# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2001

### done Rajasthan PET Solved Paper-2001

• question_answer1) If anybody is rolling on surface, then its total energy will be

A) $\frac{1}{2}m{{v}^{2}}\,+\,\frac{1}{2}I{{\omega }^{2}}$

B) $\frac{1}{2}m{{v}^{2}}\,-\,\frac{G{{m}_{1}}{{m}_{2}}}{R}$

C) $\frac{1}{2}m{{v}^{2}}\,-\,\frac{1}{2}\,m{{R}^{2}}{{\omega }^{2}}$

D) None of these

• question_answer2) A body of mass 5 kg is moving with velocity of 20 m/s. If the force of 200 N acts upon the body for 10 s, then finally the velocity of body will be

A) 150 m/s

B) 220 m/s

C) 200 m/s

D) 240 m/s

• question_answer3) What will be the moment of inertia of a ring about tangential axis in its plane?

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

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

C) $\frac{3}{2}M{{R}^{2}}$

D) None of these

• question_answer4) The escape velocity of an object on a planet whose gravity value is 2 times as on earth and whose radius is 2 times that of earth will be

A) $2{{V}_{e}}$

B) $3{{V}_{e}}$

C) $4{{V}_{e}}$

D) None of these

• question_answer5) Dimensions of universal gravitational constant will be

A) $[M{{L}^{3}}{{T}^{-2}}]$

B) $[M{{L}^{-1}}{{L}^{3}}{{T}^{-2}}]$

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

D) None of these

• question_answer6) If y = 2.4$\eta$the poisson ratio is

A) $-1$

B) 0.2

C) 0.1

D) $-0.25$

• question_answer7) Which of the following quantity are not same?

A) Planck's constant and angular momentum

B) Work and energy

C) Pressure and Young's modulus

D) Torque of force and moment of inertia

• question_answer8) The ratio of traveled distances by freely falling body in first, second and third seconds will be

A) 5 : 3 : 1

B) 1 : 4 : 9

C) 1 : 3 : 5

D) 9 : 4 : 1

• question_answer9) What will be the value of gravitational acceleration at height h from surface of earth? If h>>R, where R is radius of earth and gravitational acceleration at surface of earth is g.

A) $\frac{g}{{{\left( 1\,+\,\frac{h}{R} \right)}^{2}}}$

B) $g\left( 1-\frac{2h}{g} \right)$

C) $\frac{g}{{{\left( 1-\frac{h}{R} \right)}^{2}}}$

D) $g{{\left( 1-\frac{h}{R} \right)}^{{}}}$

• question_answer10) Two trains of length 50 m are crossing each other. If velocities in opposite directions are 10 m/s and 15 m/s, then time taken to cross each other will be

A) 2s

B) 4s

C) 6s

D) 8s

• question_answer11) Two springs of force constants k1 = 500 N/m and ${{k}_{2}}=3000\text{ }N/m$stretched by same force. Therefore ratio of their potential energies will be

A) 2 : 1

B) 1 : 2

C) 4 : 1

D) 1 : 4

• question_answer12) If potential and current are$V=(100\pm 0.5)$volt and$I=(10\pm 0.2)\text{ }A$respectively, then value of resistance will be

A) (10 ? 0.7)$\Omega$

B) (5 ? 2)$\Omega$

C) (0.1 ? 2)$\Omega$

D) None of these

• question_answer13) The range of projectile is four times of its maximum height, then angle of projection will be

A) $60{}^\circ$

B) $45{}^\circ$

C) $30{}^\circ$

D) $75{}^\circ$

• question_answer14) What will be the orbital velocity of planet revolves near earth (where R is radius of earth and g is gravitational acceleration)?

A) $\sqrt{Rg}$

B) $\sqrt{2Rg}$

C) $2\sqrt{Rg}$

D) $\sqrt{3Rg}$

• question_answer15) If bullets of mass m strikes on a wall at the rate of 27 per second, then what will be the force applied on the wall?

A) mnv

B) 4mnv

C) 2mnv

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

• question_answer16) If the length of simple pendulum increases 1%, then change in time period will be

A) 0.5%

B) 1%

C) 2%

D) 0.2%

• question_answer17) Two bodies of mass 1 kg are placed at a distance of 1 m have each other. The force between two bodies will be

A) equal to G

B) equal to gravitation

C) equal to G / 2

D) None of these

• question_answer18) As per given figure to complete the circular loop what should be its radius, if initial height is 5m?

