# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2003

### done Rajasthan PET Solved Paper-2003

• question_answer1) A stretched string of length$l,$fixed at both ends can sustain stationary waves of wavelength given by

A) $\lambda =\frac{{{n}^{2}}}{2l}$

B) $\lambda =\frac{{{I}^{2}}}{2n}$

C) $\lambda =\frac{2l}{n}$

D) $\lambda =2\ln$

• question_answer2) Moment of inertia of a thin circular ring of mass M and radius R about any diameter is

A) $M{{R}^{2}}$

B) $2M{{R}^{2}}$

C) $\frac{M{{R}^{2}}}{2}$

D) $\frac{M{{R}^{2}}}{4}$

• question_answer3) A particle moves with constant speed in circular path. During the motion its

A) velocity is constant

B) acceleration is constant

C) radial acceleration towards the inside

D) radial acceleration towards the outside

• question_answer4) A stone thrown upward with a speed u from the top of the tower, reaches the ground with velocity 3u. The height of the tower is

A) $\frac{8{{u}^{2}}}{g}$

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

C) $\frac{4{{u}^{2}}}{g}$

D) $\frac{5{{u}^{2}}}{g}$

• question_answer5) Which one of the following is scalar?

A) Electric potential

B) Momentum

C) Velocity

D) Force

• question_answer6) Dimensions of torque are

A) $[M{{L}^{2}}{{T}^{-1}}]$

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

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

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

• question_answer7) If total torque of the system is zero, then the total angular momentum of the system will be constant at

A) direction

B) both direction and magnitude

C) magnitude

D) None of the above

• question_answer8) The angular velocity of earth rotating about its own axis is

A) $\frac{2\pi }{60\,\times \,60\,\times \,2\pi }rad/s$

B) $\frac{2\pi }{60\,\times \,60}rad/s$

C) $\frac{2\pi }{60}rad/s$

D) $\frac{2\pi }{365\,\times \,24\,\times \,60\,\times \,60}rad/s$

• question_answer9) The equation of progressive wave is$y=a\text{ }sin(200$ $(200tx),$where$x$is in metre and$x$is in second. The velocity of wave will be

A) 200 m/s

B) 100 m/s

C) 50 m/s

D) None of these

• question_answer10) According to Newton's third law, which of the following statements is true?

A) Both forces are acted upon one body

B) Both forces are acted upon the different bodies

C) Directions and magnitudes of both forces are same

D) Both forces have different magnitudes and opposite directions

• question_answer11) If $\overrightarrow{F}=5\widehat{i}+3\widehat{j},\,\overrightarrow{r}=2\widehat{i}-\widehat{j},$, then work done by the system will be

A) $-7\text{ }J$

B) 7 J

C) 10 J

D) $-10\text{ }J$

• question_answer12) If n is a number and u is unit of physical quantity then which of the following is correct for measurement nu?

A) $n\propto u$

B) $n\propto \frac{1}{u}$

C) No relation between n and u

D) None of the above

• question_answer13) The force F is exterted one end of wire when second end is tight, the extension of wire is$x,$then

A) $F\propto x$

B) $F\propto {{x}^{2}}$

C) $F\propto {{x}^{3}}$

D) $F\propto {{x}^{4}}$

• question_answer14) If the length and radius of wire are doubled then Young's modulus of the wire will be

A) doubled

B) half

C) constant

D) None of these

• question_answer15) What is the formula of escape velocity?

A) $\sqrt{g{{R}_{e}}}$

B) $~2g{{R}_{e}}$

C) $\sqrt{2g{{R}_{e}}}$

D) None of these

• question_answer16) What is the true of following in an elastic collision?

A) The kinetic energy will be conservative

B) The momentum will be conservative

C) Both kinetic energy and momentum will be conservative

D) None of the above

• question_answer17) If the speed of particle became twice, then which of the following quantities will be doubled?

A) Length

B) Kinetic energy

C) Momentum

D) Acceleration

• question_answer18) If in the lift, the body of mass 5 kg is suspended to spring balance, the lift moves downward with acceleration$10\text{ }m/{{s}^{2}},$then the reading of spring balance is

A) more than 5 kg-wt

B) less than 5 kg-wt

C) 5 kg-wt

D) zero

• question_answer19) The ratio of fraction of displacement of mass with which of the following quantities is constant if its motion is simple harmonic?

A) Velocity

B) Acceleration

C) Time period

D) Mass

• question_answer20) If the maximum acceleration of motion of a particle is$16\text{ }m/{{s}^{2}},$and the maximum velocity is 24 m/s, then amplitude of the particle will be

A) 36 m

B) 20 m

C) 16 m

D) None of these

• question_answer21) Two wires A and B are made from the same material. The ratio of lengths and diameters respectively are 1:2 and 2:1. If these are stretched by a force, then the ratio of these expansion of lengths will be

A) 2 : 1

B) 1 : 4

C) 1 : 8

D) 8 : 1

• question_answer22) If gravitational potential at the surface of is zero, then gravitational potential at infinity will be

A) ${{W}_{2}}>{{W}_{1}}>{{W}_{3}}$

B) ${{W}_{2}}>{{W}_{3}}>{{W}_{1}}$

C) ${{W}_{1}}>{{W}_{2}}>{{W}_{3}}$

D) ${{W}_{1}}>{{W}_{3}}>{{W}_{2}}$

• question_answer23) Starting with the same initial conditions, an ideal gas expands from volumes${{V}_{1}}$to${{V}_{2}}$three different ways, the work done by the gas is ${{W}_{1}}$ if the process is purely isothermal, ${{W}_{2}}$ if purely isobaric and W3 if purely adiabatic, then

A) ${{W}_{2}}>{{W}_{1}}>{{W}_{3}}$

B) ${{W}_{2}}>{{W}_{3}}>{{W}_{1}}$

C) ${{W}_{1}}>{{W}_{2}}>{{W}_{3}}$

D) ${{W}_{1}}>{{W}_{3}}>{{W}_{2}}$

• question_answer24) The gas is expanded in such a way so that its pressure and volume laws follow$p{{V}^{2}}=$constant. In this process, the gas will become

A) hot

B) cold

C) nor hot neither cold

D) first hot after that cold

• question_answer25) The time period of simple pendulum depends on

A) length

B) mass

C) momentum

D) density

• question_answer26) The stored uniform energy in a spring which is displaced by distance x is

A) $k/x$

B) $\frac{1}{2}\,k/{{x}^{2}}$

C) $k/{{x}^{2}}$

D) $2k/{{x}^{2}}$

• question_answer27) A particle of mass 0.10 kg is executing simple harmonic motion at the rate of 20 oscillation/${{s}^{2}}$ and its amplitude is 0.05 m. Its energy at equilibrium position will be

A) 2 J

B) 4 J

C) 1 J

D) zero

• question_answer28) When any rigid body is in rotational motion about any axis then what is the same for all particles?

A) Angular velocity

B) Linear velocity

D) Linear acceleration

• question_answer29) The coefficients of thermal conductivities of copper, murcury and glass respectively are${{K}_{c}},{{K}_{m}}$ and${{K}_{g}}$such that${{K}_{c}}>\text{ }{{K}_{m}}>\text{ }{{K}_{g}}$. If the same quantity of heat flows per second per unit area of each and corresponding temperature gradients are${{X}_{c}},{{X}_{m}}$and${{X}_{g}},$then

A) ${{X}_{c}}=\text{ }{{X}_{m}}=\text{ }{{X}_{g}}$

B) ${{X}_{c}}>{{X}_{m}}>\text{ }{{X}_{g}}$

C) ${{X}_{c}}<{{X}_{m}}<\text{ }{{X}_{g}}$

D) ${{X}_{m}}<{{X}_{c}}<\text{ }{{X}_{g}}$

• question_answer30) The emitted energy from any body depends on

A) temperature

B) nature of matter

C) area

D) None of these

• question_answer31) What is the absorptive power of ideal black body?

A) 0

B) 1

C) $\infty$

D) None of these

• question_answer32) The initial coordinates of any system are p and V. If a gas $\left( \gamma =\frac{5}{3} \right)$is compressed to $\frac{1}{8}$ of its original volume, then the pressure of the gas will be

A) p

B) 16p

C) 4p

D) 32 p

• question_answer33) Which of the following relationships between p and T for adiabatic process is true?

