Solved papers for CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

done CET - Karnataka Engineering Solved Paper-2009

  • question_answer1) In ruby laser, the stimulated emission is due to transition from

    A) metastable state to any lower state

    B) any higher state to lower state

    C) metastable state to ground state

    D) any higher state to ground state

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  • question_answer2) A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

    A) uniform throughout the pipe but not zero

    B) zero only along the axis of the pipe

    C) zero at any point inside the pipe

    D) maximum at the centre and minimum at the edge

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  • question_answer3) A convex lens made of glass has focal length 0.15 m in air. If the refractive index of glass is \[\frac{3}{2}\] and that of water is \[\frac{4}{3}\], the focal length of lens when immersed in water is

    A) 0.45 m

    B) 0.15 m

    C) 0.30 m

    D) 0.6 m

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  • question_answer4) Two sources are said to be coherent if they produce waves

    A) having a constant phase difference

    B) of equal wavelength

    C) of equal speed

    D) having same shape of wave front

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  • question_answer5) Three resistors \[1\,\Omega ,\,2\,\Omega \] and \[3\,\Omega \] are connected to form a triangle. Across \[3\,\Omega \] resistor a \[3\,\Omega \] battery is connected. The current through \[3\,\Omega \] resistor is

    A) 0.75 A

    B) 1 A

    C) 2 A

    D) 1.5 A

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  • question_answer6) In a common emitter amplifier the input signal is applied across

    A) anywhere

    B) emitter-collector

    C) collector-base

    D) base-emitter

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  • question_answer7) In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is

    A) \[\frac{1}{{{e}^{2}}}\]

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

    C) e

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

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  • question_answer8) A ray of light is incident on a surface of glass slab at an angle \[{{45}^{o}}\]. If the lateral shift produced per unit thickness is \[\frac{1}{\sqrt{3}}m\], the angle of refraction produced is

    A) \[{{\tan }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]

    B) \[{{\tan }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\]

    C) \[{{\sin }^{-1}}\left( 1-\sqrt{\frac{2}{3}} \right)\]

    D) \[{{\tan }^{-1}}\left( \frac{2}{\sqrt{3}-1} \right)\]

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  • question_answer9) Ferromagnetic materials used in a transformer must have

    A) low permeability and high hysterisis loss

    B) high permeability and low hysterisis loss

    C) high permeability and high hysterisis loss

    D) low permeability and low hysterisis loss

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  • question_answer10) According to Newton's corpuscular theory, the speed of light is

    A) same in all the media

    B) lesser in rarer medium

    C) lesser in denser medium

    D) independent of the medium

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  • question_answer11) For the constructive interference the path difference between the two interfering waves must be equal to

    A) \[\left( 2n+1 \right)\lambda \]

    B) \[2n\pi \]

    C) \[n\lambda \]

    D) \[\left( 2n+1 \right)\frac{\pi }{2}\]

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  • question_answer12) The accurate measurement of emf can be obtained using

    A) multimeter

    B) voltmeter

    C) voltameter

    D) potentiometer

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  • question_answer13) The kinetic energy of an electron gets tripled, then the de-Broglie wavelength associated with it changes by a factor

    A) \[\frac{1}{3}\]

    B) \[\sqrt{3}\]

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

    D) 3

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  • question_answer14) Which of the following is not a thermodynamic coordinate?

    A) Gas constant (R)

    B) Pressure (p)

    C) Volume (V)

    D) Temperature (T)

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  • question_answer15) Two solid pieces, one of steel and the other of aluminium when immersed completely in water have equal weights. When the solid pieces are weighed in air

    A) the weight of aluminium is half the weight of steel

    B) steel piece will weigh more

    C) they have the same weight

    D) aluminium piece will weigh more

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  • question_answer16) The amount of energy released when one microgram of matter is annihilated is

    A) 25 kWh

    B) \[9\times {{10}^{10}}kWh\]

    C) \[3\times {{10}^{10}}kWh\]

    D) \[0.5\times {{10}^{5}}kWh\]

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  • question_answer17) The number of significant figures in the numbers \[4.8000\times {{10}^{4}}\] and 48000.50 are respectively

    A) 5 and 6

    B) 5 and 7

    C) 2 and 7

    D) 2 and 6

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  • question_answer18) \[\beta \]-decay means emission of electron from

    A) innermost electron orbit

    B) a stable nucleus

    C) outermost electron orbit

    D) radioactive nucleus

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  • question_answer19) An electric heater rated 220 V and 550 W is connected to AC mains. The current drawn by it is

    A) 0.8 A

    B) 2.5 A

    C) 0.4 A

    D) 1.25 A

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  • question_answer20) A body of mass m moving along a straight line covers half the distance with a speed of \[2\text{ }m{{s}^{-1}}\]. The remaining half of the distance is covered in two equal time intervals with a speed of \[3\text{ }m{{s}^{-1}}\] and \[5\text{ }m{{s}^{-1}}\] respectively. The average speed of the particle for the entire journey is

    A) \[\frac{3}{8}m{{s}^{-1}}\]

    B) \[\frac{3}{8}m{{s}^{-1}}\]

    C) \[\frac{4}{3}m{{s}^{-1}}\]

    D) \[\frac{16}{3}m{{s}^{-1}}\]

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  • question_answer21) The moment of inertia of a circular ring of radius r and mass M about diameter is

    A) \[\frac{2}{5}M{{r}^{2}}\]

    B) \[\frac{M{{r}^{2}}}{4}\]

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

    D) \[\frac{M{{r}^{2}}}{12}\]

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  • question_answer22) A body of mass 0.05 kg is observed to fall with an acceleration of \[9.5\text{ }m{{s}^{-2}}\]. The opposing force of air on the body is \[(g=9.8\text{ }m{{s}^{-2}})\]

    A) 0.015 N

    B) 0.15 N

    C) 0.030 N

    D) zero

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  • question_answer23) The colloidal solution in which both the dispersed phase and dispersion medium are liquids are called

    A) emulsions

    B) gels

    C) foams

    D) liquid crystals

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  • question_answer24) In fog, photographs of the objects taken with infrared radiations are more clear than those obtained during visible light because

    A) \[I-R\] radiation has lesser wavelength than visible radiation

    B) scattering of \[I-R\] light is more than visible light

    C) the intensity of \[I-R\] light from the object is less

    D) scattering of \[I-R\] light is less than visible light

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  • question_answer25) Three concurrent co-planar forces 1 N, 2 N and 3 N acting along different directions on a body

    A) can keep the body in equilibrium if 2 N and 3 N act at right angle

    B) can keep the body in equilibrium if 1 N and 2 N act at right angle

    C) cannot keep the body in equilibrium

    D) can keep the body in equilibrium in 1 N and 3 N act at an acute angle

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  • question_answer26) Sound waves transfer

    A) only energy not momentum

    B) energy

    C) momentum

    D) Both (a) and (b)

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  • question_answer27) Two rectangular \[0.15\text{ }m{{s}^{-1}}\] blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of spring constant \[10.8\text{ }N{{m}^{-1}}\] and are placed on a fricrionless horizontal surface. The block A was given an initial velocity of \[0.15\text{ }m{{s}^{-1}}\] in the direction shown in the figure. The maximum compression of the spring during motion is