A) 4 m

B) 3 m

C) 2.5 m

D) 2 m

• question_answer19) The particle moves according to given velocity-time graph. The ratio of travelling distance in last 2s and 7s will be

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

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

C) $\frac{1}{8}$

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

• question_answer20) On playing sitar the nature of wave on the reaching the observer will be

A) transverse and progressive

B) longitudinal and progressive

C) transverse and stationary

D) longitudinal and stationary

• question_answer21) The gravitation of earth is 10 m/s. If the mass of earth is 80 times, the mass of moon and radius of earth is 4 times the radius of moon, then the gravitation at moon will be

A) $\text{1 }m/{{s}^{2}}$

B) $2\text{ }m/{{s}^{2}}$

C) $\text{3 }m/{{s}^{2}}$

D) None of these

• question_answer22) The maximum acceleration in SHM will be

A) at amplitude

B) at equilibrium position

C) at any point

D) None of the above

• question_answer23) The value of ${{\varepsilon }_{0}}$ will be

A) $8.85\,\times \,{{10}^{-12}}{{C}^{2}}/N-{{m}^{2}}$

B) $8.85\,\times \,{{10}^{-12}}\,Fermi$

C) $9\,\times \,{{10}^{-13}}\,{{C}^{2}}/N-{{m}^{2}}$

D) $9\,\times \,{{10}^{-13}}\,Fermi$

• question_answer24) Rain water falls horizontally downwards with velocity v. When the velocity of air in horizontal direction is u, then water is store at the rate R m3/s. When the velocity of air becomes 2u, the rate of store of water will be

A) R

B) R/2

C) 2R

D) R$\frac{\sqrt{4{{u}^{2}}\,+\,{{v}^{2}}}}{\sqrt{{{u}^{2}}+{{v}^{2}}}}$

• question_answer25) In Carnot cycle, the temperature of source is 500 K. If engine lakes in 300 cal of heat from a source and gives 150 cal of heat to a sink. The temperature of sink will be

A) 500 K

B) 250 K

C) 750 K

D) 125 K

• question_answer26) The average kinetic energy per molecule of the gas is

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

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

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

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

• question_answer27) If the temperature of gas increases from$27{}^\circ C$to $927{}^\circ C,$the KE will be

A) double

B) half

C) one-fourth

D) four times

• question_answer28) Choose the correct relation. (where p = pressure, E = kinetic energy of gas)

A) $p=\frac{3}{2}E$

B) $p=\frac{2}{3}E$

C) $p=\frac{1}{2}E$

D) $p=\,2E$

• question_answer29) For a perfectly black body, its absorption coefficient will be

A) 1

B) 0

C) between 0 and 1

D) None of these

• question_answer30) The heat given to diatomic gas at constant pressure, the how many quantity will be change in internal energy?

A) 5/7

B) 3/5

C) 2/5

D) None of these

• question_answer31) The relation between velocities of${{O}_{2}}$and${{H}_{2}}$

A) $v{{H}_{2}}=4{{v}_{O2}}$

B) ${{v}_{O2}}=4{{V}_{H2}}$

C) ${{v}_{O2}}=2{{v}_{H2}}$

D) ${{v}_{H2}}=2{{v}_{O2}}$

• question_answer32) The quality of metal of cooking vessel

A) less specific heat and more conduction

B) more specific heat and less conduction

C) more specific heat and more conduction

D) less specific heat and less conduction

• question_answer33) Volume of gas becomes four times if

A) temperature becomes four times at constant pressure

B) temperature becomes one fourth at constant pressure

C) temperature becomes two times at constant pressure

D) temperature becomes half at constant pressure

• question_answer34) A source of frequency 150 Hz is moving in the direction of a person with a velocity of 110 m/s. The frequency heard by the person will be (speed of sound medium = 330 m/s)

A) 225 Hz

B) 250 Hz

C) 495 Hz

D) None of these

• question_answer35) To increase the frequency from 100 Hz to 400 Hz, the tension of string will be

A) 4 times

B) 16 times

C) 20 times

D) None of these

• question_answer36) A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. Finally small ball obtains velocity u and big ball v. Then what is the value of v?