A) ${{p}^{1-\gamma }}+{{T}^{\gamma }}$ = constant

B) ${{p}^{\gamma }}+{{T}^{1-\gamma }}$ = constant

C) $p{{T}^{1-\gamma }}T$= constant

D) ${{p}^{1-\gamma }}T$= constant

• question_answer34) The energy related per degree of freedom of one molecule is

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

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

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

D) $\frac{1}{2}RT$

• question_answer35) Absolute temperature is that temperature at which

A) molecular motion of all particles becomes zero

B) molecules move randomly

C) gas's atoms change to liquid

D) None of the above

• question_answer36) If the surface tension of liquid is$5\times {{10}^{-2}}N/m$ and weight of liquid column is$6.28\times {{10}^{-4}}N,$then radius of capillary is

A) $2\times {{10}^{-3}}m$

B) $2.5\times {{10}^{-3}}m$

C) $2\times {{10}^{-4}}$

D) $4\times {{10}^{-3}}m$

• question_answer37) When the liquid does not wet the sides of a solid, then angle of contact is

A) obtuse

B) acute

C) $90{}^\circ$

D) zero

• question_answer38) A tuning fork is placed on the table. It produces maximum sound due to

A) beat

B) resonance

C) interference

D) stationary waves

• question_answer39) A body cools down from$61{}^\circ C$to$59{}^\circ C$in 4 min. If the temperature of atmosphere is$30{}^\circ C,$then the time taken to cool it from$51{}^\circ C$to$49{}^\circ C$will be

A) 4 min

B) 2 min

C) 6 min

D) 8 min

• question_answer40) Temperature is a measurement of degree of coldness or hotness of an object. The definition is based on

A) Zeroth law of thermodynamics

B) First law of thermodynamics

C) Second law of thermodynamics

D) Newton's law of cooling

A) adiabatic gradient$=\gamma \times$ isothermal gradient

B) isothermal gradient$=\gamma \times$ adiabatic gradient

C) adiabatic gradient$={{\gamma }^{2}}\times$ isothermal gradient

D) isothermal gradient$={{\gamma }^{2}}\times$adiabatic gradient

• question_answer42) If root mean square velocity for hydrogen gas is 318 m/s and density is$8.99\times {{10}^{-5}}kg/{{m}^{3}}$then the pressure of gas will be

A) 3 atm

B) 1 atm

C) 2 atm

D) None of these

• question_answer43) $pV/kT$ represents

A) number of molecules

B) number of moles

C) universal gas constant

D) None of the above

• question_answer44) The spherical shape of rain drop is due to

A) surface tension

B) viscosity

C) elasticity

D) gravity

• question_answer45) The excess of pressure inside a soap bubble than that of the outer pressure is

A) $\frac{4T}{r}$

B) $\frac{2T}{r}$

C) $\frac{8T}{r}$

D) None of these

• question_answer46) There is an electric field E in$x-$direction. If the work done on moving a charge 0.2 C through a distance of 2 m along a line making an angle $60{}^\circ$ with the$x-$axis is 4.0, what is the value of E?

A) $\sqrt{3}$N/C

B) 4N/C

C) 5 N/C

D) None of these

• question_answer47) An electron is accelerated from a potential difference of${{10}^{4}}V$at distance 5 cm. The force on electron will be

A) $3.2\,\times \,{{10}^{-14}}N$

B) $4N$

C) $3.2\,\times \,{{10}^{-12}}N$

D) None of these

• question_answer48) A point charge$+q$is placed at the centre of a cube. The electric flux emerging from the cube

A) $\frac{q}{{{\varepsilon }_{0}}}$

B) $\frac{q}{2{{\varepsilon }_{0}}}$

C) $\frac{q}{6{{\varepsilon }_{0}}}$

D) $\frac{q}{3{{\varepsilon }_{0}}}$

• question_answer49) To cool a liquid rapidly, cooling system should be used

A) in middle

C) any point

D) None of these

• question_answer50) A stone is shot straight upward with a speed of 20 m/s from a tower 200 m high. The speed with which it strikes the ground is approximately

A) 60 m/s

B) 65 m/s

C) 70 m/s

D) 75 m/s

• question_answer51) When light ray goes from air to water, then its quality that remains unchanged is

A) frequency

B) wavelength

C) speed

D) None of these

• question_answer52) Sources are in phase when

A) first phase is constant with the time

B) first phase changes with the time

C) first phase is constant with the displacement

D) None of the above

• question_answer53) Find the fundamental frequency of a closed pipe, if the length of pipe is 1 m. (speed of sound in air = 320 m/s)

A) 320 Hz

B) 160 Hz

C) 80 Hz

D) 40 Hz

• question_answer54) The musical interval between two tones of frequencies 400 Hz and 200 Hz is

A) 2

B) 200

C) 1

D) None of these

• question_answer55) Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in the figure. The speed of each pulse is 2 cm/s. After 2s, the total energy of the pulses will be

A) zero

B) purely kinetic

C) purely potential

D) partly kinetic and partly potential

• question_answer56) Two charges of$3\times {{10}^{-9}}$and${{10}^{-9}}C$are placed at a distance 5 cm. The force of attraction between them is

A) $1.08\times {{10}^{5}}N$

B) $1.08\times {{10}^{-6}}N$

C) $1.08\times {{10}^{-5}}N$

D) None of these

• question_answer57) If in diffraction by single slit, the width of slit is equal to wavelength of light, then what happened at the screen?

A) Image of slit

B) Diffraction band

C) Equal illuminate

D) Unequal illuminate

• question_answer58) Two positive point charges 12$\mu$C are 8$\mu$C are placed at a distance work done to bring closer 4 cm will be

A) 5.8 J

B) 5.8 eV

C) 13 J

D) 13 eV

• question_answer59) The object at distance of 20 cm is placed in front of convex lens of focal length 10 cm, where will be image formed?

A) 10 cm

B) 20 cm

C) 5 cm

D) 25 cm

• question_answer60) The equivalent resistance between points P and Q of an infinite network of resistance each of 2$\Omega$ connected as shown in figure

A) 3.23$\Omega$

B) 4.23$\Omega$

C) 6.32$\Omega$

D) infinite

• question_answer61) Two tuning forks of frequencies 256 and 258 Hz produce 5 beats/s with the third tuning fork. The frequency of third tuning fork will be

A) 120 Hz

B) 115 Hz

C) 105 Hz

D) 95 Hz

• question_answer62) The equation of wave is$y=5\text{ }sin\text{ }n\text{ }(t+4)$. The amplitude and time period will be

A) 5 cm, 2s

B) 5 cm, $\frac{1}{2}$s

C) 5 cm, 4s

D) 5 cm, $\frac{1}{4}$s

• question_answer63) If$R=25\text{ }\Omega ,\text{ }Z=5\,\Omega$then coefficient of power will be

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

B) 2

C) 1

D) zero

• question_answer64) The formula of impedance for circuit R-L is

A) $\sqrt{{{R}^{2}}+\frac{1}{{{\omega }^{2}}{{L}^{2}}}}R$

B) ${{R}^{2}}+{{\omega }^{2}}{{L}^{2}}$

C) $\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}$

D) $\sqrt{{{\omega }^{2}}{{L}^{2}}+\frac{1}{{{R}^{2}}}}\,$

• question_answer65) Loss of power m R-L circuit is

A) $\frac{{{V}^{2}}}{({{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}R$

B) $\frac{{{V}^{2}}}{\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}}$

C) $\frac{{{V}^{2}}}{R}\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}$

D) None of these

• question_answer66) The phase difference in R-C circuit will be

A) $\phi ={{\tan }^{-1}}\left( \frac{1}{\omega CR} \right)$

B) $\phi ={{\tan }^{-1}}\left( \frac{\omega }{RC} \right)$

C) $\phi ={{\tan }^{-1}}\left( \frac{RC}{\omega } \right)$

D) $\phi ={{\tan }^{-1}}\sqrt{\frac{\omega }{RC}}$

• question_answer67) The electric field gets induced by changing magnetic force lines passing through a conductor. This can be understood by which law?

B) Ampere's law

C) Lenz's law

D) None of these

• question_answer68) In a transformer,${{e}_{p}}=110\text{ }V$and${{e}_{s}}=440\text{ }V,$then its round ratio will be

A) 4 : 1

B) 1 : 4

C) 1 : 3

D) 1 : 2

• question_answer69) The intensity of magnetic field at centre of circular coil is

A) $\frac{{{\mu }_{0}}I}{2R}$

B) $\frac{{{\mu }_{0}}NI{{R}^{2}}}{2{{({{R}^{2}}+{{x}^{2}})}^{3/2}}}$

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

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

• question_answer70) In a potentiometer experiment two cells of emf? s ${{E}_{1}}$and${{E}_{2}}$are used in series and in conjunction and the balancing length is found to be 58 cm of the wire. If the polarity of${{E}_{2}}$is reversed, then the balancing length becomes 29 cm. The ratio $\frac{{{E}_{1}}}{{{E}_{2}}}$of the emf of the two cells is

A) 1 : 1

B) 2 : 1

C) 3 : 1

D) 4 : 1

• question_answer71) Power dissipated in pure inductive circuit will be

A) $\frac{{{V}^{2}}}{({{R}^{2}}+{{\omega }^{2}}{{L}^{2}})}R$

B) zero

C) $\frac{{{V}^{2}}}{{{L}^{2}}}R$

D) $\frac{{{V}^{2}}}{{{Z}^{2}}}R$

• question_answer72) An AC circuit has voltage$V=5\text{ }sin\text{ }10t,$if$R=1\,\Omega$and$L=0.1\text{ }H,$then what is the phase difference between current and voltage?

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

B) $0$

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

D) $\infty$

• question_answer73) In R-L-C circuit,$R=100\text{ }\Omega ,\text{ }L=1\text{ }H,\text{ }C=10\mu F$ and $\omega$= 314 rad /s, then find the value of impedance.

A) 100 $\Omega$

B) 272.6 $\Omega$

C) 217.2 $\Omega$

D) 205.5$\Omega$

• question_answer74) In circuit, when the current changes to 8A from 2A in 2 s, then the value of emf becomes 2 V. The inductance of the circuit is

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

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

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

D) $\sqrt{\frac{2}{3}}\,H$

• question_answer75) Generator generates electric current. In actual, it is a source of

A) inducted force

B) emf

C) electric force

D) None of these

• question_answer76) Lenz's law is accordance on

A) conservation of energy

B) conservation of charge

C) conservation of momentum

D) None of the above

• question_answer77) When the current flows from the conductor, then force above of magnetic field is

A) in circular form around the wire

B) near the wire and parallel to wire

C) near the wire and perpendicular to wire

D) None of the above

• question_answer78) In the following figure, a coil of radius 2 cm is shown along with a coil of radius 7 cm present at its centre. Each coil has 100 round and big coil has 5 A current. What should be the current in small coil so that total magnetic field at centre is 2 mT?