    A) 0.01 m

    B) 0.02 m

    C) 0.05 m

    D) 0.03 m

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  • question_answer28) G P Thomson experimentally confirmed the existence of matter waves by the phenomena

    A) diffraction

    B) refraction

    C) polarisation

    D) scattering

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  • question_answer29) The resistance of a wire at 300 K is found to be \[0.3\,\Omega \]. If the temperature coefficient of resistance of wire is \[1.5\times {{10}^{-3}}{{K}^{-1}}\], the temperature at which the resistance becomes \[0.6\,\,\Omega \] is

    A) 720 K

    B) 345 K

    C) 993 K

    D) 690 K

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  • question_answer30) The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is

    A) 225 J

    B) 200 J

    C) 400 J

    D) 175 J

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  • question_answer31) Two luminous point sources separated by a certain distance are at 10 km from an observer. If the aperture of his eye is \[2.5\times {{10}^{-3}}m\] and the wavelength of light used is 500 nm, the distance of separation between the point sources just seen to be resolved is

    A) 12.2 m

    B) 24.2 m

    C) 2.44 m

    D) 1.22 m

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  • question_answer32) A door 1.6 m wide requires a force of 1 N to be applied at the free end to open or close it. The force that is required at a point 0.4 m distance from the hinges for opening or closing the door is

    A) 1.2 N

    B) 3.6 N

    C) 2.4 N

    D) 4 N

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  • question_answer33) \[0.1\text{ }{{m}^{3}}\] of water at \[{{80}^{o}}C\] is mixed with \[0.3\text{ }{{m}^{3}}\]of water at \[{{60}^{o}}C\]. The final temperature of the mixture is

    A) \[{{65}^{o}}C\]

    B) \[{{70}^{o}}C\]

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

    D) \[{{75}^{o}}C\]

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  • question_answer34) The spectral series of the hydrogen atom that lies in the visible region of the electromagnetic spectrum

    A) Paschen

    B) Balmer

    C) Lyman

    D) Brackett

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  • question_answer35) A graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph curve OC represents

    A) isochoric process

    B) isothermal process

    C) isobaric process

    D) adiabatic process

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  • question_answer36) Which of the following statement does not hold good for thermal radiation?

    A) The wavelength changes when it travels from one medium to another

    B) The frequency changes when it travels from one medium to another

    C) The speed changes when it travels from one medium to another

    D) They travel in straight line in a given medium

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  • question_answer37) A planet revolves around the sun in an elliptical orbit. The linear speed of the planet will be maximum at

    A) D

    B) B

    C) A

    D) C

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  • question_answer38) Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N. For a streamline flow of liquid the rate of liquid flow is

    A) changing continuously with time

    B) greater at M than at N

    C) greater at N than at M

    D) same at M and N

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  • question_answer39) A resistor and a capacitor are connected in series with an AC source. If the potential drop across the capacitor is 5 V and that across resistor is 12 V, then applied voltage is

    A) 13 V

    B) 17 V

    C) 5 V

    D) 12 V

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  • question_answer40) The amount of heat energy radiated by a metal at temperature T is E. When the temperature is increased to 3T, energy radiated is

    A) 81 E

    B) 9 E

    C) 3 E

    D) 27 E

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  • question_answer41) The angle of minimum deviation for an incident light ray on an equilateral prism is equal to its refracting angle. The refractive index of its material is

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

    B) \[\sqrt{3}\]

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

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

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  • question_answer42) In the following combinations of logic gates, the outputs of A, B and C are respectively

    (a) (b) (c)

    A) 0, 1, 1

    B) 0, 1, 0

    C) 1, 1, 0

    D) 1, 0, 1

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  • question_answer43) A stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points P and Q are at a distance of 4 m and 9 m respectively from the source. The ratio of amplitudes of the waves at P and Q is

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

    B) \[\frac{4}{9}\]

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

    D) \[\frac{9}{4}\]

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  • question_answer44) A galvanometer of resistance \[240\text{ }\Omega \] allows only 4% of the main current after connecting a shunt resistance. The value of the shunt resistance is

    A) \[10\text{ }\Omega \]

    B) \[20\text{ }\Omega \]

    C) \[8\text{ }\Omega \]

    D) \[5\text{ }\Omega \]

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  • question_answer45) The phenomena in which proton flips is

    A) nuclear magnetic resonance

    B) lasers

    C) radioactivity

    D) nuclear fusion

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  • question_answer46) \[y=3\sin \,\pi \left( \frac{t}{2}-\frac{x}{4} \right)\] represents an equation of a progressive wave, where t is in second and \[x\] is in metre. The distance travelled by the wave in 5 s is

    A) 8 m

    B) 10 m

    C) 5 m

    D) 32 m

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  • question_answer47) According to the quark model, it is possible to build all the hadrons using

    A) 2 quarks and 3 antiquarks

    B) 3 quarks and 2 antiquarks

    C) 3 quarks and 3 antiquarks

    D) 2 quarks and 2 antiquarks

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  • question_answer48) An \[\alpha \]-particle of mass \[6.4\times {{10}^{-27}}kg\] and charge \[3.2\times {{10}^{-19}}C\] is situated in a uniform electric field of \[1.6\times 10s\text{ }V{{m}^{-1}}\]. The velocity of the particle at the end of \[2\times {{10}^{-2}}m\] path when it starts from rest is

    A) \[2~\sqrt{3}\times {{10}^{5}}m{{s}^{-1}}\]

    B) \[8\times {{10}^{5}}m{{s}^{-1}}\]

    C) \[16\times {{10}^{5}}m{{s}^{-1}}\]

    D) \[4\times {{10}^{5}}m{{s}^{-1}}\]

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  • question_answer49) A cylindrical tube open at both the ends has a fundamental frequency of 390 Hz in air. If \[\frac{1}{4}th\] of the tube is immersed vertically in water the fundamental frequency of air column is

    A) 260 Hz

    B) 130 Hz

    C) 390 Hz

    D) 520 Hz

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  • question_answer50) The surface temperature of the stars is determined using

    A) Planck's law

    B) Wien's displacement law

    C) Rayleigh-Jeans law

    D) Kirchhoff?s law

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  • question_answer51) The charge deposited on 4\[\mu \]F capacitor in the circuit is

    A) \[6\times {{10}^{-6}}C\]

    B) \[12\times {{10}^{-6}}C\]

    C) \[24\times {{10}^{-6}}C\]

    D) \[36\times {{10}^{-6}}C\]

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  • question_answer52) A parallel beam of light is incident on a converging lens parallel to its principal axis. As one moves away from the lens on the other side of the principal axis, the intensity of light

    A) first decreases and then increases

    B) continuously increases

    C) continuously decreases

    D) first increases and then decreases

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  • question_answer53) Continuous emission spectrum is produced by

    A) incandescent electric lamp

    B) mercury vapour lamp

    C) sodium vapour lamp

    D) polyatomic substances

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  • question_answer54) A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength \[I\] is passed through the coil, the magnetic field at its centre is

    A) \[\frac{{{\mu }_{0}}nI}{\left( b-a \right)}{{\log }_{e}}\frac{a}{b}\]

    B) \[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}\]

