# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2002

### done Rajasthan PET Solved Paper-2002

• question_answer1) The unit of surface tension is

A) N/C

B) N/m

C) C/N

D) m/N

• question_answer2) The unit of Stefan constant is

A) $W/{{(K)}^{4}}$

B) $eV/{{(K)}^{4}}$

C) $W/{{(m)}^{2}}{{(K)}^{4}}$

D) $eV/{{(m)}^{2}}{{(K)}^{4}}$

• question_answer3) A ball is projected on the strain from the horizontal with velocity u. The maximum number of strains that can be completed crossed is

A) $\frac{2{{u}^{2}}h}{g{{b}^{2}}}$

B) $\frac{{{u}^{2}}h}{g{{b}^{2}}}$

C) $\frac{2{{u}^{2}}b}{gh}$

D) $\frac{{{u}^{2}}b}{gh}$

• question_answer4) The acceleration a of moving body from rest is 2 (t - 1). Then, the velocity at 5 s will be

A) 15 m/s

B) 25 m/s

C) 35 m/s

D) 45 m/s

• question_answer5) The positive charged ball is suspended by thread of silk. If we place a positive charge${{q}_{0}}$at one point and measure the$F/{{q}_{0}},$then this can say that electric field E

A) $>\frac{F}{{{q}_{0}}}$

B) $=\frac{F}{{{q}_{0}}}$

C) $=\frac{F}{{{q}_{0}}}$

D) $Can't\,be\,measured$

• question_answer6) If $Z=\frac{a{{b}^{2}}}{{{c}^{3}}}$, then what is the error in Z? The errors in a, b, c are$\alpha$,$\beta$and $\gamma$ respectively

A) $\alpha$ + 2$\beta$ - 3$\gamma$

B) $\alpha$- 2$\beta$ + 3$\gamma$

C) 2 $\alpha$+ 3$\beta$ +$\gamma$

D) $\alpha$ + 2$\beta$+ 3$\gamma$

• question_answer7) The momenta of two particles of masses m and 2m are 2p and p respectively. The ratio of their kinetic energies will be

A) 2 : 1

B) 4 : 1

C) 1 : 8

D) 8 : 1

• question_answer8) If the escape velocity at the earth is 11.2 km/s, then what will be the escape velocity of planet having mass 4 times of earth and gravitational acceleration equal to earth?

A) 7.9 m/s

B) 11.2 km/s

C) 15.7 km/s

D) None of these

• question_answer9) The ratio of radii to the gravitational acceleration of planets X and Y are R and a respectively. The ratio of escape velocities at them, is

A) $\sqrt{aR}$

B) $\frac{1}{\sqrt{aR}}$

C) $aR$

D) $\frac{1}{aR}$

• question_answer10) If the range and time period of projectile are related to$R=5{{T}^{2}},$then the angle of projection will be

A) $\pi /2$

B) $\pi /3$

C) $\pi /4$

D) $\pi /6$

• question_answer11) If two masses${{m}_{1}}$and${{m}_{2}}$are dropped freely from the heights${{h}_{1}}$and${{h}_{2}}$respectively, then the ratio of times to reach on earth will be

A) $\sqrt{\frac{{{h}_{2}}}{{{h}_{1}}}}$

B) $\sqrt{\frac{{{h}_{1}}}{{{h}_{2}}}}$

C) $\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}$

D) $\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}$

• question_answer12) A vehicle starting the motion on any curve path, then how much distance will it cover?

A) $\frac{{{u}^{2}}}{4\mu g}$

B) $\frac{{{u}^{2}}}{3\mu g}$

C) $\frac{{{u}^{2}}}{2\mu g}$

D) None of these

• question_answer13) At which of the following positions, the acceleration of the particle in SUM will be maximum?

A) At mean position

B) At peak position

C) At half position of amplitude

D) None of the above

• question_answer14) For following arrangement, the value of equivalent force constant is

A) $\frac{3}{2}k$

B) $\frac{2}{3}k$

C) $2k$

D) $3k$

• question_answer15) The amplitude of any damped oscillation becomes half in 1 min. After 3 s, its amplitude becomes$\frac{1}{x}$ times of initial amplitude, then$x$is $x$

A) $2\times 3$

B) ${{2}^{3}}$

C) ${{3}^{2}}$

D) $3\times {{2}^{2}}$

• question_answer16) In friction, the relation between coefficient of kinetic friction ${{\mu }_{k}}$and coefficient of static friction ${{\mu }_{s}}$is

A) ${{\mu }_{k}}\ge {{\mu }_{s}}$

B) ${{\mu }_{k}}={{\mu }_{s}}$

C) ${{\mu }_{k}}\le {{\mu }_{s}}$

D) None of these

• question_answer17) The ratio of translational kinetic energy to the total kinetic energy for rolling motion of solid sphere without sliding will be

A) $\frac{2}{7}$

B) $\frac{7}{2}$

C) $\frac{5}{7}$

D) $\frac{7}{5}$

• question_answer18) The two particles A and B remain at rest position. Both of them due to their attraction forces move towards each other. At any instant the velocity of A is v. At that instant velocity of B is 2v. The velocity of centre- of mass of the system will be

A) v

B) zero

C) 1.5 v

D) 3v

• question_answer19) The dimensional formula of latent heat is

A) [MLT]

B) $[{{M}^{0}}{{L}^{2}}{{T}^{-2}}]$

C) $[{{M}^{2}}{{L}^{2}}2]$

D) $[M{{L}^{0}}{{T}^{-2}}]$

• question_answer20) A hollow cylinder and a solid cylinder having same mass and diameter are rolled at inclined plane, then which will reach first at the bottom?

A) Both at same time

B) Hollow cylinder

C) Solid cylinder

D) Which has more density

• question_answer21) A ball is dropped towards the earth from height h, then after three jumps what will be value of height?

A) ${{e}^{h/3}}$

B) $h{{e}^{6}}$

C) $he$

D) None of these

• question_answer22) In projectile motion, the value of horizontal range is

A) ${{u}^{2}}{{\sin }^{2}}\theta /g$

B) $\frac{2{{u}^{2}}\sin \theta \cos \theta }{g}$

C) $\frac{{{u}^{2}}\sin 2\theta }{2g}$

D) $\frac{{{u}^{2}}\cos 2\theta }{g}$

• question_answer23) A player takes a complete round in path of radius R in 40 s. After 2 min 20 s, its displacement will be

A) zero

B) 2R

C) $2\pi R$

D) $7\pi R$

• question_answer24) Mars is revolving around the sun in elliptical orbit. Its velocity is minimum on

A) D

B) C

C) B

D) A

• question_answer25) If the mass and radius of planet are twice the earth, then time period of second pendulum on planet will be

A) 1 s

B) 2 s

C) $2\sqrt{2\,s}$

D) $\frac{1}{2\sqrt{2}}s$

• question_answer26) The particle of mass m moves with velocity v0 and strikes with suspended pendulum of same mass as shown in figure. After completely in elastic collision, the greatest height by particle and pendulum is

A) $\frac{{{v}_{0}}^{2}}{4g}$

B) $\frac{{{v}_{0}}^{2}}{8g}$

C) $\frac{{{v}_{0}}^{2}}{g}$

D) $\frac{4{{v}_{0}}^{2}}{g}$

• question_answer27) In gas, the velocity of sound is v = $\sqrt{\frac{\gamma RT}{M}}$, the dimensions of $\gamma$ are

A) $[{{M}^{0}}{{T}^{0}}{{T}^{0}}]$

B) $[ML{{T}^{-2}}]$

C) $[ML{{T}^{-2}}]$

D) $[L{{T}^{-2}}]$

• question_answer28) The minimum distance of reflected surface from the source for listening the echo of sound is

A) 28 m

B) 18 m

C) 19 m

D) 16.5 m

• question_answer29) Two sound waves of wavelengths 5 m and 6 m formed 30 beats in 3 s. The velocity of sound is

A) 300 m/s

B) 310 m/s

C) 320 m/s

D) 330 m/s

• question_answer30) Two waves are in phase when

A) amplitude is same

B) wavelength is same

C) amplitude and wavelength are same

D) phase difference remains constant

• question_answer31) The effective capacity between points x and y is

A) C

B) 2C/3

C) 3C/2

D) None of these

• question_answer32) Newton's law of cooling derived by

A) Stefan's law

B) Kirchhoffs law

C) Wien's displacement law

D) None of the above

• question_answer33) Which of the following laws explains the spectrum of black body?

