answer play_arrow
  • question_answer223) Head : Brain : Think

    A) Eyes : Lashes : See

    B) Skin : Sweat: Touch

    C) Feet: Dance : Toe

    D) Mouth : Teeth : Chew

    View Answer play_arrow
  • question_answer224) Jute : Cotton : Wool

    A) Potato : Carrot : Bean

    B) Canada : Chile : Asia

    C) Liver ; Heat : Blood

    D) Shark : Cod : Eel

    View Answer play_arrow
  • question_answer225) Sial ; Sima ; Mantle

    A) Core : Asteroid : Comet

    B) Pneumonia : Tetanus : Hepatitis

    C) Calcite : Magnesium : Zinc

    D) Wrestling : Karate : Boxing

    View Answer play_arrow
  • question_answer226) Rourkela : Bokaro : Durgapur

    A) They have steel plants

    B) They have coal mines

    C) They have atomic power plants

    D) They have the best technical colleges

    View Answer play_arrow
  • question_answer227) Chlorine : Fluorine : Iodine

    A) These are names of inert gases

    B) These are gases at room temperature

    C) These are transition elements

    D) These are halogens

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  • question_answer228) Petrol : Phosphorus : Cooking gas

    A) They are fuels

    B) They are highly in inflamable

    C) They can be sold without permit

    D) India has to import them

    View Answer play_arrow
  • question_answer229) Green : Violet : Orange

    A) They arc primary colours

    B) These colours occur together in a rainbow

    C) They are made by mixing other colours

    D) These colours are not found in butterflies

    View Answer play_arrow
  • question_answer230) Supernova : Protostar : Red Giant

    A) These are kinds of stars

    B) These are members of galaxies

    C) These are stages in the life of a star

    D) These move about the Sun

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  • question_answer231) The classical dance, Kathakali belongs to

    A) Tamil Nadu

    B) Karnataka

    C) Orissa

    D) Kerala

    View Answer play_arrow
  • question_answer232) The highest civilian award in India is

    A) Paramveer Chakra

    B) Bharat Ratna

    C) Bhatnagar Award

    D) Kalinga Award

    View Answer play_arrow
  • question_answer233) Who is called Nightingale of India?

    A) Sarojini Naidu

    B) Lata mangeshkar

    C) Amir Khushro

    D) Asha Bhosale

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  • question_answer234) Nehru Trophy is related with

    A) Cricket

    B) Volleyball

    C) Hockey

    D) Badminton

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  • question_answer235) The headquarters of NATO is situated at

    A) Brussels

    B) Geneva

    C) Newyork

    D) Paris

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  • question_answer236) The first Indian woman to swim across the English channel is

    A) Bachendri Pal

    B) Santosh Yadav

    C) Nirja Mishra

    D) Aarti Saha

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  • question_answer237) Which of the following river is related with Bhakra-Nagal Project?

    A) Ravi

    B) Satluj

    C) Gandak

    D) Mahanadi

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  • question_answer238) Namdhapha National Park is located in

    A) Rajasthan

    B) Orissa

    C) Arunachal Pradesh

    D) Uttar Pradesh

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  • question_answer239) Which of the following is known as evening star?

    A) Venus

    B) Mercury

    C) Saturn

    D) Jupiter

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  • question_answer240) Which of the following was the founder of Indian National Congress?

    A) Jawahar Lal Nehru

    B) Mahatma Gandhi

    C) Moti Lal Nehru

    D) A. O. Hume

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