    C) \[\frac{2{{\mu }_{0}}nI}{b}\]

    D) \[\frac{{{\mu }_{0}}nI}{2\left( b-a \right)}{{\log }_{e}}\frac{b}{a}\]

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  • question_answer55) A ray of light is incident on a plane mirror at an angle of \[{{60}^{o}}\]. The angle of deviation produced by the mirror is

    A) \[{{120}^{o}}\]

    B) \[{{30}^{o}}\]

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

    D) \[{{90}^{o}}\]

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  • question_answer56) The electric potential at any point \[x,y,z\] in metres is given by \[V=3{{x}^{2}}\]. The electric field at a point (2, 0, 1) is

    A) \[12\text{ }V{{m}^{-1}}\]

    B) \[-6\text{ }V{{m}^{-1}}\]

    C) \[6\text{ }V{{m}^{-1}}\]

    D) \[-12V{{m}^{-1}}\]

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  • question_answer57) Young's double slit experiment gives interference fringes of width 0.3 mm. A thin glass plate made of material of refractive index 1.5 is kept in the path of light from one of the slits, then the fringe width becomes

    A) zero

    B) 0.3 mm

    C) 0.45 mm

    D) 0.15 mm

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  • question_answer58) Near a circular loop of conducting wire as shown in the figure an electron moves along a straight line. The direction of the induced current if any in the loop is

    A) variable

    B) clockwise

    C) anticlockwise

    D) zero

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  • question_answer59) Hydrogen atom from excited state comes to the ground stage by emitting a photon of wavelength\[\lambda \]. If R is the Rydberg constant, the principal quantum number n of the excited state is

    A) \[\sqrt{\frac{\lambda R}{\lambda R-1}}\]

    B) \[\sqrt{\frac{\lambda }{\lambda R-1}}\]

    C) \[\sqrt{\frac{\lambda {{R}^{2}}}{\lambda R-1}}\]

    D) \[\sqrt{\frac{\lambda R}{\lambda -1}}\]

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  • question_answer60) The magnetic dipole moment of a current loop is independent of

    A) magnetic field in which it is lying

    B) number of turns

    C) area of the loop

    D) current in the loop

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  • question_answer61) The correct statement with regard to \[H_{2}^{+}\] and \[H_{2}^{-}\] is

    A) both \[H_{2}^{+}\] and \[H_{2}^{-}\] are equally stable

    B) both \[H_{2}^{+}\] and \[H_{2}^{-}\] do not exist

    C) Ha is more stable than \[H_{2}^{+}\]

    D) \[H_{2}^{+}\] is more stable than \[H_{2}^{-}\]

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  • question_answer62) Arrange the following in the increasing order of their bond order \[{{O}_{2}},O_{2}^{+},O_{2}^{-}\] and \[O_{2}^{2-}\]

    A) \[O_{2}^{2-},O_{2}^{-},{{O}_{2}},O_{2}^{+}\]

    B) \[O_{2}^{2-},O_{2}^{-},O_{2}^{+},{{O}_{2}}\]

    C) \[O_{2}^{+},{{O}_{2}},O_{2}^{-},O_{2}^{2-}\]

    D) \[{{O}_{2}},O_{2}^{+},O_{2}^{-},O_{2}^{2-}\]

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  • question_answer63) 2 g of a radioactive sample having half-life of 15 days was synthesized on 1st Jan 2009. The amount of the sample left behind on 1st March, 2009 (including both the days) is

    A) 0 g

    B) 0.125 g

    C) 1 g

    D) 0.5 g

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  • question_answer64) For a chemical reaction \[A\to B\], the rate of the reaction is \[2\times {{10}^{-3}}\,mol\,\,d{{m}^{-3}}{{s}^{-1}}\] when the initial concentration is \[0.05\,mol\,d{{m}^{-3}}\]. The rate of the same reaction is \[1.6\times {{10}^{-2}}mol\,d{{m}^{-3}}{{s}^{-1}}\] when the initial concentration is \[0.1\text{ }mol\text{ }d{{m}^{-3}}\]. The order of the reaction is

    A) 2

    B) 0

    C) 3

    D) 1

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  • question_answer65) For the decomposition of a compound AB at 600 K, the following data were obtained

    [AB] mol \[d{{m}^{-3}}\] Rate of decomposition of AB in mol \[d{{m}^{-3}}{{s}^{-1}}\]
    0.20 \[2.75\times {{10}^{-8}}\]
    0.40 \[11.0\times {{10}^{-8}}\]
    0.60 \[24.75\times {{10}^{-8}}\]
    The order for the decomposition of AB is

    A) 1.5

    B) 0

    C) 1

    D) 2

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  • question_answer66) The rate equation for a reaction \[A\to B\] is\[r=k{{[A]}^{0}}\]. If the initial concentration of the reactant is a mol \[d{{m}^{-3}}\], the half-life period of the reaction is

    A) \[\frac{a}{2k}\]

    B) \[\frac{k}{a}\]

    C) \[\frac{a}{k}\]

    D) \[\frac{2a}{k}\]

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  • question_answer67) 30 cc of \[\frac{M}{3}HCl,\,20\,cc\] of \[\frac{M}{2}HN{{O}_{3}}\] and 40 cc of \[\frac{M}{4}NaOH\] solutions are mixed and the volume was made up to \[1\text{ }d{{m}^{3}}\]. The pH of the resulting solution is

    A) 8

    B) 2

    C) 1

    D) 3

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  • question_answer68) An aqueous solution containing 6.5 g of \[NaCl\]of 90% purity was subjected to electrolysis. After the complete electrolysis, the solution was evaporated to get solid \[NaOH\]. The volume of 1 M acetic acid required to neutralise \[NaOH\] obtained above is

    A) \[1000\text{ }c{{m}^{3}}\]

    B) \[2000\text{ }c{{m}^{3}}\]

    C) \[100\text{ }c{{m}^{3}}\]

    D) \[200\text{ }c{{m}^{3}}\]

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  • question_answer69) The standard electrode potential for the half cell reactions are \[Z{{n}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Zn;\,{{E}^{o}}=-0.76\,V\] \[F{{e}^{2+}}+2{{e}^{-}}\xrightarrow{{}}Fe;\,{{E}^{o}}=-0.44\,V\] The emf of the cell reaction, \[F{{e}^{2+}}+Zn\xrightarrow{{}}Z{{n}^{2+}}+Fe\] is

    A) -0.32V

    B) -1.20V

    C) + 1.20V

    D) 4-0.32 V

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  • question_answer70) \[{{10}^{-6}}M\,NaOH\] is diluted 100 times. The pH of the diluted base is

    A) between 7 and 8

    B) between 5 and 6

    C) between 6 and 7

    D) between 10 and 11

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  • question_answer71) In the electrolysis of acidulated water, it is desired to obtain 1.12 cc of hydrogen per second under STP condition. The current to be passed is

    A) 1.93 A

    B) 9.65 A

    C) 19.3 A

    D) 0.965 A

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  • question_answer72) The one which decreases with dilution is