A) Rayleigh - Jeans's law

B) Planck's law

C) Wien's displacement law

D) Stefan's law

• question_answer34) The magnetic field at centre P is

A) $\frac{{{\mu }_{0}}I}{4r}$

B) $\frac{{{\mu }_{0}}I}{2r}$

C) $\frac{{{\mu }_{0}}I}{8r}$

D) zero

• question_answer35) The magnetic field at centre of coil having radius r and current I will be

A) $\frac{{{\mu }_{0}}I}{4r}$

B) $\frac{{{\mu }_{0}}I}{2r}$

C) zero

D) $\frac{{{\mu }_{0}}I}{r}$

• question_answer36) The two charges 7 $\mu$ C and - 5$\mu$ C are placed at some distance from each other. They experience a force F. If each of them is given and additional charge of - 2$\mu$C, the new force of attraction will be

A) F

B) 2F

C) F/2

D) zero

• question_answer37) ${{F}_{g}}$ and${{F}_{g}}$represent the gravitational and electric forces between the electrons at distance 10 cm, then the ratio of $\frac{{{F}_{g}}}{{{F}_{e}}}$ will be

A) ${{10}^{42}}$

B) 10

C) 1

D) ${{10}^{-43}}$

• question_answer38) The stored energy in capacitor will be

A) $\frac{1}{2}{{C}^{2}}V$

B) $\frac{1}{2}QV$

C) $\frac{1}{2}Q{{V}^{2}}$

D) None of these

• question_answer39) The capacity of spherical conductor is 0.1 $\mu$ F, then its radius will be

A) 90 m

B) 900 m

C) 9000 m

D) zero

• question_answer40) Burning 1 g coal gives 2 kcal useful energy. For 1 kWh, the quantity of coal needed will be

A) $9kg$

B) $\frac{4}{3}kg$

C) $\frac{3}{7}kg$

D) $\frac{3}{14}kg$

• question_answer41) The current I in B circuit is

A) 0.4 A

B) $-0.4\text{ }A$

C) 0.8 A

D) $-0.08\text{ }A$

• question_answer42) The current$I$ in the following circuit is

A) 8 A

B) 16 A

C) 12 A

D) 24 A

• question_answer43) According to Kirchhoffs law the algebraic sum of currents meeting at a junction is

A) limited

B) zero

C) infinite

D) None of these

• question_answer44) If a container filled by the ideal gas keeps in the moving car, the temperature of the gas

A) will be increased

B) will be decreased

C) will remain unchanged

D) None of the above

• question_answer45) The number of turns of primary and secondary coils of transformer are 500 and 5000 respectively. The voltage and frequency of primary coil are 800 V and 50 Hz respectively, then the frequency and voltage of secondary coil will be

A) 50 Hz, 8000 V

B) 800 Hz, 800 V

C) 50 Hz, 80 V

D) 50 Hz, 800 V

• question_answer46) If an ideal gas filled in a closed container and the container is open in vacuum, then its temperature will be

A) increased

B) decreased

C) unchanged

D) None of these

• question_answer47) In apparatus the values of potential V and flowing current I are given this type $V=2\text{ }cos\omega$ t volt $I~=2\text{ }sin\,\omega$ t amp Then, in apparatus the power dissipated will be

A) zero

B) 1.2 W

C) 4 W

D) 2.0 W

• question_answer48) The power dissipated in AC circuit will be

A) $\frac{{{V}_{0}}}{\sqrt{2}}\,\frac{{{I}_{0}}}{\sqrt{2}}\,\cos \,\phi$

B) ${{V}_{0}}{{I}_{0}}\cos \phi$

C) $\frac{{{V}_{0}}{{I}_{0}}}{4}\,\cos \phi$

D) None of these

• question_answer49) In AC circuit, in resonant position, the reading of which voltmeter is zero?

A) ${{V}_{1}}$

B) ${{V}_{2}}$

C) ${{V}_{3}}$

D) ${{V}_{4}}$

• question_answer50) 1 cm 3 water at 1 atm pressure and$100{}^\circ C$ converts into$1671\text{ }c{{m}^{3}}$steam by taking 54 cal heat. The work done (in cal) during this process will be

A) 400

B) 40

C) 540

D) None of these

• question_answer51) In the following circuit, the value of charge on capacitor of capacity 5 $\mu$ F will be

A) 4.5 $\mu$C

B) 9.0 $\mu$C

C) 7 $\mu$C

D) 30 $\mu$C

• question_answer52) Shown in the given diagram, the electric potential energy of the system will be $\left( k=\frac{1}{4\pi {{\varepsilon }_{0}}} \right)$

A) $\frac{k{{q}^{2}}}{a}[\sqrt{2}-4]$

B) $\frac{k{{q}^{2}}}{a}$

C) $0$

D) $\frac{kq}{a}[\sqrt{2}-4]$

• question_answer53) For balanced Wheatstone bridge, the value of resistance R will be

A) 8$\Omega$

B) 4$\Omega$

C) 2$\Omega$

D) 6$\Omega$

• question_answer54) In the full-wave rectifier, the output frequency will be

A) n

B) 2n

C) n/2

D) ${{n}^{2}}$

• question_answer55) The adiabatic coefficient of a gas is 7/5 .This gas will be

A) He

B) Ar

C) Ne

D) ${{H}_{2}}$

• question_answer56) In the circuit shown in figure, neglecting source resistance the voltmeter and ammeter readings will respectively be (V = 240V)

A) 0, 3 A

B) 150 V, 3 A

C) 150 V, 6 A

D) 0, 8 A

• question_answer57) Find the value of current I in the given circuit

A) 1 A

B) 4 A

C) 5 A

D) None of these

• question_answer58) In nth orbit, the angular velocity of electrons is proportional to

A) ${{n}^{-1}}$

B) ${{n}^{-2}}$

C) ${{n}^{-3}}$

D) ${{n}^{-4}}$

• question_answer59) Choose the correct relation

A) $y=\,\frac{mglL}{\pi {{r}^{2}}l}$

B) $y=\,\frac{mgL}{\pi rl}$

C) $y=\,\frac{mg{{\pi }^{2}}}{\pi L}$

D) $y=\,\frac{mgr}{\pi L}$

• question_answer60) Choose the right relation.

A) ${{t}_{1/2}}=0.693{{t}_{av}}$

B) ${{t}_{av}}=0.693{{t}_{1/2}}$

C) ${{t}_{1/2}}=0.414{{t}_{av}}$

D) None of these

• question_answer61) The nature of bond in diamond is

A) ionic

B) covalent

C) van der Waals'

D) metallic

• question_answer62) Which of the following experiments does represent the wave nature of electrons?

A) Davisson- Germer

B) de-Broglie

C) Rutherford

D) Millikan oil drop

• question_answer63) The velocity of an electron in the second orbit of sodium atom (atomic number = 1, 1) is v. The velocity of an electron in its fifth orbit will be

A) $v$

B) $\frac{22}{5}v$

C) $\frac{3}{2}v$

D) $\frac{2}{5}v$

• question_answer64) Choose the right equation.

A) $\frac{h\lambda }{E}=E$

B) $h\lambda =\frac{E}{c}$

C) $\frac{hc}{E}=\lambda$

D) None of these

• question_answer65) The temperature of star is 6060 K and maximum radiation emitted at 4653 A. For another star, the maximum radiation emitted at 4545 A. The temperature of another star will be

A) 300 K

B) 6204 K

C) 3000 K

D) 120 K

• question_answer66) In a double-slit experiment, the slits are separated by a distance d and the screen is at a distance D from the slits. For monochromatic source of wavelength X, the width of emitted fringe will be

A) $\beta =\frac{D\lambda }{d}$

B) $\beta =\frac{d\lambda }{D}$

C) $\beta =\frac{D\lambda }{d}$

D) None of these

• question_answer67) A body is walking away from a wall towards an observer at a speed of 2 m/s and blows a whistle whose frequency is 680 Hz. The number of beats heard by the observed per second is (velocity of sound in air = 340 m/s)

A) zero

B) 2

C) 8

D) 4

• question_answer68) A light ray incidents at angle of$60{}^\circ$in denser medium in such a way so that reflected and refracted rays remain perpendicular to each other. Refractive index of denser medium relative to rarer medium will be

A) $\mu =\sqrt{3}$

B) $\mu =\frac{1}{\sqrt{3}}$

C) $\mu =\sqrt{2}$

D) $\mu =\frac{1}{\sqrt{2}}$

• question_answer69) For uranium nucleus, the value of nucleon binding energy will be

A) 7.6eV

B) 7.6 $\mu$eV

C) 7.6 MeV

D) 7.6 keV

• question_answer70) The kinetic energy of neutron at temperature 300 K will be$(m=1.67\times {{10}^{-27}}kg)$

A) $6.21\times ~{{10}^{-21}}J$

B) $8.2\times {{10}^{-21}}J$

C) $9\times {{10}^{-21}}J$

D) None of these

• question_answer71) By which of the following the nucleus can't be cleaved?

A) $\alpha -$ ray

B) $\gamma$ -ray

C) $\beta$-ray

D) Laser

• question_answer72) Which of the following is not semiconductor?

A) $Si$

B) $Ge$

C) $NaCl$

D) $Cds$

• question_answer73) For good emissive should be

A) small work function and small melting point

B) small work function and high melting point

C) high work function and high melting point

D) high work function and small melting point

• question_answer74) The retarding potential for having zero photo-electron current

A) is proportional to the wavelength of incident light

B) increases uniformly with the increase in the wavelength of incident light

C) is proportional to the frequency of incident light

D) increases uniformly with the increase in the frequency of incident light wave

• question_answer75) From molecular theory of gas which of the following quantities at certainly for all gases will be same?

A) Momentum

B) Kinetic energy

C) Velocity

D) Mass

• question_answer76) At a given temperature the root mean square velocity of which gas is minimum?

A) ${{O}_{2}}$

B) ${{N}_{2}}$

C) $C{{l}_{2}}$

D) He

• question_answer77) The resonant frequency of the following circuit is

A) 9.3 Hz

B) 79 Hz

C) 930 Hz

D) None of these

• question_answer78) Which of the following instruments depends upon the coil which rotates in the magnetic field?