A) 1.44 A

B) 0.793 A

C) 2.88 A

D) 3.4 A

• question_answer79) If amplification factor and mutual conductance are 20 and${{10}^{-3}}$mho respectively, then plate resistance will be

A) 20 k$\Omega$

B) $10\,k\Omega$

C) $20\times {{10}^{-3}}\Omega$

D) None of these

• question_answer80) On the basis which of the following a nucleus can be explained?

A) By nuclear liquid drop model

B) By Thomson model

C) By Rutherford model

D) None of the above

• question_answer81) If the radius of nucleus is${{10}^{-15}}m,$the uncertainty in momentum of nuclear particle will be

A) $\frac{6.62\,\times \,{{10}^{-19}}}{4\pi }$

B) $6.62\,\times \,{{10}^{-29}}$

C) $6.62\,\times \,{{10}^{-39}}$

D) $6.62\,\times \,{{10}^{-49}}$

• question_answer82) If de-Broglie wavelength and accelerated potential difference are 6000$\overset{o}{\mathop{\text{A}}}\,$and 9000 V respectively, then value of $\frac{h}{e}$ will be

A) $1.9\times {{10}^{-10}}$

B) $18\,\times \,{{10}^{-19}}$

C) $8.2\,\times \,{{10}^{-20}}$

D) $18\,\times \,{{10}^{-20}}$

• question_answer83) Photoelectric effect will occur if

A) $v<{{v}_{0}}$

B) $v\ge {{v}_{0}}$

C) $v>2{{v}_{0}}$

D) None of these

• question_answer84) Increasing the principle quantum number, the energy gap between consequence energy state

A) increases

B) decreases

C) remains unchange

D) None of these

• question_answer85) First law of Kirchhoff is accordance on

A) conservation of charge

B) conservation of energy

C) conservation of momentum

D) None of the above

• question_answer86) Three capacitors of equal capacitances 3 $\mu$F each are connected in a circuit. Then their maximum and minimum capacities will be

A) $9\mu F,1\mu F$

B) $8\mu F,2\mu F$

C) $9\mu F,0\mu F$

D) $3\mu F,2\mu F$

• question_answer87) For non-conductors, the forbidden energy gap is

A) 5 eV

B) 1.1 eV

C) 20 eV

D) None of these

• question_answer88) Change of AC to DC is called

A) rectification

B) polarization

C) amplification

D) None of these

• question_answer89) Write the resolving powers of$\alpha ,\beta$and$\gamma$to ascending order.

A) $\alpha ,\beta ,\gamma$

B) $\gamma ,\beta ,\alpha$

C) $\beta ,\alpha ,\gamma$

D) None of these

• question_answer90) Diffraction of electron beam is proved by

A) Davisson-Germer

B) Berg

C) Newton

D) Einsteen

• question_answer91) On the basis of which photoelectric effect is explained?

A) Relativity theory

B) The electromagnetic waves of light

C) Energy spectrum of atoms

D) None of the above

• question_answer92) Which of the following atoms or ions has minimum radius?

A) H

B) ${{H}^{+}}$

C) $L{{i}^{++}}$

D) Deuteron

• question_answer93) The value of resistance R will be

A) 10$\Omega$

B) 15$\Omega$

C) 20$\Omega$

D) 25$\Omega$

• question_answer94) What will be .the stored energy in capacitor of R-C

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

B) $\frac{C{{V}^{2}}}{2}$

C) $\frac{{{q}^{2}}}{C}$

D) None of these

• question_answer95) The valancy of carbon atom is

A) 1

B) 2

C) 3

D) 4

A) Pentavalent

B) Trivalent

C) Tertravalent

D) None of these

• question_answer97) In LC-R circuit,$R=300\Omega ,\text{ }L=0.9\text{ }H,\text{ }C=$$2\mu F$and $\omega =1000$rad/s, the impedance of circuit is

A) 1300$\Omega$

B) 900$\Omega$

C) 500$\Omega$

D) 400$\Omega$

• question_answer98) What should be the capacity of capacitor of R-C circuit, in which the value of resistance is 10$\Omega$ to become the value of time constant 10?

A) $10\mu F$

B) $100\mu F$

C) $1000\mu F$

D) $10,000\mu F$

• question_answer99) The energy needed to remove the one electron from neutral helium atom is 24.6 eV. Then the energy needed to remove both the electrons from neutral helium atom is

A) 79.0 eV

B) 51.8 eV

C) 49.2 eV

D) 38.2 eV

• question_answer100) Two same light cathode gets the light of frequencies${{f}_{1}}$and${{f}_{2}}$. If the velocities of emitted photo electrons are ${{v}_{1}}$ and ${{v}_{2}}$ then

A) ${{v}^{2}}_{1}-v\frac{2}{2}=\frac{2h}{m}({{f}_{1}}-{{f}_{2}})$

B) ${{v}_{1}}+{{v}_{2}}={{\left[ \frac{2h}{m}({{f}_{1}}+{{f}_{2}}) \right]}^{2}}$

C) ${{v}^{2}}_{1}+{{v}^{2}}_{2}=\frac{2h}{m}({{f}_{1}}+{{f}_{2}})$

D) ${{v}_{1}}-{{v}_{2}}={{\left[ \frac{2h}{m}({{f}_{1}}-{{f}_{2}} \right]}^{1/2}}$

• question_answer101) For the salt of weak acid and weak base, the value of${{K}_{b}}$will be

A) ${{K}_{b}}=\frac{{{K}_{w}}}{{{K}_{a}}}$

B) ${{K}_{h}}=\frac{{{K}_{w}}}{{{K}_{b}}}$

C) ${{K}_{h}}=\frac{{{K}_{w}}}{{{K}_{a}}.{{K}_{b}}}$

D) Hydrolysis does not take place

• question_answer102) Formation of cyanohydrin from$C{{H}_{3}}COC{{H}_{3}}$is called

A) electrophilic substitution

B) nucleophilic substitution

D) electrophilic substitution

• question_answer103) Bond energy of$C-H$bond in ethane, ethane and ethyne is

A) equal in three

B) more in ethane

C) more in ethene

D) more in ethyne

• question_answer104) $C{{H}_{3}}-CH=C{{H}_{2}}+HBr\xrightarrow[{}]{{}}A;$ compound A is

A) $\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,-CH=C{{H}_{2}}$

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

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

D) $\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ Br \end{smallmatrix}}{\mathop{C{{H}_{2}}}}\,$

• question_answer105) Which of the following is represented by prefix word 'alkali' used for alkali metals?

A) Ash of plants

B) Lusture of silver

C) Metallic nature

D) Reactive metal

• question_answer106) The product is obtained on reaction of urea with ammonia

A) barbituric acid

B) semicarbazide

C) methylol urea

D) acetamide

• question_answer107) Structure of ammonia is

A) pyramidal

B) tetrahederal

C) trigonal

D) trigonal bipyramidal

• question_answer108) The decreasing order of reactivity of alkyl halide is

A) $RI>RCl>RBr$

B) $RCl>RI>RBr$

C) $RCl>RBr>RI$

D) $RI>RBr>RCl$

• question_answer109) If the pH value of$HCl$solution is 4 then its molar concentration will

A) 4 M

B) 0.0001 M

C) 0.4 M

D) 10 M

• question_answer110) The product is formed on the condensation of phenol with phthalic anhydride

A) methyl orange

B) phenol red

C) salicylic acid

D) phenolphthalein

• question_answer111) 23 g sodium metal reacts from methyl alcohol to give

A) 1 mol${{H}_{2}}$

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

C) $\frac{1}{2}$ mol${{H}_{2}}$

D) None of these

• question_answer112) Nitration of benzene is

B) electrophilic substitution

D) nucleophilic substitution

• question_answer113) Which of the following has maximum magnetic moment?

A) $3{{d}^{5}}$

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

C) $3{{d}^{9}}$

D) $3{{d}^{7}}$

• question_answer114) The correct order of atomic and ionic size of iodine is

A) $I>{{I}^{-}}>{{I}^{+}}$

B) ${{I}^{-}}>I>{{I}^{+}}$

C) $I>{{I}^{+}}>{{I}^{-}}$

D) ${{I}^{+}}>I>{{I}^{-}}$

• question_answer115) Number of$\sigma$and$\pi$bonds in l-butene-3-yne

A) $5\sigma ,5\pi$

B) $7\sigma ,3\pi$

C) $8\sigma ,6\pi$

D) $6\sigma ,4\pi$

• question_answer116) Which of the following salt does not give brown gas on heating?

A) $LiN{{O}_{3}}$

B) $KN{{O}_{3}}$

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

D) $AgN{{O}_{3}}$

• question_answer117) 2-chloropropane reacts with sodium in presence of ether to form

A) n-hexane

B) n-hexene

C) $C{{H}_{3}}-CH=C{{H}_{2}}$

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

• question_answer118) ${{C}_{6}}{{H}_{6}}+C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-Cl\xrightarrow[{}]{{}}A;$Product A is

A) benzophenone

B) benzoyl chloride

C) acetophenone

D) toluene

• question_answer119) Which group is/are present in picric acid?

A) $-OH$

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

C) $-OH$ and$-N{{O}_{2}}$

D) $-COOH$and$-N{{O}_{2}}$

• question_answer120) Number of$C-C$and$C-H$bonds in 4-methyl-2-pentyne will be

A) 4, 10

B) 5, 10

C) 4, 9

D) 5, 9

• question_answer121) The oxidation state of iron is zero in which of the following compound?