    A) molar conductance

    B) conductance

    C) specific conductance

    D) equivalent conductance

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  • question_answer73) Vapour pressure of pure ?A? is 70 mm of Hg at\[{{25}^{o}}C\]. It forms an ideal solution with ?B? in which mole fraction of A is 0.8. If the vapour pressure of the solution is 84 mm of Hg at\[{{25}^{o}}C\], the vapour pressure of pure ?B? at \[{{25}^{o}}C\] is

    A) 28 mm

    B) 56 mm

    C) 70mm

    D) 140mm

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  • question_answer74) A 6% solution of urea is isotonic with

    A) 1 M solution of glucose

    B) 0.05 M solution of glucose

    C) 6% solution of glucose

    D) 25% solution of glucose

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  • question_answer75) In countries nearer to polar region, the roads are sprinkled with \[CaC{{l}_{2}}\]. This is

    A) to minimise the wear and tear of the roads

    B) to minimise the snow fall

    C) to minimise pollution

    D) to minimise the accumulation of dust on the road

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  • question_answer76) For the reaction \[{{H}_{2}}O(l){{H}_{2}}O(g)\] at 373 K and 1 atm pressure

    A) \[\Delta H=0\]

    B) \[\Delta E=0\]

    C) \[\Delta H=T\Delta S\]

    D) \[\Delta H=\Delta E\]

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  • question_answer77) A compound of 'A' and 'B' crystallises in a cubic lattice in which 'A' atoms occupy the lattice points at the corners of the cube. The 'B' atoms occupy the centre of each face of the cube. The probable empirical formula of the compound is

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

    B)  \[{{A}_{3}}B\]

    C)  \[AB\]                                 

    D)  \[A{{B}_{3}}\]

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  • question_answer78) In electrophilic aromatic substitution reaction, the nitro group is meta directing because it

    A) decreases electron density at ortho and para positions

    B) decreases electron density at meta position

    C) increases electron density at meta position

    D) increases electron density at ortho and para positions

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  • question_answer79) \[C{{H}_{3}}COOH\xrightarrow{LiAl{{H}_{4}}}X\xrightarrow[{{300}^{o}}C]{Cu}Y\frac{Dilute}{naOH}\]In the above reaction Z is

    A) butanol

    B) aldol

    C) ketol

    D) acetal

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  • question_answer80) The best method for the conversion of an alcohol into an alkyl chloride is by treating the alcohol with

    A) \[PC{{l}_{3}}\]

    B) \[PC{{l}_{5}}\]

    C) \[SOC{{l}_{2}}\] in presence of pyridine

    D) dry \[HCl\] in the presence of anhydrous \[ZnC{{l}_{2}}\]

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  • question_answer81) The electrophile involved in the sulphonation of benzene is

    A) \[SO_{3}^{+}\]

    B) \[SO_{3}^{2-}\]

    C) \[H_{3}^{+}O\]

    D) \[S{{O}_{3}}\]

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  • question_answer82) The carbon-carbon bond length in benzene is

    A) in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{4}}\]

    B) same as in \[{{C}_{2}}{{H}_{4}}\]

    C) in between \[{{C}_{2}}{{H}_{6}}\] and \[{{C}_{2}}{{H}_{2}}\]

    D) in between \[{{C}_{2}}{{H}_{4}}\] and \[{{C}_{2}}{{H}_{2}}\]

    View Answer play_arrow
  • question_answer83) The compound which is not formed during the dry distillation of a mixture of calcium formate and calcium acetate is

    A) methanal

    B) propanal

    C) propanone

    D) ethanol

    View Answer play_arrow
  • question_answer84) An organic compound X is oxidised by using acidified \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\]. The product obtained reacts with phenyl hydrazine but does not answer silver mirror test. The possible structure of X is

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

    B) \[C{{H}_{3}}\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{-C}}\,-C{{H}_{3}}\]

    C) \[{{(C{{H}_{3}})}_{2}}CHOH\]

    D) \[C{{H}_{3}}CHO\]

    View Answer play_arrow
  • question_answer85) The reaction involved in the oil of winter green test is salicylic acid \[\xrightarrow[Conc.\,\,{{H}_{2}}S{{O}_{4}}]{\Delta }\] product. The product is treated with \[N{{a}_{2}}C{{O}_{3}}\]solution. The missing reagent in the above reaction is

    A) phenol

    B) \[NaOH\]

    C) ethanol

    D) methanol

    View Answer play_arrow
  • question_answer86) The compound which forms acetaldehyde when heated with dilute \[NaOH\], is

    A) 1, 1-dichloroethane

    B) 1, 1, 1-trichloroethane

    C) 1-chloroethane

    D) 1, 2-dichloroethane

    View Answer play_arrow
  • question_answer87) Arrange the following in the increasing order of their basic strengths\[C{{H}_{3}}N{{H}_{2}},\,{{(C{{H}_{3}})}_{2}}NH\], \[{{(C{{H}_{3}})}_{3}}N,\,N{{H}_{3}}\]

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

    B) \[N{{H}_{3}}<{{(C{{H}_{3}})}_{3}}N<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]

    C) \[{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}<C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH\]

    D) \[C{{H}_{3}}N{{H}_{2}}<{{(C{{H}_{3}})}_{2}}NH<{{(C{{H}_{3}})}_{3}}N<N{{H}_{3}}\]

    View Answer play_arrow
  • question_answer88) The one which has least iodine value is

    A) sunflower oil

    B) ginger oil

    C) ghee

    D) groundnut oil

    View Answer play_arrow
  • question_answer89) A diabetic person carries a packet of glucose with him always, because

    A) glucose reduces the blood sugar level slowly

    B) glucose increases the blood sugar level slowly

    C) glucose reduces the blood sugar level

    D) glucose increases the blood sugar level almost instantaneously

    View Answer play_arrow
  • question_answer90) There are 20 naturally occurring amino acids. The maximum number of tripeptides that can be obtained is

    A) 8000

    B) 6470

    C) 7465

    D) 5360

    View Answer play_arrow
  • question_answer91) Cooking is fast in a pressure cooker, because

    A) food particles are effectively smashed

    B) water boils at higher temperature inside the pressure cooker

    C) food is cooked at constant volume

    D) loss of heat due to radiation is minimum

    View Answer play_arrow
  • question_answer92) The ore that is concentrated by froth floatation process is

    A) zincite

    B) cinnabar

    C) bauxite

    D) malachite

    View Answer play_arrow
  • question_answer93) The correct set of four quantum numbers for outermost electron of potassium \[(Z=19)\] is

    A) \[4,1,0,\frac{1}{2}\]

    B) \[3,1,0,\frac{1}{2}\]

    C) \[4,0,0,\frac{1}{2}\]

    D) \[3,0,0,\frac{1}{2}\]

    View Answer play_arrow
  • question_answer94) A body of mass \[x\] kg is moving with a velocity of \[100\,\,m{{s}^{-1}}\]. Its de-Broglie wavelength is\[6.62\times {{10}^{-35}}m\]. Hence, \[x\] is \[(h=6.62\times {{10}^{-34}}Js)\]

    A) 0.1 kg

    B) 0.25 kg

    C) 0.15 kg

    D) 0.2 kg

    View Answer play_arrow
  • question_answer95) The correct order of ionisation energy of C, N, O, F is

    A) \[F<O<N<C\]

    B) \[F<N<C<O\]

    C) \[C<N<O<F\]