A) Electric motor

B) Dynamo

C) Both [a] & [b]

D) None of these

• question_answer79) The principle of dynamo is

A) electromagnetic induction

B) magnetic induction

C) electric induction

D) None of the above

• question_answer80) In a adiabatic process, initial pressure is 2 atm and final volume is half of initial volume, then final pressure will be ($\gamma$ = 1.3)

A) ${{2}^{2.3}}$atm

B) 4 atm

C) 6 atm

D) None of these

• question_answer81) Mutual conductance of triode is

A) ${{\left( \frac{\Delta {{I}_{p}}}{\Delta {{V}_{g}}} \right)}_{{{V}_{P}}\text{=}\,\text{constant}}}$

B) ${{\left( \frac{\Delta {{V}_{g}}}{\Delta {{I}_{g}}} \right)}_{{{V}_{g}}\text{=}\,\text{constant}}}$

C) ${{\left( \frac{\Delta {{I}_{p}}}{\Delta {{V}_{p}}} \right)}_{{{V}_{g}}\text{=}\,\text{constant}}}$

D) None of the above

• question_answer82) The potential of illuminate cathode, grid and plate of triode valve are 0, -3 and 80 V respectively. An electron moves with the kinetic energy of 5eV from the surface of cathode. On reaching the grid, the kinetic energy of electron will be

A) 15 eV

B) 2 eV

C) 85 eV

D) 30 eV

• question_answer83) In photo-electric experiment, for incident light of 4000$\overset{o}{\mathop{\text{A}}}\,$the stopping potential is 2 V. If the value of incident light is changed to 3000$\overset{o}{\mathop{\text{A}}}\,$, the stopping potential will be

A) 2 V

B) less than 2 V

C) zero

D) more than 2 V

• question_answer84) In nuclear fusion the order of binding energy is

A) ${{10}^{6}}eV$

B) ${{10}^{7}}eV$

C) ${{10}^{5}}eV$

D) ${{10}^{9}}eV$

• question_answer85) Choose the correct relation.

A) $B=\frac{\Delta p}{-\Delta V/V}$

B) $B=-\frac{\Delta V/V}{\Delta p}$

C) $B=\frac{\Delta p}{\Delta V}$

D) None of these

• question_answer86) The root mean square velocity and density of ideal gas are 1840 m/s and $0.8\text{ }kg/{{m}^{3}}$respectively. Its pressure will be

A) $9.02\times {{10}^{5}}N/{{m}^{2}}$

B) $0.02\times {{10}^{4}}N/{{m}^{2}}$

C) $9.02\times {{10}^{3}}N/{{m}^{2}}$

D) $9.02\times {{10}^{6}}N/{{m}^{2}}$

• question_answer87) If the pressure at half depth of river is$\frac{2}{3}$times of pressure of that bottom, then depth of river is

A) 10 m

B) 20 m

C) 60 m

D) 30 m

• question_answer88) Two equal drops of water with a velocity v is falling in air. If both drops are mixed, then velocity will be

A) $2v$

B) $\sqrt{2v}$

C) ${{2}^{2/3}}v$

D) $\frac{v}{\sqrt{2}}$

• question_answer89) 800 identical water drops are combined to form a big drop. Then, the ratio of the final surface energy to the initial surface energy of all the drops together is

A) 1 : 10

B) 1 : 15

C) 1 : 20

D) 1 : 25

• question_answer90) Three light bulbs of 100 W, 200 W and 40 W are connected in series with 200 V source. The current will be

A) maximum in bulb of 100 W

B) maximum in bulb of 200 W

C) maximum in bulb of 40 W

D) equal in all

• question_answer91) A gas mixture consists of 2 moles of oxygen and 4 moles of argan at temperature T. Neglecting all vibrational moles, the total internal energy of the system is

A) 4 RT

B) 15 RT

C) 9 RT

D) 11 RT

• question_answer92) One mole ($\gamma$= 5/3) of monoatomic gas mixture and the one mole of diatomic gas ($\gamma$=7/5]. For mixtured the value of y will be

A) 1.40

B) 1.50

C) 1.53

D) 3.07

• question_answer93) The weight of a metal piece in air is 46 g. When it is immersed in a liquid of relative density 1.24 at $27{}^\circ C,$then its weight becomes 30 g. When its temperature increases to$42{}^\circ ,$the weight of metal piece becomes 30.5 g. If the relative density of liquid at$42{}^\circ C$is 1.2, the coefficient of linear expansion of metal will be

A) $4.3\,\times \,{{10}^{-5}}{{/}^{o}}C$

B) $2.3\,\times \,{{10}^{-5}}{{/}^{o}}C$

C) $5.3\,\times \,{{10}^{-5}}{{/}^{o}}C$

D) $3.4\,\times \,{{10}^{-5}}{{/}^{o}}C$

• question_answer94) How many will be the heat generate in resistance of 500$\Omega$, when the switch comes from position 1 to position 2?

A) 40$\times$${{10}^{-3}}J$

B) $50\times \,{{10}^{-3}}J$

C) $60\times \,{{10}^{-3}}J$

D) $30\times \,{{10}^{-3}}J$

• question_answer95) A short circuited coil is placed in magnetic field at any time. Power loss in coil occurs due to generated induced current. If number of turns becomes 4 times and radius of wire becomes half, then the loss of electric power will be

A) half

B) equal

C) two times

D) four times

• question_answer96) The magnetic field induction at centre O will be

A) $\frac{3{{\mu }_{0}}{{I}_{a}}}{4a}$

B) $\frac{{{\mu }_{0}}{{I}_{a}}}{4\pi a}(1+\pi )$

C) $\frac{{{\mu }_{0}}I}{4\pi a}$

D) $\frac{3{{\mu }_{0}}I}{8a}$

• question_answer97) Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreased by 2% keeping all other quantities same, then

A) g decreases by 2% and K decreases by 4%

B) g decreases by 4% and K increases by 2%

C) g increases by 4% and K increases by 4%

D) g decreases by 4% and K increases by 4%

• question_answer98) The gravitational force between the point masses m and M is F. Now if an another point mass 2m placed in front and touch of m, then force on M due to m and total force on M will be

A) 2F, F

B) F, 2F

C) F, 3F

D) F, F

• question_answer99) Beat is listened by two sound sources of same amplitude and same frequency. Intensity of sound of maximum beat as compare to the intensity of any source will be

A) equal

B) two times

C) four times

D) eight times

• question_answer100) The equation of wave is $y=0.5\text{ }sin(101+x),$ This is moving along x-axis. Its velocity is

A) 10 m/s

B) 20 m/s

C) 5 m/s

D) None of these

• question_answer101) In the following reaction the product will be$C{{H}_{3}}COOH+H-\overset{\begin{smallmatrix} O \\ || \end{smallmatrix}}{\mathop{C}}\,-O-H\xrightarrow[{}]{MnO}$Product

A) $HCHO$

B) $C{{H}_{3}}C{{H}_{2}}CHO$

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

D) $C{{H}_{3}}OH$

A) caprolactum

B) phenol

C)

D) None of these

• question_answer103) In the following reaction the product will be $C{{H}_{3}}-Mg-Cl+N{{H}_{2}}-Cl\xrightarrow[{}]{{}}$Product

A) $C{{H}_{3}}-C{{H}_{2}}N{{H}_{2}}$

B) $C{{H}_{3}}-N{{H}_{2}}$

C) $C{{H}_{3}}-Cl$

D) $C{{H}_{3}}-Mg-N{{H}_{2}}$

• question_answer104) Here X, will be

A)

B)

C)

D) None of the above

• question_answer105) Above conversion is done by

A) $Sn/HCl$

B) $SnC{{l}_{2}}+HCl$

C) $N{{a}_{2}}S$

D) $Na-Hg$

• question_answer106) Which of the following is nucleophilic pair?

A) $\overset{\text{O-}}{\mathop{C}}\,\equiv N,R{{S}^{\text{O-}}}$

B) ${}_{\bullet }^{\bullet }{{C}^{\text{O-}}},AlC{{l}_{3}}$

C) $B{{r}_{2}},ZnC{{l}_{2}}$

D) $\overset{\text{O-}}{\mathop{R}}\,\overset{\oplus }{\mathop{M}}\,gX,{{H}^{\oplus }}$

• question_answer107) In the following reaction the product will be

A)

B) phenol

C) benzoic acid

D) benzaldehyde

• question_answer108) What is the name of the following reaction?

A) Friedel Craft's reaction

B) Wurtz-Fittig reaction

C) Perkin's reaction

D) Frenkland reaction

• question_answer109) $C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-H+HCN\to X\xrightarrow[{}]{{{H}_{2}}S{{O}_{4}}}$Lactic acid In the reaction X, will be

A) acetone

B) acetic acid

C) acetaldehyde cyanohydrin

D) None of the above

• question_answer110) IUPAC name of following compound will be $C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-\underset{\begin{smallmatrix} | \\ CHO \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}-C{{H}_{3}}$

A) 2-isobutyl butanal

B) 2-ethyl-3-methyl pentanal

C) 3-methyl-4-ethyl pentanal

D) 2, 3-diethyl butanal

• question_answer111) In the following reaction the product will be

A)

B)

C) Both [a] and [b]

D)

• question_answer112) Which of the following has bond dissociation energy 600 k J/mol?

A) $N=N$

B) $C-H$

C) $C=C$

D) $H-H$

• question_answer113) $LiAl{{H}_{4}}$is

A) a reducing agent

B) a oxidising agent

C) a electrophilic agent

D) a nucleophilic agent

• question_answer114) The reaction mechanism of the following reaction is done by

D) nucleophilic substitution

• question_answer115) ${{K}_{2}}Mn{{O}_{4}}$reacts with${{O}_{3}}$to form

A) $KMn{{O}_{4}}$

B) $Mn{{(OH)}_{2}}$

C) $Mn{{O}_{2}}$

D) None of these

• question_answer116) Which of the following shows optical isomerism?

A) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ COOH \end{smallmatrix}}{\overset{\begin{smallmatrix} Cl \\ | \end{smallmatrix}}{\mathop{C}}}\,-H$

B) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\overset{\begin{smallmatrix} Cl \\ | \end{smallmatrix}}{\mathop{C}}}\,-COOH$

C) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ COOH \end{smallmatrix}}{\overset{\begin{smallmatrix} COOH \\ | \end{smallmatrix}}{\mathop{C}}}\,-H$

D) $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ COOH \end{smallmatrix}}{\overset{\begin{smallmatrix} COOH \\ | \end{smallmatrix}}{\mathop{C}}}\,-C{{H}_{3}}$

• question_answer117) Which of the following is not an ore of magnesium?

A) Magnasite

B) Dolomite

C) Gypsum

D) Carnalite

• question_answer118) Nitrobenzene on electrolytic reduction with cone.${{H}_{2}}S{{O}_{4}}$gives

A) p-aminophenol

B) o-aminophenol

C) m-ammophenol

D) Both [a] and [b]

• question_answer119) Bond order in${{O}_{2}}$is

A) 1

B) 2

C) 1.5

D) 2.5

• question_answer120) Electron affinity of nitrogen is

A) 0.21

B) 3

C) 10.2

D) 13.2

• question_answer121) Which of the following test is not given by benzoic acid?

A) It gives$C{{O}_{2}}$with$NaHC{{O}_{3}}$

B) Soluble in hot medium and separates on cooling.

C) It gives buffs colour with$FeC{{l}_{3}}$solution

D) It gives Libermann's nitroso test

• question_answer122) How much${{O}_{2}}$is required for the complete combustion of$1\,L\,{{C}_{3}}{{H}_{3}}$?

A) 0.2 L

B) 0.5 L

C) 5 L

D) 4.8 L

• question_answer123) Which product is obtained, when${{C}_{2}}{{H}_{2}}$passes from red hot copper tube?

A) ${{C}_{6}}{{H}_{6}}$

C) $CH\equiv C-CH=C{{H}_{2}}$

D) ${{C}_{2}}{{H}_{4}}$

• question_answer124) The product will be

A) iodobenzene

B) cyclohexene

C) cyclohexane

D) None of these

• question_answer125) $\underset{yellow}{\mathop{MeOH}}\,\underset{red}{\mathop{M{{e}^{\oplus }}}}\,+O{{H}^{\text{O-}}}$ In acidic medium solution will be

A) red

B) yellow

C) blue

D) colourless

• question_answer126) When a solution passes from a membrane, then the solvent particles pass from the membrane but solute particles does not pass. The membrane is

A) osmosis membrane

B) diffusion membrane

C) semi-permeable membrane

D) osmotic pressure

• question_answer127) Ethene and ethyne are distinguished by

A) Baeyer's reagent

B) Tollen's reagent

C) Hager's reagent

D) None of these

• question_answer128) Which of the following shows peroxide effect?

A) $HBr$

B) $HF$

C) $HCl$

D) $HI$

• question_answer129) Structure of electron cloud of acetylene is

A) two cylinderical$\pi -$cloud

B) unsymmetrical

C) triangular symmetrical

D) None of the above

• question_answer130) The plane in triangular hybridization will be

A) $xy$

B) $yz$

C) $zx$

D) ${{x}^{2}}-{{y}^{2}}$

• question_answer131) Methane + 10%${{O}_{2}}\xrightarrow[Cu\,tube]{200{}^\circ C}$Product; product will be

A) $C{{H}_{3}}OH$

B) $HCHO$

C) $C{{H}_{3}}CHO$

D) ${{C}_{2}}{{H}_{5}}CHO$

• question_answer132) The above reaction is called

A) Aldol reaction

B) Cannizzaro reaction

C) Schmidt reaction

D) Tischenko reaction

• question_answer133) Acidic hydrolysis of acetoacetic ester gives

A) acetone

B) acetic acid

C) acetaldehyde

D) methanol

• question_answer134) pH of rain water is

A) 7

B) 14

C) 0

D) 10

• question_answer135) When$[{{H}^{+}}]$ion concentration is greater than${{10}^{-7}}$then solution will be

A) acidic

B) basic

C) neutral

D) None of these

A) $pH=p{{K}_{a}}+\log \frac{[salt]}{[acid]}$

B) $p{{K}_{a}}=pH-\log \frac{[salt]}{[acid]}$

C) $pH=p{{K}_{a}}-\log \frac{[salt]}{[acid]}$

D) $p{{K}_{a}}=pH+\log \frac{[salt]}{[acid]}$

• question_answer137) $\Delta p\times \Delta x\approx \frac{h}{4\pi }$ This law is given by

A) Schrodinger

B) Heisenberg's

C) de-Broglie

D) Pauli

• question_answer138) The correct name of the following freon is

A) Freon-11

B) Freon-318

C) Freon-12

D) Freon-114

• question_answer139) HF reacts with$CFC{{l}_{3}}$ in the presence of$Sb{{F}_{5}}$ to give

A) Freon-11

B) Freon-12

C) Freon-318

D) Freon-114

• question_answer140) Dilute$NaCl$is

A) basic

B) acidic

C) neutral

D) strong acidic

• question_answer141) Decreasing order of$-I$effect is

A) $C{{H}_{3}}<C{{H}_{3}}C{{H}_{2}}-<C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-$

B) $N{{O}_{2}}<COOH<Cl$

C) $Cl>Br>I$

D) $Br>Cl>I$

• question_answer142) pH of$0.1\text{ }mL\text{ }M\text{ }HCl$is

A) 1

B) 3

C) 2

D) 4

• question_answer143) Which of the following shows the minimum ionic character?

A) $AgI$

B) $MgC{{l}_{2}}$

C) $Ba{{(N{{O}_{3}})}_{2}}$

D) $HgS{{O}_{4}}$

• question_answer144) $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\xrightarrow[{}]{Conc.HgS{{O}_{4}}}\Pr oduct$ Product will be

A) phorone

B) mesitylene

C) paraformaldehyde

D) None of these

• question_answer145) $CH{{I}_{3}}+Ag\xrightarrow[{}]{{}}Product$ Product be in this reaction

A) $C{{H}_{4}}$

B) ${{C}_{2}}{{H}_{2}}$

C) ${{C}_{2}}{{H}_{6}}$

D) ${{C}_{2}}{{H}_{4}}$

• question_answer146) Given${{K}_{a}}=6\times {{10}^{-4}},{{K}_{{{a}_{2}}}}=1.5\times {{10}^{-4}}$The ratio of relative acidic strength is

A) 4

B) 2

C) 1

D) 3

A) $0.529\overset{o}{\mathop{\text{A}}}\,$

B) 3.125$\overset{o}{\mathop{\text{A}}}\,$

C) 2.1165$\overset{o}{\mathop{\text{A}}}\,$

D) 4.2$\overset{o}{\mathop{\text{A}}}\,$

• question_answer148) Which of the following subshell has ten electron?

A) 3d

B) 2p

C) 4s

D) 3p

• question_answer149) In the following reaction ${{H}_{3}}N+B{{F}_{3}}\xrightarrow[{}]{{}}N{{H}_{3}}\xrightarrow[{}]{{}}B{{F}_{3}}$

A) $B{{F}_{3}}$is base,$N{{H}_{3}}$is acid

B) $N{{H}_{3}}$is base,$B{{F}_{3}}$is acid

C) Both are acid

D) Both are base

• question_answer150) Which of the following compound has not hydrogen bond?

A) $N{{H}_{3}}$

B) ${{H}_{2}}O$

C) $HCl$

D) HF

• question_answer151) Correct order of electron affinity is

A) $F>Cl>Br>I$

B) $I>Br>Cl>F$

C) $Br>I>F>Cl$

D) $Cl>F>Br>I$

A) hexamethylene diamine

B) thiokol rubber

C) cis-polyisoprene

D) tons-polyisoprene

• question_answer153) Number of conformational isomers of n-butane are

A) 3

B) 4

C) 6

D) 10

• question_answer154) When pH increases from 2 to 4 then concentration

A) increases 100 times

B) decreases 100 times

C) decreases 1000 times

D) increases 1000 times

• question_answer155) Which of the following will give carbylamines reaction?