A) $\frac{M-m}{M}u$

B) $\frac{m}{M+m}u$

C) $\frac{2m}{M+m}u$

D) $\frac{M}{M+m}u$

• question_answer37) Twenty seven drops of water of the same size are equally potential V. They are then united to form a bigger drop. By what factor will the electrical potential changes?

A) 9V

B) 3V

C) 27V

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

• question_answer38) The power factor of L-C- R circuit at resonance is

A) zero

B) 1

C) 0.5

D) 0.766

• question_answer39) An alternating current of frequency / is flowing in a circuit containing a resistance R and choke L in series. The impedance of this circuit is

A) $\sqrt{{{R}^{2}}+\,{{(2\pi fL)}^{2}}}$

B) $\sqrt{{{R}^{2}}+\,{{(2\pi {{f}^{2}})}^{2}}}$

C) $\sqrt{{{R}^{2}}+\,L\pi {{f}^{2}}}$

D) ${{R}^{2}}-\,{{(2\pi {{f}^{2}})}^{2}}$

• question_answer40) V rms = 220 V, then the peak value of voltage is

A) 311 V

B) 281 V

C) 200 V

D) 181 V

• question_answer41) The magnetic moment of coil is M and area is A. Then value of current will be

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

B) $\frac{M}{A}$

C) $\frac{A}{M}$

D) $\frac{M}{2A}$

• question_answer42) In the circuit shown below, the current of 2A is flowing, the impedance of circuit will be

A) 170 $\Omega$

B) 70 $\Omega$

C) 130 $\Omega$

D) 120 $\Omega$

• question_answer43) In AC circuit$E={{E}_{0}}sin$at and$I={{I}_{0}}sin$$\left( \omega t-\frac{\pi }{2} \right)$then power dissipated will be

A) zero

B) $\frac{{{E}_{0}}{{I}_{0}}}{2}$

C) ${{E}_{rms}}{{I}_{rms}}$

D) None of these

• question_answer44) If${{C}_{air}}=10$$\mu$F, then effective capacity will be

A) 30$\mu$F

B) 15$\mu$F

C) 3 $\mu$F

D) 10 $\mu$F

• question_answer45) A voltmeter has a resistance of G ohm and range V volt. The value of resistance used in series to convert it into a voltmeter of range nV volt is

A) nG

B) (n-1)G

C) $\frac{G}{n}$

D) $\frac{G}{(n-1)}$

• question_answer46) The magnetic moment of current loop is$2.1\times {{10}^{-25}}$$A-{{m}^{2}}$. The magnetic field at distance 1 $\overset{o}{\mathop{\text{A}}}\,$from centre on axis of loop will be

A) $4.2\times {{10}^{2}}Wb/{{m}^{2}}$

B) $4.2\times {{10}^{-3}}Wb/{{m}^{2}}$

C) $4.2\times {{10}^{-4~}}Wb/{{m}^{2}}$

D) $4.2\times {{10}^{-5}}Wb/{{m}^{2}}$

• question_answer47) The intensity of electric field at a point on the axis of an electric dipole depends on the distance r from the centre of the dipole as

A) $E\propto \frac{1}{{{r}^{2}}}$

B) $E\,\propto \frac{1}{{{r}^{3}}}$

C) $E\propto \,{{r}^{2}}$

D) $E\propto \,\frac{1}{{{r}^{4}}}$

• question_answer48) How many electrons are in 1 coulomb charge

A) $6.25\times {{10}^{18}}$

B) $1.6\times {{10}^{19}}$

C) 100

D) $6.25\times {{10}^{12}}$

• question_answer49) When charge q enters perpendicular in magnetic field B, then frequency will be

A) $\frac{2\pi m}{qB}$

B) $\frac{qB}{2\pi m}$

C) $\frac{qB}{\pi m}$

D) $\frac{\pi m}{qB}$

• question_answer50) The resistance of ammeter is 99ft. The current of ammeter is 10% of main current, then the resistance of shunt will be