    D) \[C<O<N<F\]

    View Answer play_arrow
  • question_answer96) The oxide of an element whose electronic configuration is \[1{{s}^{2}},2{{s}^{2}},2{{p}^{6}},3{{s}^{1}}\] is

    A) neutral

    B) amphoteric

    C) basic

    D) acidic

    View Answer play_arrow
  • question_answer97) The characteristic not related to alkali metal is

    A) high ionisation energy

    B) their ions are isoelectronic with noble gases

    C) low melting point

    D) low electronegativity

    View Answer play_arrow
  • question_answer98) Among the following, the compound that contains ionic, covalent and coordinate linkage is

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

    B) \[N{{H}_{4}}Cl\]

    C) \[NaCl\]

    D) \[CaO\]

    View Answer play_arrow
  • question_answer99) A covalent molecule \[A{{B}_{3}}\] has pyramidal structure. The number of lone pair and bond pair of electrons in the molecule are respectively

    A) 2 and 2

    B) 0 and 4

    C) 3 and 1

    D) 1 and 3

    View Answer play_arrow
  • question_answer100) Excess of carbon dioxide is passed through 50 mL of 0.5 M calcium hydroxide solution. After the completion of the reaction, the solution was evaporated to dryness. The solid calcium carbonate was completely neutralised with N hydrochloric acid. The volume of hydrochloric acid required is (Atomic mass of calcium = 40)

    A) \[300\,\,c{{m}^{3}}\]

    B) \[200\,\,c{{m}^{3}}\]

    C) \[500\,\,c{{m}^{3}}\]

    D) \[400\,\,c{{m}^{3}}\]

    View Answer play_arrow
  • question_answer101) A bivalent metal has an equivalent mass of 32. The molecular mass of the metal nitrate is

    A) 182

    B) 168

    C) 192

    D) 188

    View Answer play_arrow
  • question_answer102) The rms velocity of molecules of a gas of density \[4\,kg\,{{m}^{-3}}\] and pressure \[1.2\times {{10}^{5}}N{{m}^{-2}}\] is

    A) \[300\,\,m{{s}^{-1}}\]

    B) \[900\,\,m{{s}^{-1}}\]

    C) \[120\,\,m{{s}^{-1}}\]

    D) \[600\,\,m{{s}^{-1}}\]

    View Answer play_arrow
  • question_answer103) 0.5 mole of each of \[{{H}_{2}},S{{O}_{2}}\] and \[C{{H}_{4}}\] are kept in a container. A hole was made in the container. After 3 h, the order of partial pressures in the container will be

    A) \[pS{{O}_{2}}>p{{H}_{2}}>pC{{H}_{4}}\]

    B) \[pS{{O}_{2}}>pC{{H}_{4}}>p{{H}_{2}}\]

    C) \[p{{H}_{2}}>pS{{O}_{2}}>pC{{H}_{4}}\]

    D) \[p{{H}_{2}}>pC{{H}_{4}}>pS{{O}_{2}}\]

    View Answer play_arrow
  • question_answer104) The enthalpy of formation of \[N{{H}_{3}}\] is\[-46\,\,kJ\,\,mo{{l}^{-1}}\]. The enthalpy change for the reaction \[2N{{H}_{3}}(g)\xrightarrow{{}}{{N}_{2}}(g)+3{{H}_{2}}(g)\] is

    A) +184 kJ

    B) +23 kJ

    C) +92 kJ

    D) +46 kJ

    View Answer play_arrow
  • question_answer105) 5 moles of \[S{{O}_{2}}\] and 5 moles of \[{{O}_{2}}\] are allowed to react. At equilibrium, it was found that 60% of \[S{{O}_{2}}\] is used up. If the partial pressure of the equilibrium mixture is one atmosphere, the partial pressure of \[{{O}_{2}}\] is

    A) 0.82 atm

    B) 0.52 atm

    C) 0.21 atm

    D) 0.41 atm

    View Answer play_arrow
  • question_answer106) \[2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)\] The equilibrium constant of the above reaction is 6.4 at 300 K. If 0.25 mole each of \[{{H}_{2}}\] and \[{{I}_{2}}\] are added to the system, the equilibrium constant will be

    A) 6.4

    B) 0.8

    C) 3.2

    D) 1.6

    View Answer play_arrow
  • question_answer107) Rate of physical adsorption increases with

    A) decrease in surface area

    B) decrease in temperature

    C) decrease in pressure

    D) increase in temperature

    View Answer play_arrow
  • question_answer108) IUPAC name of \[{{(C{{H}_{3}})}_{2}}CCl\] is

    A) n-butyl chloride

    B) 3-chloro butane

    C) 2-chloro 2-methyl propane

    D) t-butyl chloride

    View Answer play_arrow
  • question_answer109) Lucas test is associated with

    A) aldehydes

    B) phenols

    C) carboxylic acids

    D) alcohols

    View Answer play_arrow
  • question_answer110) An organic compound on heating with CuO produces \[C{{O}_{2}}\] but no water. The organic compound may be

    A) carbon tetrachloride

    B) chloroform

    C) methane

    D) ethyl iodide

    View Answer play_arrow
  • question_answer111) The condensation polymer among the following is

    A) rubber

    B) protein

    C) PVC

    D) polyethene

    View Answer play_arrow
  • question_answer112) The order of stability of metal oxides is

    A) \[A{{l}_{2}}{{O}_{3}}<MgO<F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}\]

    B) \[C{{r}_{2}}{{O}_{3}}<MgO<A{{l}_{2}}{{O}_{3}}<F{{e}_{2}}{{O}_{3}}\]

    C) \[F{{e}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<MgO\]

    D) \[F{{e}_{2}}{{O}_{3}}<A{{l}_{2}}{{O}_{3}}<C{{r}_{2}}{{O}_{3}}<MgO\]

    View Answer play_arrow
  • question_answer113) The temperature of the slag zone in the metallurgy of iron using blast furnace is

    A) \[1200-{{1500}^{o}}C\]

    B) \[1500-{{1600}^{o}}C\]

    C) \[400-{{700}^{o}}C\]

    D) \[800-{{1000}^{o}}C\]

    View Answer play_arrow
  • question_answer114) The function of \[Fe{{(OH)}_{3}}\] in the contact process is

    A) to remove arsenic impurity

    B) to detect colloidal impurity

    C) to remove moisture

    D) to remove dust particles

    View Answer play_arrow
  • question_answer115) In which of the following, \[N{{H}_{3}}\] is not used?