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

B) $Fe{{(CO)}_{4}}$

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

D) $FeC{{l}_{3}}$

• question_answer122) Which of the following overlapping does not give$\pi -$bond in a molecule AB? (z-axis is the axis of molecule)

A) ${{p}_{x}}-{{p}_{x}}$

B) ${{p}_{y}}-{{p}_{xy}}$

C) ${{p}_{y}}-s$

D) ${{p}_{y}}-{{p}_{y}}$

• question_answer123) Which of the following equilibrium does not affect from change in pressure?

A) $2N{{O}_{2}}(g){{N}_{2}}{{O}_{4}}(g)$

B) $2HI(g){{H}_{2}}(g)+{{I}_{2}}(g)$

C) $2{{O}_{3}}(g)3{{O}_{2}}(g)$

D) $PC{{l}_{5}}(g)PC{{l}_{3}}(g)+C{{l}_{2}}(g)$

• question_answer124) The concentration of a acidic solution is 0.1 M and degree of dissociation is 1%. The dissociation constant of acid will be

A) $1.01\times {{10}^{-5}}$

B) $1.01\times {{10}^{-3}}$

C) $1.01\times {{10}^{3}}$

D) $1.01\times {{10}^{5}}$

• question_answer125) Number of elements in s-block are

A) more from elements of p-block

B) less from elements of d-block

C) more from elements of d-block

D) None of the above

• question_answer126) On doubling the concentration of A and B in reaction$A+BAB,$the equilibrium constant will be

A) unchanged

B) halved

C) doubled

D) four times

• question_answer127) The compound is not used in redox titration

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

B) ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$

C) ${{(COOH)}_{2}}$

D) None of these

• question_answer128) Which of the following does not used as primary standard in redox titration?

A) ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$

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

C) ${{(COOH)}_{2}}$

D) Mohr's salt

• question_answer129) The solubility product of a metal sulphide MS is$7\times {{10}^{-24}}mo{{l}^{2}}{{L}^{-2}}$. The solubility of MS will be

A) $7\times {{10}^{-24}}mo{{l}^{2}}{{L}^{2}}$

B) $2.65\times {{10}^{-12}}mol\,{{L}^{-1}}$

C) $1.32\times {{10}^{-12}}mol\,{{L}^{-1}}$

D) $14\times {{10}^{-24}}mo{{l}^{3}}{{L}^{2}}$

• question_answer130) Which ion has the maximum hydration energy?

A) $M{{g}^{2+}}$

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

C) $C{{a}^{2+}}$

D) $S{{r}^{2+}}$

• question_answer131) What will form on reduction of${{P}_{2}}{{O}_{5}}$from acetic acid?

A) Acetic anhydride

B) Acetyl chloride

C) Acetic ester

D) None of these

• question_answer132) Possible number of isomers of alkane${{C}_{5}}{{H}_{12}}$will be

A) 4

B) 3

C) 5

D) 6

• question_answer133) Molecular formula of chrornyl chloride is

A) $Cr{{O}_{2}}C{{l}_{2}}$

B) $Cr{{O}_{2}}Cl$

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

D) ${{(CrOCl)}_{2}}$

• question_answer134) Phenol reacts with dil.$HN{{O}_{3}}$to give

A) o-nitrophenol

B) p-nitrophenol

C) o- and p-nitrophenol

D) picric acid

• question_answer135) Which of the following compound is obtained from ozonolysis of benzene?

A) Benzene triozonide

B) Glyoxal

C) Ethane dial

D) All of these

• question_answer136) Oxidation state of iron and sulphur in copper pyrite are respectively

A) + 2 and -2

B) + 2 and - 4

C) + 3 and -4

D) + 3 and - 6

• question_answer137) What will obtain on distillation of acetic acid with$PC{{l}_{3}}$?

A) Acetic anhydride

B) Chloroacetic acid

C) Acetyl chloride

D) Ethyl acetate

A) $C{{l}_{2}}CH.CHOOH$

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

C) $CC{{l}_{3}}COOH$

D) $ClC{{H}_{2}}.COOH$

• question_answer139) The gas is released in fermentation reaction

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

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

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

D) $S$

• question_answer140) Which of the following molecule of compound will be linear structure?

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

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

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

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

• question_answer141) Which of the following ion is colourless?

A) $C{{u}^{+}}$

B) $C{{u}^{2+}}$

C) $C{{u}^{3+}}$

D) $F{{e}^{3+}}$

• question_answer142) The colour of iodine solution disappears on reaction with which of the following compound?

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

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

C) $CC{{l}_{4}}$

D) $CHC{{l}_{3}}$

• question_answer143) $PC{{l}_{5}}$is used in the

A) synthesis of $C{{H}_{3}}COCl$

B) synthesis of ${{C}_{6}}{{H}_{5}}OH$

C) synthesis of ${{C}_{2}}{{H}_{5}}-O-{{C}_{2}}{{H}_{5}}$

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

• question_answer144) It is cleared by the a-particle scattering experiment of Rutherford. That

A) $\alpha -$particle is heavier than electron

B) $\alpha -$particle is positively charged

C) mostly part of atom is hollow

D) $\alpha -$particle moves with high velocity

• question_answer145) Which of the following compound has maximum covalent character?

A) $NaF$

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

C) $BeB{{r}_{2}}$

D) $KI$

• question_answer146) The suitable indicator in the titration of strong acid and weak base is

A) methyl orange

B) bromothymol blue

C) phenol red

D) phenolphthalein

• question_answer147) The product is formed on the reaction of ethylene bromide with Zn

A) alkane

B) alkene

C) alkyne

D) All of these

• question_answer148) Which of the following is formed on the hydrolysis of product, formed by the reaction of$C{{H}_{3}}CHO$and$C{{H}_{3}}MgBr$?

A) Primary alcohol

B) Secondary alcohol

C) Tertiary alcohol

D) Ketone

• question_answer149) Bond angle is$s{{p}^{2}}$hybridization is

A) $180{}^\circ$

B) $120{}^\circ$

C) $90{}^\circ$

D) $109{}^\circ 45'$

• question_answer150) Scientist who discovered the positron?

A) Pauling

B) Anderson

C) Yukava

D) Sanger

• question_answer151) Number of electrons are required for the complete reduction of one molecule of ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$

A) 3

B) 4

C) 5

D) 6

• question_answer152) Which of the following pair has same oxidation number of sulphur and chromium?

A) $SO_{3}^{2-},CrO_{4}^{2-}$

B) $S{{O}_{3}},CrO_{4}^{2-}$

C) $S{{O}_{2}},CrO_{4}^{2-}$

D) $S{{O}_{2}},C{{r}_{2}}O_{7}^{2-}$

• question_answer153) Which of the following gives haloform reaction?

A) Acetaldehyde

B) Propionaldehyde

C) iso-butyraldehyde

D) All of these

• question_answer154) The percentage of nitrogen will equal in oximes of which of the following compound pairs?

A) Acetone and acetaldehyde

B) Acetone and propionaldehyde

C) Aqetone and acraldehyde

D) Acetaldehyde and acraldehyde

• question_answer155) The highest atomic number radioactive element in p-block elements is

A) Pb

B) Te

C) Rn

D) Po

• question_answer156) Which of the following reagent evolves nitrogen on reaction with ethyl amine?

A) Nitrosyl chloride

B) Acetyl chloride

C) Carbon disulphide

D) Benzoyl chloride

• question_answer157) The density of ice is less than water because

A) ice floats on water

B) the structure of ice is three dimensional with porous

C) H-bond does not present in ice

D) water is a polar solvent

• question_answer158) The value of energy will increase in sub energy level because

A) on increasing the value of principal quantum number

B) on increasing the value of azimuthal quantum number

C) on increasing the value of both principal quantum number and azimuthal quantum number

D) on increasing the value of spin quantum Number

• question_answer159) The density of Na is higher than K because

A) ionization potential of Na is greater than K

B) size of Na is smaller than K

C) atomic weight of K is greater than Na

D) only eight electrons are present in third shell of K

• question_answer160) Same magnetic moment ions are

A) $C{{u}^{+}},F{{e}^{3+}}$

B) $M{{n}^{2+}},F{{e}^{3+}}$

C) $C{{u}^{2+}},F{{e}^{2+}}$

D) $M{{n}^{2+}},T{{i}^{2+}}$

• question_answer161) The set of oxidation of nitrogen in ammonium nitrate is

A) $-3,+3$

B) $-1,+1$

C) $+1,-1$

D) $-3,+5$

• question_answer162) At$300{}^\circ C,$the vapour density of$PC{{l}_{5}}$is 60. At this temperature, its dissociation percentage will be

A) 73

B) 77

C) 83

D) 87

• question_answer163) The degree of dissociation of A is$\alpha$in equilibrium reaction$A\xrightarrow[{}]{{}}2B+C$. If one mole of A is taken initially then total .number of moles will in equilibrium.

A) $1-\alpha$

B) $1+\alpha$

C) $1-2\alpha$

D) $1+2\alpha$

• question_answer164) Which of the following compounds will form mesitylene on distillation with cone.${{H}_{2}}S{{O}_{4}}$?

A) Acetaldehyde

B) Acetone

C) Acetophenone

D) Acetyl chlorine

• question_answer165) Generally, alkenes and alkynes show the following type of reaction

D) electrophilic substitution

• question_answer166) Which of the following is not a polymer?