A) $C{{H}_{3}}N{{H}_{2}}$

B) ${{(C{{H}_{3}})}_{2}}NH$

C) ${{(C{{H}_{3}})}_{3}}N$

D) ${{(C{{H}_{3}})}_{4}}{{N}^{\oplus }}$

• question_answer156) Magnetic moment of$C{{u}^{+}}$is

A) 2.59

B) 0

C) 3.2

D) 5.1

• question_answer157) Gangue is removed from its ore by

A) concentration

B) calcination

C) roasting

D) smelting

• question_answer158) For 2a, 3b, c the Miller indices will be

A) 2, 3, 1

B) 1, 2, 4

C) 3, 2, 6

D) 1, 2, 3

• question_answer159) The wavelength of photon of yellow light is 5890$\overset{o}{\mathop{\text{A}}}\,$. Its energy will be

A) 2.3 erg

B) $3.37\times {{10}^{-12}}erg$

C) $4.1\times {{10}^{-8}}erg$

D) $1.5\times {{10}^{-2}}erg$

• question_answer160) Na conducts the electricity because

A) it releases hydrogen on reaction with water

B) it contains movable electron

C) it consists hydration energy

D) it consists combustion energy

• question_answer161) All d-black elements are

A) metal

B) non-metal

C) Both [a] and [b]

D) None of these

• question_answer162) Sodium reacts with oxygen to form

A) monoxide

B) peroxide

C) superoxide

D) $NaOH$

• question_answer163) On moving from top to bottom (from$B{{e}^{2+}}$to $B{{e}^{2+}}$) the degree of hydration

A) decreases

B) increases

C) first decreases and then increases

D) first increases and then decreases

• question_answer164) From$B{{e}^{2+}}$to$B{{e}^{2+}},$on moving from top to bottom the ionic radius

A) decreases

B) increases

C) first decreases and then increases

D) first increases and then decreases

A) $F{{e}_{2}}{{O}_{3}}$

B) $F{{e}_{3}}{{O}_{4}}$

C) $FeC{{O}_{3}}$

D) $F{{e}_{2}}{{O}_{3}}.3{{H}_{2}}O$

• question_answer166) ${{K}_{2}}C{{r}_{2}}{{O}_{3}}\xrightarrow[{}]{{}}C{{r}^{3+}}$ In the above process, oxidation number of Cr changes to

A) from 6 to 3

B) from -6 to 3

C) from + 3 to 0

D) from + 6 to 0

• question_answer167) For$n=1,\text{ }T=1,\text{ }R=$constant, the relationship between osmotic pressure and volume is

A) $p\propto V$

B) $p\propto \frac{1}{V}$

C) $p=V$

D) None of these

• question_answer168) Which of the following has$1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},$$3{{s}^{2}}3{{p}^{6}},4{{s}^{1}}$configuration?

A) K

B) $Al$

C) Na

D) $Ca$

• question_answer169) Which of the following has maximum ionization energy?

A) $(I,{{I}^{+}})$

B) $(Br,B{{r}^{+}})$

C) $(Li,L{{i}^{+}})$

D) $(Cu,C{{u}^{+}})$

• question_answer170) The reaction is used in bessemerisation process

A) $C{{u}_{2}}S+2C{{u}_{2}}O\xrightarrow[{}]{{}}6Cu+S{{O}_{2}}$

B) $Si+{{O}_{2}}\xrightarrow[{}]{{}}Si{{O}_{2}}$

C) $F{{e}_{2}}{{O}_{3}}+3C\xrightarrow[{}]{{}}2Fe+3CO$

D) $4Fe+3{{O}_{2}}\xrightarrow[{}]{{}}2F{{e}_{2}}{{O}_{3}}$

• question_answer171) Which of the following relationship is correct for reversible reaction, ${{H}_{2}}+{{I}_{2}}2HI$?

A) ${{K}_{p}}<1$

B) ${{K}_{p}}={{K}_{c}}$

C) ${{K}_{p}}>1$

D) None of these

• question_answer172) For an exothermic reaction, the favourable condition to obtain maximum product is

A) low pressure

B) low concentration of reactants

C) low temperature

D) high pressure

• question_answer173) When$CaO$dissolves in water, then heat releases. On increasing temperature its solubility

A) increases

B) decreases

C) unchanged

D) first increases, then decreases

• question_answer174) For bcc structure of Na, crystal${{N}_{0}}=6\times {{10}^{23}},$atomic weight of Na =23, radius$=5\overset{o}{\mathop{\text{A}}}\,,$ then density will be

A) $0.6\text{ }g/c{{m}^{3}}$

B) $1.2\text{ }g/c{{m}^{3}}$

C) $0.4\text{ }g/c{{m}^{3}}$

D) $1.0\text{ }g/c{{m}^{3}}$

• question_answer175) Rate of zero order reaction does not depend on

A) volume

B) temperature

C) time

D) concentration

• question_answer176) Size of colloidal particle is between

A) $1\overset{o}{\mathop{\text{A}}}\,-100\overset{o}{\mathop{\text{A}}}\,$

B) $10\overset{o}{\mathop{\text{A}}}\,-200\overset{o}{\mathop{\text{A}}}\,$

C) $1000\overset{o}{\mathop{\text{A}}}\,-2000\overset{o}{\mathop{\text{A}}}\,$

D) $>2000\overset{o}{\mathop{\text{A}}}\,$

• question_answer177) When any 2 g solute dissolves in 50 g water than boiling point comes$100.5{}^\circ C$. If${{K}_{b}}=0.5$ then molecular weight will be

A) 4

B) 40

C) 80

D) 100

• question_answer178) Which of the following is not a characteristic of colloidal particles?

A) They pass from filter paper easily.

B) They are invisible.

C) They forms heterogeneous mixture.

D) They pass from parchment paper.

• question_answer179) On moving left to right the correct order of hybridization of carbon atoms in compound $C{{H}_{3}}-CH=C=C{{H}_{2}}.$.

A) $s{{p}^{3}},s{{p}^{2}},sp,s{{p}^{2}}$

B) $s{{p}^{2}},sp,s{{p}^{2}}$

C) $sp,s{{p}^{2}},s{{p}^{2}},s{{p}^{3}}$

D) $s{{p}^{3}},s{{p}^{2}},s{{p}^{2}},sp$

• question_answer180) In the following reaction X will be $X+B{{r}^{2}}+KOH\xrightarrow[{}]{{}}C{{H}_{3}}N{{H}_{2}}$

A) $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-N{{H}_{2}}$

B) $C{{H}_{3}}-C{{H}_{2}}-N{{H}_{2}}$

C) $C{{H}_{3}}-N{{O}_{2}}$

D) $C{{H}_{3}}-C{{H}_{2}}-N{{O}_{2}}$

• question_answer181) Sodium lauryl sulphate is an example of

A) neutral detergent

B) cationic detergent

C) anionic detergent

D) soap detergent

• question_answer182) $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-Cl+KCN\to C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-CN\xrightarrow[{}]{{{H}_{2}}O}X$ Here X will be

A) $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-COOH$

B) $C{{H}_{3}}-C{{H}_{2}}-COOH$

C) $C{{H}_{3}}COOH$

D) None of these

• question_answer183) The correct order of acidic strength of following

 I. $F-C{{H}_{2}}-COOH$ II.$Cl-C{{H}_{2}}-COOH$ III. $Br-C{{H}_{2}}-COOH$

A)  $I>II>III$

B)  $III>II>I$

C)  $II>III>I$

D)  $II>I>III$

• question_answer184) In the following reaction product will be $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-ON{{H}_{4}}\xrightarrow[{}]{{{P}_{4}}{{O}_{10}}}Product$

A) $C{{H}_{3}}-C=N$

B) $C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}$

C) $C{{H}_{3}}-C-N{{H}_{2}}$

D) $C{{H}_{3}}COOH$

• question_answer185) In the following reaction product will be $nC{{H}_{2}}=CH-O-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\xrightarrow[{}]{Polymerization}Product$

A) polyvinyl acetate

B) polyacrylonitrile

C) vinyl acetate

D) acrylonitrile

A) mostly positive

B) always negative

C) sometime positive and sometime neutral

D) sometime positive and sometime negative

• question_answer187) Acetic acid is polar in nature but soluble in non-polar solvents because

A) it forms dimer

B) entropy increases

C) enthalpy decreases

D) None of these

• question_answer188) The ratio of butadiene and styrene in Buna-S polymer is

A) $1:1$

B) $1:2$

C) $3:1$

D) $1:3$

• question_answer189) An organic compound is purified by electrolytic purification method. It was proposed by

A) Kolbe

B) Wurtz

C) Frenkland

D) Clemmensen

• question_answer190) IUPAC name of following compound is

A) vinyl propene

B) 1-isopropene ethylene

C) 2-methyl-3-butene

D) 3-methyl-1-butene

• question_answer191) Name the compound which obtains sufficient energy for combustion on stirring

A) methanol

B) chloroform

C) ether

D) power alcohol

• question_answer192) Which of the following smell comes, when some drops of${{H}_{2}}S{{O}_{4}}$adds in acetate solution?

A) Apple like smell

B) Banana like smell

C) Vinegar like smell

D) White precipitate

• question_answer193) Which of the following is the most stable?

A) Methane

B) Ethane

C) Butane

D) Propane

• question_answer194) Mixture of camphor and benzoic acid can be separated by

A) sublimation

B) extraction with a solvent

C) chemical method

D) fractional crystallization

• question_answer195) Which of the following is the example of double salt?

A) Potash alum

B) Hypo

C) ${{K}_{4}}[Fe{{(CN)}_{6}}]$

D) Bleaching powder

• question_answer196) On passing IF electricity in acid solution, the oxygen liberates

A) $11.2\,d{{m}^{3}}$

B) $5.6\,d{{m}^{3}}$

C) $22.4\text{ }d{{m}^{3}}$

D) $1.0\text{ }d{{m}^{3}}$

• question_answer197) Example of colloidal solution is

A) alkaline solution of${{C}_{6}}{{H}_{5}}COOH$

B) aqueous solution of$N{{H}_{2}}CON{{H}_{2}}$

C) milk

D) None of the above

• question_answer198) Which of the following is not an example of molecular crystal?

A) Hydrogen

B) Iodine

C) Ice

D) Sodium chloride

• question_answer199) Oxidation number of$'N'$ in${{N}_{3}}H$is

A) $-\frac{1}{3}$

B) $+3$

C) 0

D) $-3$

• question_answer200) Chloramphenicol is used for curing in which of the following?