    A) Tollen's reagent

    B) Nessler's reagent

    C) Group reagent for the analysis of IV group basic radicals

    D) Group reagent for the analysis of III group basic radicals

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  • question_answer116) Argon is used

    A) in filling airships

    B) to obtain low temperature

    C) in high temperature welding

    D) in radiotherapy for treatment of cancer

    View Answer play_arrow
  • question_answer117) The incorrect statement in respect of chromyl chloride test is

    A) formation of red vapours

    B) formation of lead chromate

    C) formation of chromyl chloride

    D) -liberation of chlorine

    View Answer play_arrow
  • question_answer118) The magnetic moment of a transition metal ion is \[\sqrt{15}\,BM\]. Therefore, the number of unpaired electrons present in it, is

    A) 3

    B) 4

    C) 1

    D) 2

    View Answer play_arrow
  • question_answer119) The IUPAC name of \[{{[Co{{(N{{H}_{3}})}_{5}}ONO]}^{2+}}\] ion is

    A) penta ammine nitrito cobalt (IV) ion

    B) penta ammine nitrito cobalt (III) ion

    C) penta ammine nitro cobalt (III) ion

    D) penta ammine nitro cobalt (IV) ion

    View Answer play_arrow
  • question_answer120) The oxidation state of Fe in the brown ring complex: \[[Fe{{({{H}_{2}}O)}_{5}}NO]S{{O}_{4}}\] is

    A) +3

    B) 0

    C) +2

    D) +1

    View Answer play_arrow
  • question_answer121) The smallest positive integral value of n such that \[{{\left[ \frac{1+\sin \frac{\pi }{8}+i\,\cos \frac{\pi }{8}}{1+\sin \frac{\pi }{8}-i\,\cos \frac{\pi }{8}} \right]}^{n}}\] is purely imaginary is equal to

    A) \[4\]

    B) \[3\]

    C) \[2\]

    D) \[8\]

    View Answer play_arrow
  • question_answer122) Which one of the following is possible?

    A) \[\sin \theta =\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}},(a\ne b)\]

    B) \[\sin \theta =\frac{4}{5}\]

    C) \[\sin \theta =45\]

    D) \[\cos \theta =\frac{7}{3}\]

    View Answer play_arrow
  • question_answer123) If one side of a triangle is double the other and the angles opposite to these sides differ by \[{{60}^{o}},\]then the triangle is

    A) obtuse angled

    B) acute angled

    C) isosceles

    D) right angled

    View Answer play_arrow
  • question_answer124) \[3{{(\sin x-\cos x)}^{4}}+6{{(\sin \,x+\operatorname{cosx})}^{2}}\]\[+({{\sin }^{6}}x+{{\cos }^{6}}x)\] is equal to

    A) \[12\]

    B) \[13\]

    C) \[14\]

    D) \[11\]

    View Answer play_arrow
  • question_answer125) A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes \[44\text{ }m,\] when it has traced out \[{{72}^{o}}\]at the centre, the length of the rope is

    A) \[22\,\,m\]

    B) \[56\,\,m\]

    C) \[45\,\,m\]

    D) \[35\,\,m\]

    View Answer play_arrow
  • question_answer126) If \[\left| \begin{matrix} 1+{{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\,\sin \,2\theta \\ {{\sin }^{2}}\theta & 1+{{\cos }^{2}}\theta & 4\sin 2\theta \\ {{\sin }^{2}}\theta & {{\cos }^{2}}\theta & 4\sin 2\theta -1 \\ \end{matrix} \right|=0\] and \[0<\theta <\frac{\pi }{2},\] then \[\cos \,\,4\theta \] is equal to

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

    B) \[0\]

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

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

    View Answer play_arrow
  • question_answer127) The locus of the mid points of the chords of the circle \[{{x}^{2}}+{{y}^{2}}=4\]which subtend a right angle at the origin is

    A) \[{{x}^{2}}+{{y}^{2}}=1\]

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

    C) \[x+y=1\]

    D) \[x+y=2\]

    View Answer play_arrow
  • question_answer128) The length of the chord joining the points\[(4\,\cos \theta ,4sin\theta )\] and \[(4\,\cos (\theta +{{60}^{o}}),\] \[4sin(\theta +{{60}^{o}}))\]of the circle \[{{x}^{2}}+{{y}^{2}}=16\]is

    A) \[4\]

    B) \[8\]

    C) \[16\]

    D) \[2\]

    View Answer play_arrow
  • question_answer129) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-y=0\] and \[{{x}^{2}}+{{y}^{2}}+y=0\] and \[{{x}^{2}}+{{y}^{2}}+y=0\]is

    A) \[2\]

    B) \[3\]

    C) \[0\]

    D) \[1\]

    View Answer play_arrow
  • question_answer130) The coordinates of the centre of the smallest circle passing through the origin and having \[y=x+1\] as a diameter are

    A) \[\left( \frac{1}{2},\frac{-1}{2} \right)\]

    B) \[\left( \frac{1}{2},\frac{1}{3} \right)\]

    C) \[(-1,0)\]

    D) \[\left( -\frac{1}{2},\frac{1}{2} \right)\]

    View Answer play_arrow
  • question_answer131) The length of the diameter of the circle which cuts three circles \[{{x}^{2}}+{{y}^{2}}-x-y-14=0\] \[{{x}^{2}}+{{y}^{2}}+3x-5y-10=0\] \[{{x}^{2}}+{{y}^{2}}-2x+3y-27=0\] orthogonally, is

    A) \[8\]

    B) \[6\]

    C) \[4\]

    D) \[2\]

    View Answer play_arrow
  • question_answer132) For the parabola \[{{y}^{2}}=4x,\]the point P whose focal distance is 17, is

    A) \[(8,8)\] or \[(8,-8)\]

    B) \[(4,8)\] or \[(4,-8)\]

    C) \[(2,8)\] or \[(2,-8)\]

    D) \[(16,8)\] or \[(16,-8)\]

    View Answer play_arrow
  • question_answer133) The angle between the tangents drawn to the parabola \[{{y}^{2}}=12x\]from the point \[(-3,2)\]is

    A) \[{{90}^{o}}\]

    B) \[{{60}^{o}}\]

    C) \[{{30}^{o}}\]

    D) \[{{45}^{o}}\]

    View Answer play_arrow
  • question_answer134) The number of values of c such that the line \[y=4x+c\]touches the curve \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\] is

    A) \[1\]

    B) \[2\]

    C) \[\infty \]

    D) \[0\]

    View Answer play_arrow
  • question_answer135) If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] intersects the hyperbola \[xy={{c}^{2}}\]four points \[P({{x}_{1}},{{y}_{1}}),\] \[Q({{x}_{2}},{{y}_{2}}),\] \[R({{x}_{3}},{{y}_{3}})\] and \[S({{x}_{4}},{{y}_{4}})\] then,

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

    B)  \[{{x}_{1}}{{x}_{2}}{{x}_{3}}{{x}_{4}}=2{{c}^{4}}\]

    C)  \[{{y}_{1}}{{y}_{2}}{{y}_{3}}{{y}_{4}}=2{{c}^{4}}\]

    D)  \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}=0\]

    View Answer play_arrow
  • question_answer136) The foot of the perpendicular from the point\[(2,4)\] upon \[x+y=4\]is

    A) \[(2,2)\]

    B) \[(4,0)\]

    C) \[(1,3)\]

    D) \[(3,-1)\]

    View Answer play_arrow
  • question_answer137) The vertices of a triangle are \[(6,0),(0,6)\] and \[(6,6)\]. The distance between its circumventer and centroid is

    A) \[2\]

    B) \[\sqrt{2}\]

    C) \[1\]

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

    View Answer play_arrow
  • question_answer138) The angle between the pair of lines \[{{x}^{2}}+2xy-{{y}^{2}}=0\] is

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

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

    C) \[0\]