A) Teflon

B) Nylon

C) Orion

D) Phorone

• question_answer167) The formula of wavelength of spectral lines for hydrogen atom is

A) $\frac{1}{\lambda }=R\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)$

B) $\frac{1}{\lambda }=R\left( \frac{1}{n_{2}^{2}}-\frac{1}{n_{1}^{2}} \right)$

C) $\frac{1}{\lambda }=R{{\left( \frac{1}{{{n}_{1}}}-\frac{1}{{{n}_{2}}} \right)}^{2}}$

D) $\frac{1}{\lambda }=R{{\left( \frac{1}{{{n}_{2}}}-\frac{1}{{{n}_{1}}} \right)}^{2}}$

A) absolute alcohol$+C{{H}_{3}}OH$

B) absolute alcohol$+{{C}_{6}}{{H}_{5}}OH$

C) absolute alcohol + petrol 4- benzene

D) absolute alcohol $+C{{H}_{3}}COOH$

• question_answer169) $C{{H}_{3}}C{{H}_{2}}OH$and$C{{H}_{3}}-O-C{{H}_{3}}$are

A) positive isomers

B) functional isomers

C) chain isomers

D) geometrical isomers

• question_answer170) Alkaline$KMn{{O}_{4}}$solution is called

A) Tollen's reagent

B) Baeyer's reagent

C) Benedict's solution

D) None of these

• question_answer171) The bond angle and bond length in benzene are respectively

A) $120{}^\circ$and 1.34$\overset{o}{\mathop{\text{A}}}\,$

B) $120{}^\circ$and 1.39$\overset{o}{\mathop{\text{A}}}\,$

C) $180{}^\circ$and 1.33$\overset{o}{\mathop{\text{A}}}\,$

D) $120{}^\circ$and 1.54$\overset{o}{\mathop{\text{A}}}\,$

• question_answer172) ${{(C{{H}_{3}}CO)}_{2}}O+HCl\xrightarrow[{}]{{}}X+C{{H}_{3}}COH;$ compound X is

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

B) $C{{H}_{3}}COCl$

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

D) None of these

• question_answer173) The main product of the reaction of $C{{H}_{3}}C{{H}_{2}}N{{H}_{2}}$with nitrous acid is

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

B) $C{{H}_{3}}ONO$

C) $C{{H}_{3}}C{{H}_{2}}OH$

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

• question_answer174) $RX+2Na+BX\xrightarrow[{}]{{}}R-R+2NaX$ This reaction is known as

A) Wurtz reaction

B) Williamson's synthesis

C) Kolbe's electrolysis

D) Sabatier-Sendern's reaction

• question_answer175) In froth floatation method of ore concentration, ore particles rise to the surface because

A) they are light

B) these are insoluble

C) their surface do not wet with water easily

D) these contain electric charge

• question_answer176) The number of k electrons present in aromatic ring are

A) $(4+2)n$

B) $(4+2n)$

C) $(4n+2)$

D) None of these

• question_answer177) $C{{H}_{3}}C{{H}_{2}}I+NaOR\to C{{H}_{3}}C{{H}_{2}}R+NaI$ This reaction is

A) Wurtz reaction

B) Williamson's synthesis

C) Wittig reaction

D) Curtius reaction

• question_answer178) Absolute alcohol can obtained from rectified spirit by the process of

A) Steam distillation

B) Fractional distillation

C) Azeotropic distillation

D) Hydrolysis

• question_answer179) The product of the reaction of benzene with$CO+HCl$in the presence of anhydrous$AlC{{l}_{3}}$is

A) benzoyl chloride

B) benzal chloride

C) chlorobenzene

D) benzaldehyde

• question_answer180) The suitable indicator for the titration of $N{{H}_{4}}OH$and$HCl$is

A) phenolphthalein

B) methyl orange

C) bromothymol blue

D) litmus paper

• question_answer181) Which of the following is not Lewis acid?

A) $FeC{{l}_{3}}$

B) $BC{{l}_{3}}$

C) $AlC{{l}_{3}}$

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

• question_answer182) Which of the following metal can displace Cu from copper sulphate solution?

A) Fe

B) Ag

C) Au

D) Pt

• question_answer183) Which enzyme is used for the conversion of starch into maltose?

A) Zymase

B) Invertase

C) Maltase

D) Diastase

• question_answer184) Which of the following is used in the extraction of copper?

A) $C{{u}_{2}}S$

B) Pyrite

C) Silver argentocyanide

D) $CuFe{{S}_{2}}$

• question_answer185) The product of the reaction of ethanol with ethyl magnesium iodide is

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

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

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

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

• question_answer186) Which of the following element has the maximum tendency of loose the electron?

A) Be

B) B

C) Mg

D) Rb

• question_answer187) Which of the following is formed on the hydrolysis of the product, formed by the reaction of acetone with methyl magnesium iodide?

A) Primary alcohol

B) Secondary alcohol

C) Tertiary alcohol

D) Carboxylic acid

• question_answer188) Which complex forms on adding sodium cyanide solution in$A{{g}_{2}}S,$in the cyanide method of silver extraction?

A) $N{{a}_{2}}[Ag{{(CN)}_{2}}]$

B) $Na[Ag{{(CN)}_{2}}]$

C) $NaAgCN$

D) $Na[Ag{{(CN)}_{4}}]$

• question_answer189) Benzene was discovered by

B) Prisetly

C) Kekule

D) Hofmann

• question_answer190) Which substance is used in the preparation of absolute alcohol from rectified spirit?

A) $Ca{{(OH)}_{2}}$

B) $CaO$

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

D) Wire of Na

• question_answer191) Benzenediazonium chloride reacts with phenol to give

A) ${{C}_{6}}{{H}_{5}}-NH-{{C}_{6}}{{H}_{5}}$

B) ${{C}_{6}}{{H}_{5}}-NH=N-{{C}_{6}}{{H}_{5}}$

C) ${{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} \downarrow \\ O \end{smallmatrix}}{\mathop{N}}\,=N-{{C}_{6}}{{H}_{5}}$

D)

• question_answer192) The first ionization potentials of nitrogen and oxygen are respectively

A) 14.6 eV, 13.6 eV

B) 13.6 eV, 14.6 eV

C) 13.6 eV, 13.6 eV

D) 14.6 eV, 14.6 eV

• question_answer193) Which of the following compound forms 3-hydroxy butanal on reaction with dil. alkali?

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

B) $HCHO$

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

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

• question_answer194) The product of the reaction of ethylidene chloride with zinc dust is

A) $C{{H}_{2}}=C{{H}_{2}}$

B) $CH\equiv CH$

C) $C{{H}_{3}}-CH=CH-C{{H}_{3}}$

D) $C{{H}_{3}}C{{H}_{2}}-CH=C{{H}_{2}}$

• question_answer195) Which of the following pair shows the paramagnetic character?

A) $FeS{{O}_{4}}$and$NiC{{l}_{2}}$

B) $ZnC{{l}_{2}}$and$FeS{{O}_{4}}$

C) $MgC{{l}_{2}}$and$NiC{{l}_{4}}$

D) $KCl$and$ZnC{{l}_{2}}$

• question_answer196) The quantum number which shows the orientation of electron cloud in the presence of external magnetic field?

A) Principal quantum number

B) Azimuthal quantum number

C) Magnetic quantum number

D) Spin quantum number

• question_answer197) Oxidation number of$Mn$in$MnO_{4}^{-}$is

A) +5

B) + 6

C) +7

D) + 4

• question_answer198) Which of the following salt gives anionic hydrolysis?

A) $NaCl$

B) $NaCN$

C) $N{{H}_{4}}Cl$

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

• question_answer199) Which of the following compounds will form chloropicrin on reaction with cone.$HN{{O}_{3}}$?

A) $CC{{l}_{4}}$

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

C) $CHC{{l}_{3}}$

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

• question_answer200) ${{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow[{}]{Zn+NaOH}$ Product The product of reaction is

A) ${{C}_{6}}{{H}_{5}}-NH-NH-{{C}_{6}}{{H}_{5}}$

B) ${{C}_{6}}{{H}_{5}}-N=N-{{C}_{6}}{{H}_{5}}$

C) ${{C}_{6}}{{H}_{5}}-\underset{\downarrow }{\mathop{N}}\,={{C}_{6}}{{H}_{5}}$

D) ${{C}_{6}}{{H}_{5}}N{{H}_{2}}$

• question_answer201) If the base of an equilateral triangle is$x+y=2$and vertex,$(2,-1)$is, then length of each side is equal to

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

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

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

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

• question_answer202) Minimum number of zeros in an upper triangular matrix is

A) $\frac{n(n+1)}{2}$

B) $\frac{n(n-1)}{2}$

C) $\frac{2n(n-1)}{2}$

D) None of these

• question_answer203) $\left| \begin{matrix} {{1}^{2}} & {{2}^{2}} & {{3}^{2}} \\ {{2}^{2}} & {{3}^{2}} & {{4}^{2}} \\ {{3}^{2}} & {{4}^{2}} & {{5}^{2}} \\ \end{matrix} \right|$is equal to

A) 8

B) $-8$

C) 400

D) 1

• question_answer204) For any complex number z, minimum value of$|z|+|z-1|$is equal to

A) 1

B) 0

C) 1/2

D) 3/2

• question_answer205) $\left| \begin{matrix} 1/a & {{a}^{2}} & bc \\ 1/b & {{b}^{2}} & ca \\ 1/c & {{c}^{2}} & ab \\ \end{matrix} \right|$is equal to

A) $abc$

B) 0

C) 1

D) $a+b+c$

• question_answer206) lf$^{n}{{C}_{3}}{{+}^{n}}{{C}_{4}}{{>}^{n+1}}{{C}_{3}},$then