A) 11$\Omega$

B) 22$\Omega$

C) 99$\Omega$

D) 33$\Omega$

• question_answer51) $E=2\text{ }V/m$at distance 60 cm from the charge, then charge will be

A) $8\times {{10}^{-11}}C$

B) $8\times {{10}^{11}}C$

C) $4\times {{10}^{11}}C$

D) $4\times {{10}^{-11}}C$

• question_answer52) AB is a wire of uniform resistance. The galvanometer G shows no current when the length AB=20 cm and BC =80 cm. The resistance R is equal to

A) 20$\Omega$

B) 80$\Omega$

C) 10$\Omega$

D) 40$\Omega$

• question_answer53) The potential difference on capacitor of 4.5 $\mu$F

A) 8 V

B) 4 V

C) 2 V

D) 6 V

• question_answer54) If in a transformer, the Lechlanche cell is connected across the primary, then in the secondary coil

A) emf will be induced

B) any emf will not be induced

C) emf will be increase

D) emf will be decrease

• question_answer55) The unit of inductance

A) $\frac{volt\,\times \,\sec ond}{ampere}$

B) $\frac{volt\,\times \,ampere}{\sec ond}$

C) $\frac{volt}{ampere}$

D) $\frac{volt\,\times \,{{(ampere)}^{2}}}{\sec ond}$

• question_answer56) Where does the intensity of electric field become zero in hollow sphere?

A) At external points

B) At outer surface

C) At internal points

D) At inside and outside

• question_answer57) In Young's double slit experiment, the screen is kept at a distance 2m from source. The distance between light wavelength of 6000$\overset{o}{\mathop{\text{A}}}\,$and phase mode source is 4 mm. The band width will be

A) 0.2 m

B) 2 cm

C) 20 cm

D) 0.03 cm

• question_answer58) The mean distance between the atoms of metal is $3\times {{10}^{-10}}m$and interatomic force constant for metal is$3.6\times {{10}^{-9}}N/A,$then Young's modulus of metal is

A) $1.2\times {{10}^{11}}N/{{m}^{2}}$

B) $4.2\times {{10}^{11}}N/{{m}^{2}}$

C) $10.8\times {{10}^{-19}}N/{{m}^{2}}$

D) $2.4\times {{10}^{10}}N/{{m}^{2}}$

• question_answer59) If light polarized by the reflection then the angle between reflected wave and refracted wave will be

A) $\pi$

B) $\pi /2$

C) $2\pi$

D) $\pi /4$

• question_answer60) Condition of diffraction is

A) $\frac{a}{\lambda }=1$

B) $\frac{a}{\lambda }>>1$

C) $\frac{a}{\lambda }<<1$

D) None of these

• question_answer61) If photoelectric effect experiment, the intensity of incident ray increases, then the correct statement is

A) the kinetic energy of emitted electron will be maximum

B) work function will be unchanged

C) stopping potential will be increases

D) the kinetic energy of emitted electron will be become less

• question_answer62) During the ${{\beta }^{-}}$ decay

A) neutron, converts into proton

B) proton converts into neutron

C) neutron-proton ratio increases

D) None of the above

• question_answer63) In depletion layer, there are

A) immobile ions

B) free charge carries

C) charge carrier and immobile ions

D) None of the above

• question_answer64) The relation among the forbidden energy band gap in conductors, semiconductors and insulators is

A) $\Delta E{{g}_{c}}$>$\Delta E{{g}_{s}}$>$\Delta E{{g}_{i}}$

B) $\Delta E{{g}_{i}}$>$\Delta E{{g}_{s}}$>$\Delta E{{g}_{c}}$

C) $\Delta E{{g}_{c}}$>$\Delta E{{g}_{c}}$>$\Delta E{{g}_{s}}$

D) $\Delta E{{g}_{s}}$>$\Delta E{{g}_{c}}$>$\Delta E{{g}_{s}}$

• question_answer65) By increasing the temperature of semi- conductors, its resistance

A) increase

B) decrease

C) remain constant

D) None of these

• question_answer66) The value of current in the circuit

A) zero

B) 1 A

C) 0.1 A

D) 0.2 A

• question_answer67) Good nuclear fuel is

A) ${{U}^{238}}$

B) $P{{u}^{238}}$

C) $T{{h}^{234}}$

D) ${{U}^{235}}$

• question_answer68) The binding energy of K-shell of electron is$-40000$eV. Applied the potential of 60000 V in Coolidge tube, X-rays will be