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

    View Answer play_arrow
  • question_answer139) \[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{3.2}^{n+1}}-{{4.5}^{n+1}}}{{{5.2}^{n}}+{{7.5}^{n}}}\] is equal to

    A) \[\frac{3}{5}\]

    B) \[-\frac{4}{7}\]

    C) \[-\frac{20}{7}\]

    D) \[0\]

    View Answer play_arrow
  • question_answer140) The function \[f(x)=\frac{\log (1+ax)-\log (1-bx)}{x}\] is not defined at \[x=0\]. The value which should be assigned to f at \[x=0\] so that it is continuous at \[x=0\] is

    A) \[a-b\]

    B) \[a+b\]

    C) \[\log a+\log b\]

    D) \[0\]

    View Answer play_arrow
  • question_answer141) If \[f(x)=1+nx+\frac{n(n-1)}{2}{{x}^{2}}\]\[+\frac{n(n-1)(n-2)}{6}{{x}^{3}}+.....+{{x}^{n}},\]then \[f''\] (1) is equal to

    A) \[n(n-1){{2}^{n-1}}\]

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

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

    D) \[n(n-1){{2}^{n}}\]

    View Answer play_arrow
  • question_answer142) If \[f(x)={{\log }_{{{x}^{2}}}}({{\log }_{e}}x),\] then \[f'(x)\] at \[x=e\] is

    A) \[1\]

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

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

    D) \[0\]

    View Answer play_arrow
  • question_answer143) If \[y={{\sin }^{2}}x\,\cos \,nx,\]then \[\frac{dy}{dx}\] is

    A) \[n\,\,{{\sin }^{n-1}}x\,\sin (n+1)x\]

    B) \[n\,\,{{\sin }^{n-1}}x\,\cos (n-1)x\]

    C) \[n\,\,{{\sin }^{n-1}}\,x\,\cos nx\]

    D) \[n{{\sin }^{n-1}}x\,\cos (n+1)x\]

    View Answer play_arrow
  • question_answer144) If \[f(x)=\frac{g(x)+g(-x)}{2}+\frac{2}{{{[h(x)+h(-x)]}^{-1}}}\]where g and h are differentiable function, then \[f'(0)\]

    A) \[1\]

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

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

    D) \[0\]

    View Answer play_arrow
  • question_answer145) The tangent to a given curve \[y=f(x)\]is perpendicular to the x-axis, if

    A) \[\frac{dy}{dx}=1\]

    B) \[\frac{dx}{dy}=0\]

    C) \[\frac{dx}{dy}=1\]

    D) \[\frac{dy}{dx}=0\]

    View Answer play_arrow
  • question_answer146) The minimum value of s

    A) \[-5\]

    B) \[\frac{1}{5}\]

    C) \[\frac{1}{243}\]

    D) \[\frac{1}{27}\]

    View Answer play_arrow
  • question_answer147) A stone is thrown vertically upwards from the top of a tower \[64\text{ }m\]high according to the law \[s=48t-16{{t}^{2}}.\]The greatest height attained by the stone above ground is

    A) \[36\,m\]

    B) \[32\,m\]

    C) \[100\,\,m\]

    D) \[64\,\,m\]

    View Answer play_arrow
  • question_answer148) The length of the subtangent at t on the curve\[x=a(t+\sin t),\] \[y=a(1-\cos t)\] is

    A) \[a\,\,\sin \,t\]

    B) \[2a\,\,\sin \,\left( \frac{t}{2} \right)\tan \left( \frac{t}{2} \right)\]

    C) \[2a\,\,\sin \,\frac{t}{2}\]

    D) \[2a\,\,{{\sin }^{3}}\,\left( \frac{t}{2} \right)\sec \left( \frac{t}{2} \right)\]

    View Answer play_arrow
  • question_answer149) \[\int{\text{cosec (x-a) cosec x dx}}\] is equal to

    A) \[x{{e}^{{{\tan }^{-1}}x}}+c\]

    B) \[{{e}^{{{\tan }^{-1}}x}}+c\]

    C) \[\frac{1}{2}{{e}^{{{\tan }^{-1}}x}}+c\]

    D) \[\frac{1}{2}x{{e}^{{{\tan }^{-1}}x}}+c\]

    View Answer play_arrow
  • question_answer150) \[\int{\text{cosec (x - a) cosec x dx}}\]is equal to

    A) \[\frac{-1}{\sin a}\log |\sin \,x\,\text{cosec(x-a) }\!\!|\!\!\text{ +c}\]

    B) \[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)\sin x]+c\]

    C) \[\frac{-1}{\sin a}\log |\sin \,x\,(x-a)cosecx]+c\]

    D) \[\frac{1}{\sin a}\log |\sin \,(\lambda -a)\sin x]+c\]

    View Answer play_arrow
  • question_answer151) If \[f(x)=\int_{-1}^{x}{|t|\,\,dt,}\] then for any \[x\ge 0,\] \[f(x)\]equal to

    A) \[1-{{x}^{2}}\]

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

    C) \[1+{{x}^{2}}\]

    D) \[\frac{1}{2}(1-{{x}^{2}})\]

    View Answer play_arrow
  • question_answer152) \[\int_{1}^{3}{\frac{\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}}dx\] is equal to

    A) \[1\]

    B) \[3\]

    C) \[2\]

    D) \[0\]

    View Answer play_arrow
  • question_answer153) The area bounded between the parabola\[{{y}^{2}}=4x\]and the line \[y=2x-4\]is equal to

    A) \[\frac{17}{3}sq\,unit\]

    B) \[\frac{19}{3}sq\,unit\]

    C) \[9\,sq\,unit\]

    D) \[15\,sq\,unit\]

    View Answer play_arrow
  • question_answer154) The differential equation of the family of circles passing through the orign and having their centres on the x-axis is

    A) \[{{y}^{2}}={{x}^{2}}+2xy\,\frac{dy}{dx}\]

    B) \[{{y}^{2}}={{x}^{2}}-2xy\,\frac{dy}{dx}\]

    C) \[{{x}^{2}}={{y}^{2}}+xy\,\frac{dy}{dx}\]

    D) \[{{x}^{2}}={{y}^{2}}+3xy\,\frac{dy}{dx}\]

    View Answer play_arrow
  • question_answer155) A population grows at the rate of 10% of the population per year. How long does it take for the population to double?

    A) \[20\text{ }log\text{ }2\text{ }yr\]

    B) \[10\text{ }log\text{ }2\text{ y}r\]

    C) \[5\text{ }log\text{ }2\text{ }yr\]

    D) \[2\text{ }log\text{ }10\text{ }yr\]

    E) None of these

    View Answer play_arrow
  • question_answer156) On the set of all natural numbers N, which one of the following * is a binary operation?

    A) \[a*b=\sqrt{ab}\]

    B) \[a*b=\frac{a-b}{a+b}\]

    C) \[a*b=a+3b\]

    D) \[a*b=3a-4b\]

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  • question_answer157) If \[\int_{0}^{1}{f(x)\,dx=5,}\] then the value of \[....+100\int_{0}^{1}{{{x}^{9}}\,\,f({{x}^{10}})dx}\]is equal to

    A) \[125\]

    B) \[625\]

    C) \[275\]

    D) \[55\]

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  • question_answer158) If \[ax+by=1,\] where a, b, x and y are integers, then which one of the following is not true?