A) Tuberculosis

B) Typhoid

D) Cough

• question_answer201) Both roots of the following quadratic equation are $(x-b)(x-c)+(x-c)(x-a)$ $+(x-a)(x-b)=0$

A) positive

B) negative

C) real

D) complex

• question_answer202) For what value of m, the roots of the quadratic equation$12{{x}^{2}}+mx+5=0$are in the ratio$3:2$?

A) $10\sqrt{5}$

B) $-5\sqrt{10}$

C) 50

D) 25

• question_answer203) Maximum value of the expression$\frac{1}{4{{x}^{2}}+2x+1}$is

A) $\frac{4}{3}$

B) $\frac{5}{2}$

C) $\frac{13}{4}$

D) $\frac{3}{4}$

• question_answer204) The value of$\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{\frac{1}{2}(1-\cos 2x)}}{x}$is

A) 1

B) $-1$

C) 0

D) None of these

• question_answer205) If the function$f(x)=\left\{ \begin{matrix} \frac{1-\sin x}{\pi -2x}, & x\ne \frac{\pi }{2} \\ \lambda , & x=\frac{\pi }{2} \\ \end{matrix} \right.$ is continuous at$x=\frac{\pi }{2},$then$\lambda$is equal to

A) 1

B) $-1$

C) $1/2$

D) 0

• question_answer206) If$y={{\tan }^{-1}}\left( \frac{\cos x-\sin x}{\cos x+\sin x} \right),$then$\frac{dy}{dx}$is equal to

A) 1

B) $-1$

C) $\sin x$

D) $\cos x$

• question_answer207) Minimum value of$x+\frac{1}{x}$is

A) 2

B) $-2$

C) 0

D) None of these

• question_answer208) If$x=-1$and$x=2$are the extreme points of the function$y=a\log |x|+b{{x}^{2}}+x,$then

A) $a=2,b=1/2$

B) $a=2,b=-1/2$

C) $a=-2,b=-1/2$

D) $a=-2,b=1/2$

• question_answer209) Function$f(x)=\frac{x}{1+x}-\log (1+x),x>0$is

A) decreasing function

B) increasing function

C) not monotonic

D) None of the above

• question_answer210) $\int{{{\cos }^{-1}}\left( \frac{1}{x} \right)}\,dx$is equal to

A) $x{{\sec }^{-1}}x+{{\cosh }^{-1}}x+c$

B) $x{{\sec }^{-1}}x-{{\cosh }^{-1}}x+c$

C) ${{\cosh }^{-1}}x-{{\sec }^{-1}}x+c$

D) None of the above

• question_answer211) $\int{\frac{x{{e}^{x}}}{{{(1+x)}^{2}}}}dx$is equal to

A) $\frac{{{e}^{x}}}{x+1}+c$

B) $\frac{{{e}^{x}}}{{{(x+1)}^{2}}}+c$

C) $\frac{-{{e}^{x}}}{(x+1)}+c$

D) None of these

• question_answer212) $\int{\cos e{{c}^{4}}xdx}$is equal to

A) $-\cot x+\frac{{{\cot }^{3}}x}{3}+c$

B) $\frac{{{\cot }^{3}}x}{3}-\cot x+c$

C) $-\cot x-\frac{{{\cot }^{3}}x}{3}+c$

D) $\cot x-\frac{{{\cot }^{2}}x}{3}+c$

• question_answer213) Points$(-1,1)(0,-3),(5,2)$and (4, 6) are the vertices of

A) square

B) parallelogram

C) rectangle

D) rhombus

• question_answer214) Triangle made by the lines$x+y=0,$ $3x+y=4,\text{ }x+3y=4$is

A) equilateral

B) isosceles

C) right angled

D) None of these

• question_answer215) From any point on the circle${{x}^{2}}+{{y}^{2}}={{a}^{2}},$two tangents are drawn to the circle ${{x}^{2}}+{{y}^{2}}={{a}^{2}}si{{n}^{2}}\alpha ,$then angle between them is

A) $\frac{\alpha }{2}$

B) $\alpha$

C) $2\alpha$

D) None of these

• question_answer216) A variable chord is drawn to the circle ${{x}^{2}}+{{y}^{2}}-2ax=0$from the origin, then the locus of the centre of the circle which is made by taking the chord as the diameter, is

A) ${{x}^{2}}+{{y}^{2}}+ax=0$

B) ${{x}^{2}}+{{y}^{2}}-ax=0$

C) ${{x}^{2}}+{{y}^{2}}+ay=0$

D) ${{x}^{2}}+{{y}^{2}}-ay=0$

• question_answer217) The point from which the length of tangents to the circles${{x}^{2}}+{{y}^{2}}-8x+40=0,$$5{{x}^{2}}+5{{y}^{2}}-25x+80=0$and ${{x}^{2}}+{{y}^{2}}-8x+16y+160=0$are equal, is

A) $\left( 8,\frac{15}{2} \right)$

B) $\left( -8,\frac{15}{2} \right)$

C) $\left( 8,-\frac{15}{2} \right)$

D) None of these

• question_answer218) The point where the tangent to the curve $y={{e}^{2x}}$at (0,1) meets$x-$axis, is

A) (1, 0)

B) $(-1,0)$

C) $\left( -\frac{1}{2},0 \right)$

D) None of these

• question_answer219) Image of the point$(4,-3)$with respect to the line$y=x,$is

A) $(-4,-3)$

B) $(3,-4)$

C) $(-3,4)$

D) $(-3,-4)$

• question_answer220) If$a+b+c=0,$then the line$3ax+4by+c=0$passes through a fixed point which has the coordinate

A) $\left( \frac{1}{3},\frac{1}{4} \right)$

B) $\left( -\frac{1}{3},\frac{1}{4} \right)$

C) $\left( \frac{1}{3},-\frac{1}{4} \right)$

D) None of these

• question_answer221) The tangents drawn from the focal chord PQ to the parabola meets the directrix at point Q. Then angle PSQ is

A) $\frac{\pi }{4}$

B) $\frac{\pi }{3}$

C) $\frac{\pi }{2}$

D) $\pi$

• question_answer222) If$\overrightarrow{A}=2\hat{i}+2\hat{j}+3\hat{k},\overrightarrow{B}=-\hat{i}+2\hat{j}+\hat{k}$and$\overrightarrow{C}=3\hat{i}+\hat{j}$and$(\overrightarrow{A}+t\overrightarrow{B})\bot \overrightarrow{C},$ihent is equal to

A) 5

B) 4

C) 6

D) 8

• question_answer223) If sum of two unit vectors is also a unit vector, then angle between them is

A) $\frac{\pi }{3}$

B) $\frac{2\pi }{3}$

C) $\frac{\pi }{2}$

D) $\frac{\pi }{4}$

• question_answer224) $\overrightarrow{a}.\{(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})\}$is equal to

A) $2[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]$

B) 0

C) $[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]$

D) None of these

• question_answer225) Area of small part between the circle${{x}^{2}}+{{y}^{2}}=9$and the line$x=1$is

A) ${{\sec }^{-1}}3-\sqrt{8}$

B) $9{{\sec }^{-1}}3-\sqrt{8}$

C) $9\cos e{{c}^{-1}}3-\sqrt{8}$

D) None of these

• question_answer226) Area between the vertex and the latusrectum of the parabola${{y}^{2}}=4ax$is

A) $\frac{4}{3}{{a}^{2}}sq\,units$

B) $\frac{8}{3}{{a}^{2}}sq\,units$

C) $\frac{2}{3}{{a}^{2}}sq\,units$

D) $\frac{5}{3}{{a}^{2}}sq\,units$

• question_answer227) $\int_{0}^{\infty }{\log \left( x+\frac{1}{x} \right)}\frac{dx}{1+{{x}^{2}}}$is equal to

A) $-\frac{\pi }{2}\log 2$

B) $-\pi \log 2$

C) $\pi \log 2$

D) None of these

• question_answer228) Intersection point of the tangents drawn to the parabola${{y}^{2}}=4ax$from the points $(at_{1}^{2},2a{{t}_{1}})$and$(at_{2}^{2},2a{{t}_{2}})$is

A) $(a{{t}_{1}}{{t}_{2}},a({{t}_{1}}+{{t}_{2}}))$

B) $(a({{t}_{1}}+{{t}_{2}}),a{{t}_{1}}{{t}_{2}})$

C) $(t_{1}^{2}t_{2}^{2},{{t}_{1}}+{{t}_{2}})$

D) None of these

• question_answer229) If a line makes the angles$\alpha ,\beta ,\gamma$and$\delta$respectively with all the four diagonals of a cube, then$co{{s}^{2}}\alpha +co{{s}^{2}}\beta +co{{s}^{2}}\gamma +co{{s}^{2}}\delta$is equal to

A) 3

B) 4

C) 4/3

D) 3/4

• question_answer230) The cosine of the angle between any two diagonals of a cube is

A) $\frac{1}{3}$

B) $\frac{1}{2}$

C) $\frac{2}{3}$

D) $\frac{1}{\sqrt{3}}$

• question_answer231) Line$\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{0}$is

A) parallel to yz-plane

B) parallel to zx-plane

C) perpendicular to z-axis

D) parallel to z-axis

• question_answer232) Total number of lines having same slope with the coordinate axes, is

A) 1

B) 2

C) 3

D) 4

• question_answer233) A line makes an angle of$60{}^\circ$with$x$and y-axes, then the angle which is made by the line with the positive direction of to z-axis, is