A) $n>7$

B) $n<6$

C) $n>6$

D) None of these

• question_answer207) If ${{x}^{2}}+{{y}^{2}}=t-\frac{1}{t},{{x}^{4}}+{{y}^{4}}={{t}^{2}}+\frac{1}{{{t}^{2}}},$then$\frac{dy}{dx}$is equal to

A) $\frac{1}{x{{y}^{3}}}$

B) $\frac{1}{{{x}^{3}}y}$

C) $-\frac{1}{x{{y}^{3}}}$

D) $-\frac{1}{{{x}^{3}}y}$

• question_answer208) $\hat{i}\times (\hat{j}\times \hat{k})+\hat{j}\times (\hat{k}\times \hat{i})+\hat{k}(\hat{i}\times \hat{j})$is equal to

A) 1

B) 0

C) 3

D) 4

• question_answer209) The area of a rectangle of given perimeter is minimum, if the ratio of its length to width is

A) 1:1

B) 2:1

C) 4:3

D) 3:2

• question_answer210) If AB = A, BA = B for any two square matrices A and B, then${{A}^{2}}$is equal to

A) A

B) B

C) AB

D) ${{B}^{2}}$

• question_answer211) If$z=x+iy,$then $z\overline{z}+2(z+\overrightarrow{z})+c=0$will define a

A) circle

B) straight line

C) parabola

D) point

• question_answer212) If$(3,\lambda )$and (5,6) are the conjugate points of ${{x}^{2}}+{{y}^{2}}=3,$then $\lambda$is equal to

A) 2

B) $-2$

C) 1

D) $-1$

• question_answer213) The argument of${{\left( \frac{1+\cos \theta +i\sin \theta }{1+\cos \theta -i\sin \theta } \right)}^{n}}$is

A) $n\theta$

B) $\frac{n\theta }{2}$

C) $-\frac{n\theta }{2}$

D) $-n\theta$

• question_answer214) The figure made by the lines$ax\pm by\pm c=0$is

A) rectangle

B) square

C) rhombus

D) None of these

• question_answer215) If focal chord of a parabola${{y}^{2}}=4ax$intercepted at b and k, then k is equal to

A) $\frac{ab}{b-a}$

B) $\frac{b}{b-a}$

C) $\frac{a}{b-a}$

D) $\frac{ba}{a-b}$

• question_answer216) If$\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$and$|\overrightarrow{a}|=5,|\overrightarrow{b}|=3,|\overrightarrow{c}|=7,$then angle between a and b is

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

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

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

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

• question_answer217) If a coin is tossed n times, then the probability that head comes odd number of times is

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

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

C) $\frac{1}{{{2}^{n-1}}}$

D) None of these

• question_answer218) $\int{\sqrt{1+\sec x}}dx$is equal to

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

B) $-2{{\sin }^{-1}}\left( \sqrt{2}\sin \frac{x}{2} \right)+c$

C) $2{{\sin }^{-1}}\left( \sqrt{2}\sin \frac{x}{2} \right)+c$

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

• question_answer219) $\int{\cos (\log x)dx}$is equal to

A) $\frac{x}{2}[\sin (\log x)-\cos (\log x)]+c$

B) $\frac{x}{2}[\sin (\log x)+\cos (\log x)]+c$

C) $\frac{1}{2}[\sin (\log x)-\cos (\log x)]+c$

D) $\frac{1}{2}[\sin (\log x)+\cos (\log x)]+c$

• question_answer220) The value of$|{{z}_{1}}+{{z}_{2}}{{|}^{2}}+|{{z}_{1}}-{{z}_{2}}{{|}^{2}}$is

A) $\frac{1}{2}[|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}]$

B) $2[|{{z}_{1}}{{|}^{2}}+|{{z}_{2}}{{|}^{2}}]$

C) $2[|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}}]$

D) $\frac{1}{2}[|{{z}_{1}}{{|}^{2}}-|{{z}_{2}}{{|}^{2}}]$

• question_answer221) If 5th term and 11th term of a harmonic progression are$\frac{1}{45}$and$\frac{1}{69}$respectively, then 16th term is

A) $\frac{1}{89}$

B) $\frac{1}{85}$

C) $\frac{1}{81}$

D) $\frac{1}{77}$

• question_answer222) The geometric mean of the roots of the equation${{x}^{2}}-18x+9=0$is

A) $9\sqrt{2}$

B) $9$

C) $\frac{1}{81}$

D) $\frac{1}{77}$

• question_answer223) If the roots of the equation ${{x}^{2}}-8x+{{a}^{2}}-60=0$are real, then the value of$a$is

A) $-2<a<8$

B) $-2<a<8$

C) $-2<a<8$

D) $2<a<8$

• question_answer224) The equation of common tangent to the circle ${{x}^{2}}+{{y}^{2}}=2$and the parabola${{y}^{2}}=8x$is

A) $y=x+1$

B) $y=x+2$

C) $y=x-2$

D) $y=-x+2$

• question_answer225) The angle between the tangents drawn from the origin to the circle${{(x-7)}^{2}}+{{(y+1)}^{2}}=25$is

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

B) $\frac{\pi }{6}$

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

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

• question_answer226) ${{\left( \frac{\sqrt{3}+i}{2} \right)}^{6}}+{{\left( \frac{i-\sqrt{3}}{2} \right)}^{6}}$is equal to

A) 0

B) $-1$

C) 2

D) $-2$

• question_answer227) If$A=\left[ \begin{matrix} 3 & 2 \\ 1 & -4 \\ \end{matrix} \right],$then A (adj A) is equal to

A) $-14I$

B) $-10I$

C) $8I$

D) $-\frac{1}{14}I$

• question_answer228) Maximum value of$\frac{\log x}{x}$is.

A) e

B) 1

C) 2e

D) 2

• question_answer229) If the line$lx+my=1$is the tangent to the circle${{x}^{2}}+{{y}^{2}}={{r}^{2}},$then locus of$(l,m)$is

A) ${{x}^{2}}+{{y}^{2}}=1$

B) ${{r}^{2}}({{x}^{2}}+{{y}^{2}})=1$

C) ${{x}^{2}}+{{y}^{2}}={{r}^{2}}$

D) ${{x}^{2}}+{{y}^{2}}=2{{r}^{2}}$

• question_answer230) $\frac{d}{dx}{{\cosh }^{-1}}(\sec x)$is equal to

A) $sin\text{ }x$

B) $sec\text{ }x$

C) $tan\text{ }x$

D) $cosec\text{ }x$

• question_answer231) If$\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k},\overrightarrow{b}=\hat{j}+\hat{k}$and$\overrightarrow{c}=\hat{i}-\hat{k}$and $\overrightarrow{a}+\overrightarrow{b}$and$\overrightarrow{b}+\overrightarrow{c}$are the diagonals of a parallelogram, then it's vector area is equal to

A) $\hat{i}+\hat{j}+\hat{k}$

B) $-\hat{i}+\hat{j}+\hat{k}$

C) $\hat{i}-\hat{j}+\hat{k}$

D) $\hat{i}+\hat{j}-\hat{k}$

• question_answer232) If$\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c},$then$\overrightarrow{a}(\overrightarrow{b}\times \overrightarrow{c})$is equal to

A) $\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})$

B) $2\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})$

C) $\overrightarrow{b}.(\overrightarrow{a}+\overrightarrow{c})$

D) None of these

• question_answer233) $\int_{0}^{1}{\sqrt{\frac{1-x}{1+x}}}dx$is equal to

A) $\frac{\pi }{2}-1$

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

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

D) $\pi +1$

• question_answer234) If$\alpha$and$\beta$are the roots of the equationx${{x}^{2}}-(1+{{n}^{2}})x+\frac{1}{2}(1+{{n}^{2}}+{{n}^{4}})=0$then${{\alpha }^{2}}+{{\beta }^{2}}$is equal to

A) ${{n}^{2}}+2$

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

C) ${{n}^{2}}$

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

• question_answer235) If${{(1+x)}^{n}}{{=}^{n}}{{C}_{0}}{{+}^{n}}{{C}_{1}}x{{+}^{n}}{{C}_{2}}{{x}^{2}}+....{{+}^{n}}{{C}_{n}}{{x}^{n}},$then the value of $\frac{^{n}{{C}_{1}}}{^{n}{{C}_{0}}}+2.\frac{^{n}{{C}_{2}}}{^{n}{{C}_{1}}}+3.\frac{^{n}{{C}_{3}}}{^{n}{{C}_{2}}}+....+n.\frac{^{n}{{C}_{n}}}{^{n}{{C}_{n-1}}}$is

A) $\frac{n(n+1)}{2}$

B) $\frac{(n+1)}{n!}$

C) $\frac{n({{n}^{2}}+1)}{2}$

D) $n\frac{(n+1)}{2}$

• question_answer236) $\frac{1-2i}{2+i}+\frac{4-i}{3+2i}$is equal to

A) $-\frac{24}{13}+\frac{10}{13}i$

B) $\frac{24}{13}-\frac{10}{13}i$

C) $\frac{10}{13}-\frac{24}{13}i$

D) $\frac{10}{13}+\frac{24}{13}i$

• question_answer237) If$\omega$is the cube root of unity, then the value of $\left| \begin{matrix} 1 & \omega & {{\omega }^{2}} \\ \omega & {{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & \omega \\ \end{matrix} \right|$is equal to

A) 1

B) 0

C) $\omega$

D) ${{\omega }^{2}}+1$

• question_answer238) If $z=\frac{(1-i)(2+i)}{3+i},$then$|z|$is equal to

A) $-1$

B) 1

C) $1/2$

D) $-1/2$

• question_answer239) In the expansion of${{\left( 2{{x}^{4}}-\frac{1}{{{x}^{7}}} \right)}^{11}},$the term independent of $x$is