    A) \[(a,y)=1\]

    B) \[(x,y)=1\]

    C) \[(b,y)=1\]

    D) \[(a,b)=1\]

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  • question_answer159) The digit in the unit place of the number \[2009!+{{3}^{7886}}\]is

    A) \[7\]

    B) \[3\]

    C) \[1\]

    D) \[9\]

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  • question_answer160) If \[\left| \begin{matrix} x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \\ \end{matrix} \right|=0,\] then a, b, c are

    A) in GP

    B) in HP

    C) equal

    D) in AP

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  • question_answer161) The value of \[\left| \begin{matrix} 1 & {{\log }_{x}}y & {{\log }_{x}}z \\ {{\log }_{y}}x & 1 & {{\log }_{y}}z \\ {{\log }_{z}}x & {{\log }_{e}}y & 1 \\ \end{matrix} \right|\] is equal to

    A) \[0\]

    B) \[1\]

    C) \[xyz\]

    D) \[\log \,xyz\]

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  • question_answer162) If \[A=\left[ \begin{matrix} 2 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & 2 \\ \end{matrix} \right],\]then \[|adj\,A|\]is equal to

    A) \[0\]

    B) \[9\]

    C) \[\frac{1}{9}\]

    D) \[81\]

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  • question_answer163) If A and B are square matrices of the same order such that \[(A+B)\,(A-B)={{A}^{2}}-{{B}^{2}},\] then \[{{(AB{{A}^{-1}})}^{2}}\]is equal to

    A) \[{{B}^{2}}\]

    B) \[I\]

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

    D) \[{{A}^{2}}\]

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  • question_answer164) If \[\vec{a}.\vec{b}=-|\vec{a}||\vec{b}|,\]then the angle between \[\vec{a}\] and \[\vec{b}\] is

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

    B) \[{{180}^{o}}\]

    C) \[{{90}^{o}}\]

    D) \[{{60}^{o}}\]

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  • question_answer165) If \[\vec{a}+2\vec{b}+3\vec{c}=\vec{0},\] then \[\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}\] is equal to

    A) \[2(\vec{b}\times \vec{c})\]

    B) \[3(\vec{c}\times \vec{a})\]

    C) \[\vec{0}\]

    D) \[6(\vec{b}\times \vec{c})\]

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  • question_answer166) If the volume of the parallelepiped with \[\vec{a},\] \[\vec{b}\] and \[\vec{c}\]as coterminous edges is \[40\text{ }cu\]unit, then the volume of the parallelepiped having \[\vec{b}+\vec{c},\] \[\vec{c}+\vec{a}\] and \[\vec{a}+\vec{b}\] as coterminous edges in cubic unit is

    A) \[80\]

    B) \[120\]

    C) \[160\]

    D) \[40\]

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  • question_answer167) In the group \[G\{0,1,2,3,4,5\}\] under addition modulo \[6,{{(2{{+}_{6}}{{3}^{-1}}{{+}_{6}}4)}^{-1}}\] is equal to

    A) \[2\]

    B) \[3\]

    C) \[5\]

    D) \[0\]

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  • question_answer168) Which one of the following is not true?

    A) Inverse of an element in a group is unique.

    B) Fourth roots of unity form an additive abelian group.

    C) Cancellation laws hold in a group.

    D) Identity element in a group is unique.

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  • question_answer169) The number of subgroups of the group \[({{Z}_{5}},{{+}_{5}})\] is

    A) \[1\]

    B) \[3\]

    C) \[4\]

    D) \[2\]

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  • question_answer170) The negation of \[p\wedge (q\to \tilde{\ }r)\] is

    A) \[\tilde{\ }p\wedge (q\wedge r)\]

    B) \[p\vee (q\vee r)\]

    C) \[p\vee (q\wedge r)\]

    D) \[\tilde{\ }p\vee (q\wedge r)\]

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  • question_answer171) If \[n=(2020)!\]then\[\frac{1}{{{\log }_{2}}n}+\frac{1}{{{\log }_{3}}n}+\frac{1}{{{\log }_{4}}n}+....+\frac{1}{{{\log }_{2020}}n}\]is equal to

    A) \[2020\]

    B) \[1\]

    C) \[(2020)!\]

    D) \[0\]

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  • question_answer172) If 'n' is a positive integer, then \[{{n}^{3}}+2n\]is divisible by

    A)  \[2\]                                    

    B)  \[6\]

    C)  \[15\]                                  

    D)  \[3\]

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  • question_answer173) On the set of integers Z, define \[f:z\to z\] as \[f(n)=\left\{ \begin{matrix} \frac{n}{2}, & n\,is\,\,even \\ 0, & n\,\,\,is\,\,odd \\ \end{matrix} \right.\], then f is

    A) injective but not subjective

    B) neither injective nor subjective

    C) surjective but not injective

    D) objective

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  • question_answer174) If \[\alpha \] and \[\beta \] are the roots of then \[{{\alpha }^{16}}+{{\beta }^{16}}\] is equal to

    A) \[1\]

    B) \[-1\]

    C) \[2\]

    D) \[0\]

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  • question_answer175) The total number of terms in the expansion of \[{{(x+y)}^{100}}+{{(x-y)}^{100}}\] after simplification is

    A) \[51\]

    B) \[202\]

    C) \[100\]

    D) \[50\]

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  • question_answer176) \[{{\cot }^{-1}}({{2.1}^{2}})+co{{t}^{-1}}({{2.2}^{2}})+{{\cot }^{-1}}({{2.3}^{2}})+...\] upto \[\infty \] is equal to

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

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

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

    D) \[\frac{\pi }{5}\]

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  • question_answer177) If 'x' takes negative permissible value, then \[{{\sin }^{-1}}x\] is equal to

    A) \[-{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]

    B) \[{{\cos }^{-1}}\sqrt{{{x}^{2}}-1}\]

    C) \[\pi -{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]

    D) \[{{\cos }^{-1}}\sqrt{1-{{x}^{2}}}\]

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  • question_answer178) If \[1+\sin +{{\sin }^{2}}x+...\] upto \[\infty =4+2\sqrt{3},\] \[0<x<\pi \]and \[x\ne \frac{\pi }{2},\] then x is equal to

    A) \[\frac{\pi }{3},\frac{5\pi }{6}\]

    B) \[\frac{2\pi }{3},\frac{\pi }{6}\]

    C) \[\frac{\pi }{3},\frac{2\pi }{3}\]

    D) \[\frac{\pi }{6},\frac{\pi }{3}\]

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  • question_answer179) The complex number \[\frac{1+2i}{1-i}\] lies in

    A) second quadrant

    B) third quadrant

    C) fourth quadrant

    D) first quadrant

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  • question_answer180) If P is the point in the Agrand diagram corresponding to the complex number \[\sqrt{3}+i\] and if OPQ is an isosceles right angled triangle, right angled at ?O?, then Q represents the complex number

    A) \[-1+i\sqrt{3}\] or \[1-i\sqrt{3}\]

    B) \[1\pm i\sqrt{3}\]

    C) \[\sqrt{3}-i\] or \[1-i\sqrt{3}\]

    D) \[-1\pm i\sqrt{3}\]

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