A) $45{}^\circ$or $135{}^\circ$

B) $60{}^\circ$or$90{}^\circ$

C) $90{}^\circ$or$120{}^\circ$

D) $60{}^\circ$or$120{}^\circ$

• question_answer234) Equation of line passing through the points$\overrightarrow{a}={{a}_{1}}\hat{i}+{{a}_{2}}\hat{j}+{{a}_{3}}\hat{k}$and $\overrightarrow{b}={{b}_{1}}\hat{i}+{{b}_{2}}\hat{j}+{{b}_{3}}\hat{k}$is (where t is a scalar)

A) $\overrightarrow{r}=\overrightarrow{a}+\overrightarrow{b}$

B) $\overrightarrow{r}=\overrightarrow{a}+t(\overrightarrow{b}-\overrightarrow{a})$

C) $\overrightarrow{r}=\overrightarrow{a}+t\overrightarrow{b}$

D) None of these

• question_answer235) Polar of the circle${{x}^{2}}+{{y}^{2}}=5$with respect to the point$(1,-2)$is a line for the circle ${{x}^{2}}+{{y}^{2}}-8x+6y+20=0$which is

A) a tangent

B) cut at two real points

C) cut at two imaginary points

D) None of the above

• question_answer236) The ratio in which the line made by joining the points$(2,-1,-3)$and$(3,2,-1)$cuts the yz-plane, is

A) $-2:3$

B) $3:-2$

C) $1:2$

D) $2:1$

• question_answer237) If$|z+4|\le 3,$ then maximum value of$|z+1|$ is

A) 0

B) 4

C) 3

D) 6

• question_answer238) If$z=x+iy$and are$\left( \frac{z-2}{z+2} \right)=\frac{\pi }{6},$then locus of $z$is a

A) straight line

B) circle

C) parabola

D) None of these

• question_answer239) The value of$\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{{{(\sin \theta +i\cos \theta )}^{5}}}$is

A) $\cos 9\theta -i\sin 9\theta$

B) $\cos \theta -i\sin \theta$

C) $\sin 9\theta +i\cos 9\theta$

D) $\sin 9\theta -i\cos 9\theta$

• question_answer240) ${{(1+i)}^{6}}+{{(1-i)}^{6}}$is equal to

A) $16i$

B) 16

C) 1

D) 0

• question_answer241) If$z=\frac{\sqrt{3}+i}{2},$then${{z}^{69}}$is equal to

A) $1$

B) 2

C) $-2$

D) $-1$

• question_answer242) $cosh\text{ }2x$ is equal to

A) $cos{{h}^{2}}x-sin{{h}^{2}}x$

B) $2\text{ }cos{{h}^{2}}x-1$

C) $1-2\text{ }sin{{h}^{2}}x$

D) None of these

• question_answer243) If$x$is real, then$cos{{h}^{-1}}x$is equal to

A) $\log (x+\sqrt{{{x}^{2}}+1})$

B) $\log (x\pm \sqrt{{{x}^{2}}-1})$

C) $\log (x\mp \sqrt{{{x}^{2}}+1})$

D) $\log (x-\sqrt{{{x}^{2}}-1})$

• question_answer244) If ${{\tan }^{-1}}(\alpha +i\beta )=x+iy,$then$x$is equal to

A) $\frac{1}{2}\tan \left( \frac{2\alpha }{1+{{\alpha }^{2}}+{{\beta }^{2}}} \right)$

B) $\frac{1}{2}{{\tan }^{-1}}\left( \frac{2\alpha }{1+{{\alpha }^{2}}+{{\beta }^{2}}} \right)$

C) $\frac{1}{2}{{\tanh }^{-1}}\left( \frac{2\beta }{1+{{\alpha }^{2}}+{{\beta }^{2}}} \right)$

D) $\frac{1}{2}{{\tan }^{-1}}\left( \frac{2\beta }{1-{{\alpha }^{2}}-{{\beta }^{2}}} \right)$

• question_answer245) Determinant$\left| \begin{matrix} 1 & a & {{a}^{2}}-bc \\ 1 & b & {{b}^{2}}-ac \\ 1 & c & {{c}^{2}}-ab \\ \end{matrix} \right|$is equal to

A) $a+b+c$

B) ${{a}^{2}}+{{b}^{2}}+{{c}^{2}}$

C) 0

D) 1

• question_answer246) $\left| \begin{matrix} 1/a & 1 & bc \\ 1/b & 1 & ca \\ 1/c & 1 & ab \\ \end{matrix} \right|$is equal to

A) 1

B) 0

C) $(a+b+c)$

D) 2

• question_answer247) If${{A}^{3}}=I$for any matrix A, then${{A}^{-1}}$is equal to

A) ${{A}^{2}}$

B) A

C) ${{A}^{3}}$

D) None of these

• question_answer248) For any two square matrices A and$B,{{(AB)}^{-1}}$is equal to

A) ${{A}^{-1}}{{B}^{-1}}$

B) ${{B}^{-1}}{{A}^{-1}}$

C) ${{(BA)}^{-1}}$

D) None of these

• question_answer249) For any matrix A, A (adj A) is equal to

A) $A$

B) $|A|{{I}_{n}}$

C) $|A|$

D) None of these

• question_answer250) If$a,b,c$are in GP, then${{\log }_{a}}x,{{\log }_{b}}x$and${{\log }_{c}}x$are in

A) AP

B) GP

C) HP

D) None of these

• question_answer251) If$a,b,c,d,e$are in AP, then the value of$a-4b+6c-4d+e$is equal to

A) 1

B) 2

C) 0

D) None of these

• question_answer252) If first term of a GP is double the sum of all consecutive terms starting from second term, then the common ratio is

A) $\frac{2}{5}$

B) $\frac{2}{3}$

C) $\frac{1}{3}$

D) $\frac{1}{4}$

• question_answer253) Sum of the series${{11}^{3}}+{{12}^{3}}+...\text{ +}{{20}^{3}}$is

A) odd and divisible by 5

B) divisible by 10

C) odd and not divisible by 5

D) None of the above

• question_answer254) $\left| \begin{matrix} 1 & 1 & 1 \\ 1 & \omega & {{\omega }^{2}} \\ 1 & {{\omega }^{2}} & \omega \\ \end{matrix} \right|$is equal to

A) 0

B) $3\sqrt{3}i$

C) $-3\sqrt{3}i$

D) $1$

• question_answer255) If${{a}^{2}}+{{b}^{2}}+{{c}^{2}}=1,$then range of$ab+bc+ca$is

A) $\left[ -\frac{1}{2},\infty \right)$

B) $[0,\infty )$

C) $\left[ -\frac{1}{2},1 \right]$

D) $[1,\infty )$

• question_answer256) Range of the function$\frac{x+2}{|x+2|}$is

A) $\{-1,0,1\}$

B) $\{-1,1\}$

C) $[-1,1]$

D) None of these

• question_answer257) Range of$\frac{x}{3}$is

A) $[-1,1]$

B) $\left[ -\frac{1}{3},\frac{1}{3} \right]$

C) [0,2]

D) None of these

• question_answer258) Domain of the function${{\sin }^{-1}}\left( {{\log }_{2}}\frac{x}{2} \right)$is

A) $\left[ \frac{1}{2},\frac{1}{4} \right]$

B) $[-1,3]$

C) $[1,4]$

D) $[0,1]$

• question_answer259) $^{47}{{C}_{4}}+\sum\limits_{i=1}^{5}{^{52-i}{{C}_{3}}}$is equal to

A) $^{50}{{C}_{4}}$

B) $^{50}{{C}_{4}}$

C) $^{10}{{C}_{5}}$

D) $^{52}{{C}_{6}}$

• question_answer260) Coefficient of the middle term in the expansion

A) $^{10}{{C}_{4}}$

B) ${{-}^{10}}{{C}_{4}}$

C) $^{10}{{C}_{5}}$

D) $^{10}{{C}_{6}}$

• question_answer261) If the coefficient of second, third and fourth terms in the expansion of${{(1+x)}^{n}}$are in AP, then n is equal to

A) 7, 5

B) 5, 4

C) 4, 2

D) 3, 6

• question_answer262) If$y=\sqrt{x+\sqrt{x+\sqrt{x+......\infty }}},$then-y is equal to

A) $\frac{x}{2y-1}$

B) $\frac{1}{2y-1}$

C) $\frac{2}{y-1}$

D) None of these

• question_answer263) Maximum value of the function$f(x)=\frac{\log x}{x}$in the interval$0<x<\infty$is

A) e

B) $\sqrt{e}$

C) $\frac{1}{e}$

D) $\frac{2}{e}$

• question_answer264) $\int{\frac{dx}{\sqrt{x}(1+x)}}$is equal to

A) ${{\tan }^{-1}}\sqrt{x}+c$

B) $2{{\tan }^{-1}}\sqrt{x}+c$

C) $2{{\tan }^{-1}}x+c$

D) None of these

• question_answer265) $\int_{0}^{\pi /2}{\log \tan xdx}$is equal to

A) $0$

B) $\pi$

C) $\frac{\pi }{2}$

D) $\frac{\pi }{4}$

• question_answer266) If$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are the position vectors of a$\Delta ABC,$ then$\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}$is equal to

A) $\overrightarrow{0}$

B) $2\text{ }\overrightarrow{AB}$

C) $2\text{ }\overrightarrow{BA}$

D) None of these

• question_answer267) The point (in first quadrant) on which the slope of the normal to the curve${{x}^{3}}=8{{a}^{2}}y$is, $-2/3,$ is