A) 330

B) 42240

C) 114050

D) $-32190$

• question_answer240) The equation of radical axis of the circles $2{{x}^{2}}+2{{y}^{2}}-7x=0$and${{x}^{2}}+{{y}^{2}}-4y-7=0$is

A) $7x+8y+14=0$

B) $7x-8y-14=0$

C) $7x-8y+14=0$

D) $8x-7y+14=0$

• question_answer241) If$f(\theta )=\tan \theta ,$then the value of$\frac{f(\theta )-f(\phi )}{1+f(\theta )f(\phi )}$is

A) $f(\theta )+f(\phi )$

B) $f(\theta -\phi )$

C) $f\left( \frac{\theta }{\phi } \right)$

D) $\theta -\phi$

• question_answer242) If$A=\left[ \begin{matrix} 2 & 14 \\ 0 & 3 \\ \end{matrix} \right]$and$B=\left[ \begin{matrix} 1 & 2 \\ 0 & 5 \\ \end{matrix} \right],$then$4A-3B$is equal to

A) $\left[ \begin{matrix} 7 & 14 \\ 0 & 7 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 5 & 10 \\ 0 & -3 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} -5 & -10 \\ 0 & 3 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 1 & 2 \\ 0 & 2 \\ \end{matrix} \right]$

• question_answer243) If two vertices of a triangle are (6, 4) and (2,6) and centroid is (4,6), then the third vertex is

A) (4, 8)

B) (8, 4)

C) (6, 4)

D) None of these

• question_answer244) $\frac{d}{dx}({{\sec }^{-1}}x)$is equal to

A) $\frac{1}{x\sqrt{1-{{x}^{2}}}}$

B) $\frac{1}{x\sqrt{1+x}}$

C) $\frac{1}{x\sqrt{{{x}^{2}}-1}}$

D) $\frac{1}{x\sqrt{x-1}}$

• question_answer245) Differential coefficient of${{\sin }^{-1}}x$with respect to ${{\cos }^{-1}}\sqrt{1-{{x}^{2}}}$is

A) $\frac{2}{\sqrt{1-{{x}^{2}}}}$

B) $\frac{1}{\sqrt{1-{{x}^{2}}}}$

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

D) None of these

• question_answer246) $\int{{{\cos }^{3}}xdx}$is equal to

A) ${{\sin }^{3}}x+c$

B) $\frac{\sin 3x}{3}+\frac{\sin x}{2}+c$

C) $\frac{\sin 3x}{12}+\frac{3}{4}\sin x+c$

D) $\frac{\sin 3x}{4}+3\sin x+c$

• question_answer247) $\frac{d}{dx}{{(\sin x)}^{\tan x}}$is equal to

A) ${{(\sin x)}^{\tan x}}[1+{{\sec }^{2}}x\log \sin x]$

B) ${{(\sin x)}^{\tan x}}[1-{{\sec }^{2}}x\log \sin x]$

C) ${{(\tan x)}^{\sin x}}[\log {{\sec }^{2}}x\log \sin x]$

D) None of the above

• question_answer248) When two dices are thrown together, then the probability that sum of the digits is seven, is

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

B) $\frac{1}{12}$

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

D) None of these

• question_answer249) A card is drawn from a pack of cards. The probability that this card is diamond or ace, is

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

B) $\frac{17}{52}$

C) $\frac{1}{52}$

D) $\frac{1}{13}$

• question_answer250) The value of the determinant$\left| \begin{matrix} a+ib & c+ib \\ c-id & a-ib \\ \end{matrix} \right|$is

A) $(a+b)(c-d)$

B) $({{a}^{2}}+{{b}^{2}})({{c}^{2}}-{{d}^{2}})$

C) ${{a}^{2}}+{{b}^{2}}-{{c}^{2}}-{{d}^{2}}$

D) ${{a}^{2}}-{{b}^{2}}+{{c}^{2}}-{{d}^{2}}$

• question_answer251) The value of$\left| \begin{matrix} 43 & 1 & 6 \\ 35 & 7 & 4 \\ 17 & 3 & 2 \\ \end{matrix} \right|$is

A) 150

B) 0

C) $-110$

D) $-6$

• question_answer252) If roots of the equation${{x}^{2}}-ax+b=0$are a and$\beta$and${{V}_{n}}={{\alpha }^{n}}+{{\beta }^{n}},$then

A) ${{V}_{n+1}}=\alpha {{V}_{n}}-b{{V}_{n-1}}$

B) ${{V}_{n+1}}=b{{V}_{n}}+a{{V}_{n-1}}$

C) ${{V}_{n+1}}=b{{V}_{n}}-a{{V}_{n-1}}$

D) ${{V}_{n+1}}=b{{V}_{n}}+b{{V}_{n-1}}$

• question_answer253) If arithmetic mean and harmonic mean of two numbers be 27 and 12, then their geometric mean is equal to

A) 36

B) 24

C) 18

D) 9

• question_answer254) Real part of$(\alpha +i\beta )$is

A) $cosh\text{ }\alpha \text{ }cos\text{ }\beta$

B) $cos\text{ }\alpha \text{ }cos\text{ }\beta$

C) $cos\text{ }\alpha \text{ }cosh\text{ }\beta$

D) $sin\text{ }\alpha \text{ }sinh\text{ }\beta$

• question_answer255) If A be a square matrix and$A+{{A}^{T}}$is a symmetric matrix, then$A-{{A}^{T}}$is

A) a unit matrix

B) a symmetric matrix

C) a skew-symmetric matrix

D) a zero matrix

• question_answer256) If$\alpha$and$\beta$be the roots of the equation ${{x}^{2}}-2x+4=0,$then the value of${{\alpha }^{n}}+{{\beta }^{n}}$is

A) ${{2}^{n-1}}\cos \left( \frac{n\pi }{3} \right)$

B) $i{{2}^{n-1}}\sin \left( \frac{n\pi }{3} \right)$

C) ${{2}^{n+1}}\cos \left( \frac{n\pi }{3} \right)$

D) $i{{2}^{n+1}}\sin \left( \frac{n\pi }{3} \right)$

• question_answer257) If the normal to any curve is parallel to$x-$axis, then the true statement is

A) $\frac{dy}{dx}=0$

B) $\frac{dx}{dy}=0$

C) $\frac{dy}{dx}=1$

D) $\frac{dx}{dy}=-1$

• question_answer258) Differential coefficient of${{x}^{3}}$with respect to${{x}^{2}}$

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

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

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

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

• question_answer259) If A and B are two events, then$P\left( \frac{\overline{A}}{B} \right)$is equal to

A) $1-P\left( \frac{A}{B} \right)$

B) $\frac{1-P(AB)}{P(B)}$

C) $\frac{1-P(A+B)}{P(\overline{B})}$

D) $\frac{P(\overline{A})}{P(\overline{B})}$

• question_answer260) $\overrightarrow{a}\times (\overrightarrow{b}\times \overrightarrow{c})$is equal to

A) $(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}+(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}$

B) $(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}-(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}$

C) $(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}$

D) $(\overrightarrow{a}.\overrightarrow{c})\overrightarrow{b}+(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{c}$

• question_answer261) For any two events A and B, which of the following is true?

A) $P(A\cap B)\ge P(A)+P(B)-1$

B) $P(A\cap B)\le P(A)+P(B)-1$

C) $P(A\cap B)\ge P(A)+P(B)$

D) $P(A\cap B)\le P(A)+P(B)$

• question_answer262) $P\left( \frac{\overline{A}}{A\cup B} \right)$is equal to

A) $\frac{P(\overline{B})}{P(A\cup B)}$

B) $\frac{P(\overline{A})}{P(A\cup B)}$

C) $\frac{P(\overline{A}\cap B)}{P(A\cup B)}$

D) $\frac{P(A)}{P(A\cup B)}$

• question_answer263) If the vectors$2\hat{i}+\hat{j}-\hat{k}$and$\hat{i}-4\hat{j}+\lambda \hat{k}$are perpendicular to each other, then$\lambda$is equal to

A) 0

B) $-1$

C) $-2$

D) $-3$

• question_answer264) If$f(a-x)=f(x),$then$\int_{0}^{a}{x}f(x)dx$is equal to

A) $a\int_{0}^{a}{f(x)dx}$

B) $\frac{a}{2}\int_{0}^{a}{f(x)dx}$

C) $\int_{0}^{a}{f(x)dx}$

D) None of these

• question_answer265) If$A=\left[ \begin{matrix} i & 0 \\ 0 & i \\ \end{matrix} \right]$and$B=\left[ \begin{matrix} 0 & -i \\ -i & 0 \\ \end{matrix} \right],$then $(A+B)(A-B)$is equal to

A) 2A

B) 2B

C) $2I$

D) 0

• question_answer266) If${{x}^{y}}={{e}^{x-y}},$then$\frac{dy}{dx}$ is equal to

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

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

C) $\frac{x-y}{1+\log \,\,x}$

D) $\frac{y-x}{x(1+log\,\,x)}$

• question_answer267) If intercept on made by a line on the axes are a and b and its distance from the origin is p, then

A) $\frac{1}{{{p}^{2}}}={{a}^{2}}+{{b}^{2}}$

B) ${{p}^{2}}={{a}^{2}}+{{b}^{2}}$

C) ${{p}^{2}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}$

D) $\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}$

• question_answer268) If the circle${{x}^{2}}+{{y}^{2}}+2ax+8y+16=0$touches the$x-$axis, then a is equal to

A) ?16

B) ? 8

C) ? 1

D) ? 4

• question_answer269) The true statement is

A) $cos{{h}^{2}}x+sin{{h}^{2}}x=1$

B) $cos{{h}^{2}}x-sin{{h}^{2}}x=cos{{h}^{2}}x$

C) $1+tan{{h}^{2}}x=sec{{h}^{2}}x$

D) $cos{{h}^{2}}x-sin{{h}^{2}}x=1$

• question_answer270) If the points (1,2),$(-1,x)$and (2,3) are collinear, then$x$is equal to

A) 1

B) 2

C) 0

D) $-1$

• question_answer271) A hits an aim four times out of 5 trials, B hits three times out of 4 trials and C hits two times out of 3 trials. The probability that only two hits the target is

A) $\frac{5}{12}$

B) $\frac{5}{6}$

C) $\frac{25}{60}$

D) $\frac{26}{60}$

• question_answer272) A card is drawn from a pack of cards. The probability that this card is an ace or a queen is

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

B) $\frac{17}{52}$

C) $\frac{3}{13}$

D) None of these

• question_answer273) The probability of occuring 1 or 6 when a dice is thrown, is

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

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

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

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

• question_answer274) Which one is not true from the following?