A) continuous X-ray

B) white X-rays

C) continuous and all characteristics X-rays

D) None of the above

• question_answer69) The typical ionization energy of a donor in silicon is

A) 10.0 eV

B) 1.0 eV

C) 0.1 eV

D) 0.001 Ev

• question_answer70) If the threshold frequency of sodium metal is 6800 A, then work function will be

A) 1.8 eV

B) 2.5 eV

C) 2.1 eV

D) 1.4 eV

• question_answer71) If elements with quantum number n > 4 are not in the nature, the number of possible elements is

A) 60

B) 32

C) 4

D) 64

• question_answer72) If capillary experiment is performed in vacuum, then for a liquid there

A) it will rise

B) will remain same

C) it will fall

D) rise to the top

• question_answer73) The reason of Avalanche breakdown is

A) collision of minority charge carriers

B) increasing of depletion layer

C) decreasing of depletion layer

D) None of the above

• question_answer74) Which of the following relations are correct?

A) $E=\,\frac{hc}{\lambda }$

B) $E=\,\frac{1}{2}m{{u}^{2}}$

C) $P=\,\frac{E}{2v}$

D) $E=\,\frac{1}{2}m{{c}^{2}}$

• question_answer75) Ionic potential for second electron of helium is

A) 13.6 eV

B) 27.2 eV

C) 54.4 eV

D) 100 eV

• question_answer76) Which of the following relations are correct for characteristics X-rays?

A) $\lambda \,\alpha \,\frac{1}{{{Z}^{2}}}$

B) $\lambda \,\alpha \,{{Z}^{2}}$

C) $\lambda \times Z$

D) $1\,\alpha \frac{1}{V}$

• question_answer77) The beam of 1 $\mu$A of proton whose cross-section area is$0.5\text{ }m{{m}^{2}}$and velocity is$3\times {{10}^{4}}m/s,$then charge density of beam

A) $6.6\,\times \,{{10}^{-4}}C/{{m}^{3}}$

B) $6.6\,\times \,{{10}^{-5}}C/{{m}^{3}}$

C) $6.6\,\times \,{{10}^{-6}}C/{{m}^{3}}$

D) None of these

• question_answer78) The correct relation for elastic potential energy is

A) energy density = $\frac{1}{2}$$\times$strain$\times$stress

B) energy density =${{(strain)}^{2}}$$\times$ volume

C) energy density = strain $\times$ volume

D) energy density = ${{(strain)}^{2}}$$\times$ volume

• question_answer79) The ratio of the longest to shortest wavelengths in Brackett series of hydrogen spectrum is

A) $\frac{25}{9}$

B) $\frac{17}{6}$

C) $\frac{9}{5}$

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

• question_answer80) An Indian rubber cord L metre long and area of cross-section A metre2 is suspended vertically. Density of rubber is$D\text{ }kg/{{m}^{2}}$and Young's modulus of rubber is$E\text{ }n/{{m}^{2}}$. If the wire extends by 1 m under its own height; then extension in length / is

A) ${{L}^{2}}Dg/E$

B) ${{L}^{2}}Dg/2E$

C) ${{L}^{2}}Dg/4E$

D) $L$

• question_answer81) The nature of electromagnetic waves is

A) transverse

B) logitudinal

C) Both [a] and [b]

D) None of these

• question_answer82) Radius of a soap bubble is increased from R to 2R, work done is this process in terms of surface tension is

A) $24\pi {{R}^{2}}T$

B) $12T\pi {{r}^{2}}$

C) $6T\pi {{r}^{2}}$

D) $4T\pi {{r}^{2}}$

• question_answer83) Light is incident normally on diffraction grating through which the first order, diffraction is seen$32{}^\circ$. The second order diffraction will be seen at

A) $48{}^\circ$

B) $64{}^\circ$

C) $80{}^\circ$

D) There is no second order diffraction in this case

• question_answer84) If liquid level fall in a capillary, then radius of curvature in capillary tube will