A) (2a, a)

B) $(-2a,a)$

C) (a, 2a)

D) $(a,-2a)$

• question_answer268) $\int_{a}^{2a}{f(x)}\,dx$ is equal to

A) $2\int_{a}^{2a}{f(x)}\,dx$

B) 0

C) $\int_{a}^{a}{f(x)}\,dx+\int_{0}^{2a}{f(2a-x)dx}$

D) None of the above

• question_answer269) If$2\hat{i}-\hat{j}+\hat{k},\hat{i}+2\hat{j}-3\hat{k}$and$3\hat{i}+p\hat{j}+5\hat{k}$are coplanar, then p is equal to

A) 1

B) -2

C) 4

D) -4

• question_answer270) Domain of the function$\frac{1}{\sqrt{(x+2)(x-1)}}$is

A) $(-\infty ,-2)\cup (1,\infty )$

B) $R-[-1,1]$

C) $(-\infty ,-2)\cup (2,\infty )$

D) $(-\infty ,1)\cup (2,\infty )$

• question_answer271) If three dice are thrown together, then the probability of getting same digit on all the dice

A) $\frac{1}{6}$

B) $\frac{3}{36}$

C) $\frac{1}{36}$

D) $\frac{2}{3}$

• question_answer272) If a dice is thrown twice, then the probability of getting 5 in first attempt only

A) $\frac{1}{36}$

B) $\frac{2}{36}$

C) $\frac{5}{36}$

D) $\frac{31}{36}$

• question_answer273) If two dice are thrown together, then probability of getting 7 as the sum, is

A) $\frac{1}{36}$

B) $\frac{11}{36}$

C) $\frac{2}{36}$

D) $\frac{1}{36}$

• question_answer274) A coin is tossed n times, then the probability of getting head odd number of times is

A) $\frac{1}{4}$

B) ${{\left( \frac{1}{2} \right)}^{n}}$

C) $\frac{1}{2}$

D) $\frac{3}{8}$

• question_answer275) From the positive integers, four integers are selected randomly and then multiplied, then the probability of getting the digit 1, 3, 5 or 7 at the first place is

A) $\frac{16}{625}$

B) $\frac{8}{625}$

C) $\frac{10}{17}$

D) None of these

• question_answer276) 15 persons shaked their hands with one another in a room. Total number of shake hand is

A) 90

B) 105

C) 110

D) 115

• question_answer277) The value of x for which $|x-1|+|x-2|+|x-3|\ge 6,$is

A) $0\le x\le 4$

B) $x\le -2$and $x\le 4$

C) $x\le 0$and$x\ge 4$

D) None of these

• question_answer278) $a+ib<c+id$is true only when

A) $a=0,c=0$

B) $a=0,d=0$

C) $b=0,c=0$

D) $b=0,d=0$

• question_answer279) If${{z}_{1}},{{z}_{2}}$are any two complex numbers, then

A) $|{{z}_{1}}+{{z}_{2}}|\ge |{{z}_{1}}|+|{{z}_{2}}|$

B) $|{{z}_{1}}+{{z}_{2}}|>|{{z}_{1}}|+|{{z}_{2}}|$

C) $|{{z}_{1}}+{{z}_{2}}|\le |{{z}_{1}}|+|{{z}_{2}}|$

D) $|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}|+|{{z}_{2}}|$

• question_answer280) $\int{\sqrt{\frac{1+x}{1-x}}}dx$is equal to

A) $-{{\sin }^{-1}}x\sqrt{1-{{x}^{2}}}+c$

B) ${{\sin }^{-1}}x-\sqrt{{{x}^{2}}-1}+c$

C) ${{\sin }^{-1}}x-\sqrt{1-{{x}^{2}}}+c$

D) $-{{\sin }^{-1}}x-\sqrt{{{x}^{2}}-1}+c$

• question_answer281) Equation of tangent to the curve${{x}^{2/3}}+{{y}^{2/3}}={{a}^{2/3}}$at the point$({{x}_{1}},{{y}_{1}})$is

A) $xx_{1}^{1/3}+yy_{1}^{1/3}={{a}^{2/3}}$

B) $\frac{x}{{{x}^{1/3}}}+\frac{y}{{{y}^{1/3}}}={{a}^{2/3}}$

C) $x_{1}^{2/3}+yy_{1}^{2/3}={{a}^{1/3}}$

D) None of the above

• question_answer282) If$y=|x-1|+|x-3|,$then the value of$\frac{dy}{dx}$at $x=2$is

A) 1

B) 0

C) $-1$

D) does not exist

• question_answer283) $\frac{{{d}^{n}}}{d{{x}^{n}}}(\log x)$is equal to

A) $\frac{{{(-1)}^{n-1}}(n-1)!}{{{x}^{n}}}$

B) $\frac{{{(-1)}^{n}}(n-1)!}{{{x}^{n-1}}}$

C) $\frac{{{(-1)}^{n}}n!}{{{x}^{n-1}}}$

D) $\frac{{{(-1)}^{n}}(n-1)!}{{{x}^{n-1}}}$

• question_answer284) If the vectors$\overrightarrow{AB}=3\hat{i}+5\hat{j}+4\hat{k}$and$\overrightarrow{Ac}=5\hat{i}-5\hat{j}+2\hat{k}$are the sides of the$\Delta ABC,$then length of median passing from A is

A) $\sqrt{3}$units

B) $2\sqrt{5}$units

C) 5 units

D) 10 units

• question_answer285) If the lines$3x-4y+4=0$and$6x-8y-7=0$are the tangents of a circle, then radius of the circle is

A) $\frac{3}{2}$

B) $\frac{3}{4}$

C) $\frac{1}{10}$

D) $\frac{1}{20}$

• question_answer286) Parametric coordinates of${{x}^{2}}=4ay$are

A) $(a{{t}^{2}},2at)$

B) $(a{{t}^{2}},-2at)$

C) $(-2at,a{{t}^{2}})$

D) $(2at,a{{t}^{2}})$

• question_answer287) Cofactors of the elements of second row of the determinant $\left| \begin{matrix} 2 & -1 & 4 \\ 4 & 2 & -3 \\ 1 & 1 & 2 \\ \end{matrix} \right|$are

A) 5, 1, 8

B) 6, 0, -3

C) 5, 6, 4

D) None of these

• question_answer288) If $A=\left[ _{-1}^{4}\,\,_{1}^{2} \right]\,\,,$ then $(A-2I)(A-3I)$ is equal to

A)  ${{A}^{2}}+6I$

B)  $I$

C)  null matrix

D)  None of these

• question_answer289) If$A=\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right],$then${{A}^{2}}-6A$is equal to

A) $3I$

B) $5I$

C) $-5I$

D) None of these

• question_answer290) If the points$(x+1,2),(1,x+2)$and $\left( \frac{1}{x+1},\frac{2}{x+1} \right)$are collinear, then$x$is equal to

A) 2

B) 4

C) $-4$

D) None of these

• question_answer291) If${{x}_{n}}=\cos \left( \frac{\pi }{{{2}^{n}}}+i\sin \frac{\pi }{{{2}^{n}}} \right),n=1,2,3.....$then the value${{x}_{1}}.{{x}_{2}}.{{x}_{3}}.....\infty$is

A) 1

B) $-1$

C) 0

D) None of these

• question_answer292) The number of ways to make a team of 10 players out of 22 players when 4 players are always in the team and 5 players are never in the team

A) $^{14}{{C}_{4}}$

B) $^{14}{{C}_{6}}$

C) $^{19}{{C}_{6}}$

D) $^{13}{{C}_{6}}$

• question_answer293) Equation$\frac{{{x}^{2}}}{2-r}+\frac{{{y}^{2}}}{r-5}+1=0$represents an ellipse, if

A) $r>5$

B) $r>2$

C) $2<r<5$

D) None of these

• question_answer294) If equation of latusrectum of a parabola is $x+y=8$and equation of tangent at its vertex is$x+y=12,$then length of its latusrectum is

A) $4\sqrt{2}$

B) $2\sqrt{2}$

C) $8$

D) $8\sqrt{2}$

• question_answer295) If area of the circle$4{{x}^{2}}+4{{y}^{2}}-8x+16y+k=0$is$9\pi$sq units, then the value of k is

A) 4

B) $10$

C) $-16$

D) ?16

• question_answer296) A rod of length 7 is kept with the support of a wall and floor of a room. If rod starts slipping, then the locus of its midpoint is

A) a straight line

B) a circle

C) a parabola

D) an ellipse

• question_answer297) Two points on the curve$y={{x}^{2}}+2x$with abscissae 1 and 3, slope of the line joining these two points

A) 3

B) 5

C) 6

D) 4

• question_answer298) $si{{n}^{6}}A+co{{s}^{6}}A+3si{{n}^{2}}Aco{{s}^{2}}A$is equal to

A) 3

B) 2

C) 1

D) 0

• question_answer299) The equation which has the roots$\frac{1}{3+\sqrt{2}}$and$\frac{1}{3-\sqrt{2}}$is

A) $7{{x}^{2}}-6x+1=0$

B) $6{{x}^{2}}-7x+1=0$

C) ${{x}^{2}}-6x+7=0$

D) ${{x}^{2}}-7x+6=0$

• question_answer300) If$f(x)=\frac{2\sqrt{x+4}}{\sin 2x},(x\ne 0)$is continuous at $x=0,$then$f(0)$is equal to

A) 1/4

B) $-1/4$

C) 1/8

D) $-1/8$