A) ${{(A+B)}^{T}}={{A}^{T}}+{{B}^{T}}$

B) ${{({{A}^{T}})}^{T}}=A$

C) ${{(KA)}^{T}}=K{{A}^{T}}$

D) ${{(AB)}^{T}}={{A}^{T}}{{B}^{T}}$

• question_answer275) If${{z}_{1}}$and${{z}_{2}}$are any two complex numbers, then true relation is

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

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

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

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

• question_answer276) The equation of parabola which has the vertex at origin and axis is$x-$axis and also passes through the point (4,3), is

A) $9{{y}^{2}}=4x$

B) $9{{y}^{2}}=-4x$

C) $4{{y}^{2}}=-9x$

D) $4{{y}^{2}}=9x$

• question_answer277) If$3{{y}^{2}}-4{{x}^{2}}=0,$then$\frac{{{d}^{2}}y}{d{{x}^{2}}}$is equal to

A) $\frac{{{y}^{3}}}{2{{y}^{2}}-4{{x}^{2}}}$

B) $\frac{2{{y}^{2}}-4{{x}^{2}}}{{{y}^{3}}}$

C) $\frac{4y-8x}{{{y}^{3}}}$

D) 0

• question_answer278) The equation of that circle which passes through the origin and cut the axes$x$and y of length 6 and 8 on respectively, is

A) ${{x}^{2}}+{{y}^{2}}\pm 6x\pm 8y=0$

B) ${{x}^{2}}+{{y}^{2}}\pm 8x\pm 6y=0$

C) ${{x}^{2}}+{{y}^{2}}\pm 12x\pm 16y=0$

D) ${{x}^{2}}+{{y}^{2}}\pm 16x\pm 12y=0$

• question_answer279) The equation of directrix of the parabola ${{y}^{2}}=-12x$is

A) $x+3=0$

B) $x=3$

C) $y+3=0$

D) $y-3=0$

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

A) $x\tan \frac{x}{2}+2\log \cos \frac{x}{2}+c$

B) $x\tan \frac{x}{2}-\log \cos \frac{x}{2}+c$

C) $2\left\{ x\tan \frac{x}{2}+\log \cos \frac{x}{2} \right\}+c$

D) $x\tan \frac{x}{2}-\log \cos \frac{x}{2}+c$

• question_answer281) If$x=a\text{ }cos\text{ }t,\text{ }y=b\text{ }sin\text{ }t,$then$\frac{dy}{dx}$is equal to

A) $-\frac{b}{a}\tan t$

B) $-\frac{b}{a}\cot t$

C) $-\frac{a}{b}\cot t$

D) $-\frac{a}{b}\tan t$

• question_answer282) If$y=\frac{1}{(t+2)(t+1)},$then$\frac{dy}{dx}$is equal to

A) $-\frac{1}{{{(t+1)}^{2}}}+\frac{1}{{{(t+2)}^{2}}}$

B) $\frac{1}{{{(t+1)}^{2}}}+\frac{1}{{{(t+2)}^{2}}}$

C) $-\frac{1}{{{(t+1)}^{2}}}-\frac{1}{{{(t+2)}^{2}}}$

D) None of the above

• question_answer283) The equation of tangents at that point where the curve$y={{x}^{2}}-3x+2$cut the$x-$axis, is

A) $x+y-1=0,x-y-2=0$

B) $x-y-1=0,\text{ }x-y=0$

C) $x-y+2=0,x-y-1=0$

D) $x+y=0,\text{ }x-y=0$

• question_answer284) $\int_{0}^{a}{\sqrt{\frac{a}{a-x}}}dx$is equal to

A) $4a$

B) $-4a$

C) $2a$

D) $a$

• question_answer285) $\int{\frac{2dx}{{{x}^{2}}-1}}$ is equal to

A) $\frac{1}{2}\log \frac{x-1}{x+1}+c$

B) $\log \frac{x-1}{x+1}+c$

C) $\frac{1}{2}\log \frac{x+1}{x-1}+c$

D) $\log \frac{x+1}{x-1}+c$

• question_answer286) Two cards are drawn one by one from a pack of 52 cards. The probability that these axes, is

A) $\frac{1}{26}$

B) $\frac{1}{221}$

C) $\frac{2}{21}$

D) None of these

• question_answer287) If there are 4 copper coins and 3 silver coins in a purse while 6 copper coins and 2 silver coins in an another purse a coin is taken randomly from any one of the purse, the probability that this is of copper coin is

A) $\frac{4}{7}$

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

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

D) $\frac{37}{56}$

• question_answer288) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\tan x-\sin x}{{{x}^{3}}}$is equal to

A) $-1$

B) $1/2$

C) 2

D) $-2$

• question_answer289) The order of a matrix A is$P\times Q$and that of B is$R\times S,$then for$A-B,$the values of P and Q are

A) $P=Q$

B) $P=Q,R=S$

C) $P=R,\text{ }Q=S$

D) None of these

• question_answer290) If$f(x)=\frac{x}{\sqrt{1+{{x}^{2}}}},$then$fofof(x)$is equal to

A) $\frac{x}{\sqrt{1+3{{x}^{2}}}}$

B) $\frac{x}{\sqrt{1+{{x}^{2}}}}$

C) $\frac{x}{\sqrt{1+2{{x}^{2}}}}$

D) None of these

• question_answer291) Argument of$\left( \frac{1-i\sqrt{3}}{1+i\sqrt{3}} \right)$is

A) $60{}^\circ$

B) $120{}^\circ$

C) $-120{}^\circ$

D) $-135{}^\circ$

• question_answer292) If$^{n-1}{{C}_{3}}{{+}^{n-1}}{{C}_{4}}{{>}^{n}}{{C}_{3}},$then n is equal to

A) 4

B) 6

C) 8

D) 7

• question_answer293) Which one of the following is an even function?

A) $f(x)=\frac{{{a}^{x}}+{{a}^{-x}}}{{{a}^{x}}-{{a}^{-x}}}$

B) $f(x)=\frac{{{a}^{x}}+1}{{{a}^{x}}-1}$

C) $f(x)=x\frac{{{a}^{x}}-1}{{{a}^{x}}+1}$

D) $f(x)={{\log }_{e}}(x+\sqrt{{{x}^{2}}+1})$

• question_answer294) Locus of the centroid of the triangle with vertices$(a\text{ }cos\text{ }t,a\text{ }sin\text{ }t),(b\text{ }sin\text{ }t,-b\text{ }cos\text{ }t)$ and (1,0), where t is a parameter, is

A) ${{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}$

B) ${{(3x-1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}$

C) ${{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}+{{b}^{2}}$

D) ${{(3x+1)}^{2}}+{{(3y)}^{2}}={{a}^{2}}-{{b}^{2}}$

• question_answer295) If sum of squares of the roots of the equation ${{x}^{2}}-(a-2)x-(a+1)=0$is minimum, then the value of a is

A) 0

B) 2

C) $-1$

D) $1$

• question_answer296) If${{A}^{T}}$is the transpose matrix of the matrix A, then $A{{A}^{T}}$is

A) symmetric matrix

B) inverse matrix

C) skew-symmetric matrix

D) None of the above

• question_answer297) If$y=f(x)=\frac{ax+b}{cx-a},$then$x$is equal to

A) $\frac{1}{f(x)}$

B) $\frac{1}{f(y)}$

C) $yf(x)$

D) $f(y)$

• question_answer298) Domain of the function$f(x)=\sqrt{2-2x-{{x}^{2}}}$is

A) $-\sqrt{3}\le x\le \sqrt{3}$

B) $-1-\sqrt{3}\le x\le -1+\sqrt{3}$

C) $-2\le x\le 2$

D) $-2+\sqrt{3}\le x\le -2-\sqrt{3}$

• question_answer299) Equation of tangent to the ellipse ${{x}^{2}}+16{{y}^{2}}=16$which makes an angle of$60{}^\circ$with$x-$axis, is

A) $\sqrt{3}x-y+7=0$

B) $\sqrt{3}x-y-7=0$

C) $\sqrt{3}x-y\pm 7=0$

D) None of these

• question_answer300) Intersection points of the circles${{x}^{2}}+{{y}^{2}}=25$ and ${{x}^{2}}+{{y}^{2}}-8x+7=0,$are

A) (4, 3) and $(4,-3)$

B) $(4,-3)$and$(-4,-3)$

C) $(-4,3)$and (4, 3)

D) (4, 3) and (3, 4)