A) increase

B) decrease

C) unchanged

D) None of these

• question_answer85) The relative velocity of two consecutive layer is 8 cm/s. If the perpendicular distance between the layers is 0.1 m, then the velocity gradient will be

A) $50\text{ }{{s}^{-1}}$

B) $\text{60 }{{s}^{-1}}$

C) $\text{75 }{{s}^{-1}}$

D) $\text{80 }{{s}^{-1}}$

• question_answer86) The pressure below in surface area of water in the capillary tube will be

A) equal to atmospheric pressure

B) equal to above pressure

C) less than above pressure

D) more than above pressure

• question_answer87) The ratio of intensities of bright and dark fringes are given by 4:1. The ratio of the amplitudes of the two waves is

A) 1 : 1

B) 3 : 1

C) 1 : 3

D) 1 : 9

• question_answer88) An object is at a temperature of$400{}^\circ C$. At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible

A) $200{}^\circ C$

B) 200 K

C) $800{}^\circ C$

D) 800 K

• question_answer89) tress to strain ratio is equivalent to

A) Modulus of elasticity

B) Poisson's ratio

C) Reynold number

D) Fund number

• question_answer90) In an isothermal reversible expansion, if the volume of 96 g of oxygen at$27{}^\circ C$is increased from 70 litre to 140 litre, then the work done by the gas will be

A) $300\text{ }R\text{ }lo{{g}_{10}}2$

B) $81\text{ }R\text{ }lo{{g}_{e}}2$

C) $900\text{ }R\text{ }lo{{g}_{10}}2$

D) $2.3\times 900\text{ }R\text{ }lo{{g}_{10}}2$

• question_answer91) To get the maximum current from a parallel combination of n identical cells each of internal resistance r in an external resistance R when

A) R>>r

B) R<<r

C) R = r

D) None of these

• question_answer92) A mass M is suspended by two springs of force constants${{k}_{1}}$and${{k}_{2}}$respectively as shown in the diagram. The total elongation (stretch) of the two springs is

A) $\left( \frac{{{k}_{1}}+{{k}_{2}}}{{{k}_{1}}{{k}_{2}}} \right)$

B) $\frac{2({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}mg$

C) $\frac{2({{k}_{1}}+{{k}_{2}})}{{{k}_{1}}{{k}_{2}}}mg$

D) None of the above

• question_answer93) A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is $40\times {{10}^{-8}}m$ and current passing through it is 15 A, cross-section area of the wire is$18\times {{10}^{-6}}{{m}^{2}}$. The potential gradient along the potentiometer wire is

A) 25 V/m

B) 2.5 V/cm

C) 2.5 V/m

D) 0.33 V/m

• question_answer94) Work done in splitting a drop of water of 1 mm radius into ${{10}^{6}}$droplets is (surface tension of water$=72\times {{10}^{-3}}J/{{m}^{2}}$)

A) $89.5\times {{10}^{-5}}J$

B) 0.895 J

C) $895\times {{10}^{-5}}J$

D) None of these

• question_answer95) The size of magnet to generate the radial magnetic field in moving coil galvanometer will be

A) concave

B) horse shoe magnet

C) convex

D) None of these

• question_answer96) Transverse elastic wave can passes

A) in gas and solid

B) in solid but not in gas

C) in gas but not in solid

D) None of the above

• question_answer97) The equivalent resistance between the points A and B is

A) 1$\Omega$

B) 2$\Omega$

C) 3$\Omega$

D) 4$\Omega$

• question_answer98) A potentiometer has uniform potential gradient across it. Two cells connected in series (i) to support each other and (ii) to oppose each other are balanced over 6 m and 2 m respectively on the potentiometer wire. The emf's of the cells are in the ratio of

A) 1 : 2

B) 1 : 1

C) 3 : 1

D) 2 : 1

• question_answer99) A Carnot engine working between 300 K and 600 K has work output of 800 j per cycle. What is amount of heat energy supplied to the engine from source, per cycle?

A) 1800 J

B) 1000 J

C) 2000 J

D) 1600 J

• question_answer100) The ideal gas expands in such a manner that its pressure and volume can be related by equation$p{{V}^{2}}=$constant. During this process, the gas is

A) heated

B) cooled

C) neither heated nor cooled

D) first heated and then cooled

• question_answer101) Structure of${{C}_{2}}{{H}_{2}}$ is

A)  linear

B)  trigonal planar

C)  pyramidal

D)  None of these

• question_answer102) In $CsCl$crystal, if$C{{s}^{+}}$ ion is surrounded from $8C{{l}^{-}}$ions and $C{{l}^{-}}$ion from$C{{s}^{+}}$ ion then coordination number will be

A)  4

B)  6

C)  8

D)  12

A)  energy used in the formation of 1 mole of solid crystal

B)  energy released in the formation of 1 mole of solid crystal

C)  energy released in the formation of 1 g of solid crystal

D)  None of the above

• question_answer104) If the value of ${{K}_{a}}$ for acid is (I) $1.36\times {{10}^{-5}}$ (II) $125\times {{10}^{-5}}$ (III) $260\times {{10}^{-5}}$ (IV) $67\times {{10}^{-5}}$ then the strongest acid will be

A)  I

B)  II

C)  III

D)  IV

• question_answer105) A solution obtained on mixing 0.1 N, 50 mL $HCl$and 0.1 N, 50 mL$NaOH$. The value of pH of the solution will be

A)  4

B)  6

C)  8

D)  7

• question_answer106) The oxidation number of Cr in${{K}_{2}}C{{r}_{2}}{{O}_{7}}$is

A)  6

B)  4

C)  7

D)  3

• question_answer107) Correct order of bond length is

A)  $HC\equiv CH>{{H}_{2}}C=C{{H}_{2}}>{{H}_{3}}C-C{{H}_{3}}$

B)  ${{H}_{2}}C=C{{H}_{2}}>HC\equiv CH>{{H}_{3}}C-C{{H}_{3}}$

C)  $C{{H}_{3}}-C{{H}_{3}}>C{{H}_{2}}=C{{H}_{2}}>HC\equiv CH$

D)  $C{{H}_{3}}-C{{H}_{3}}>HC\equiv CH>{{H}_{2}}C=C{{H}_{2}}$

• question_answer108) $A+BC+D$ If the concentration of A is doubled then the rate of reaction will

A)  remain unchanged

B)  become four times

C)  become two times

D)  become quarter

• question_answer109) For endothermic reaction, on increasing temperature the value of${{K}_{eq}}$will

A)  increase

B)  decrease

C)  approximately remain unchanged

D)  None of the above

• question_answer110) The type of hybridization in$C{{H}_{2}}=C=C{{H}_{2}}$is

A)  only $s{{p}^{2}}$

B)  only$sp$

C) $sp$and$s{{p}^{2}}$

D)  $s{{p}^{2}}$and$s{{p}^{3}}$

• question_answer111) Which of the following has the maximum electronegativity?

A)  F

B)  $Cl$

C)  N

D)  $O$

• question_answer112) Which of the following effect will observe, on passing light from colloidal solution?

A)  Electrophoresis

B)  Tyndall effect

C)  Electro osmosis

D)  Coagulation

• question_answer113) The order of the following reaction is three, $6KI+2FeC{{l}_{3}}\xrightarrow[{}]{{}}2FeI+6KCl+2{{I}_{2}}$ What will be the molecularity of this reaction?

A)  3

B)  8

C) $-1$

D)  2

• question_answer114) Which of the following indicator will be used in the following reaction? $KMn{{O}_{4}}+F{{e}^{2+}}\xrightarrow[{}]{{}}$Product

A)  Methyl red

B)  Phenolphthalein

C)  Phenol red

D)  Self indicator

• question_answer115) At constant temperature, the relationship between osmotic pressure and volume will be

A)  $p\propto V$

B)  $p\propto \frac{1}{V}$

C)  $p\propto \sqrt{V}$

D)  $p$

• question_answer116) The pH of a solution is 4.0. On adding phenolphthalein in this solution, the colour of solution will be

A)  pink

B)  yellow

C)  red

D)  colourless

• question_answer117) The nature of${{H}_{2}}{{O}_{2}}$ is

A)  weak basic

B)  weak acidic

C)  strong acidic

D)  strong basic

• question_answer118) The product will be obtained in the following reaction ${{K}_{4}}[Fe{{(CN)}_{6}}]+{{O}_{3}}\xrightarrow[{}]{{{H}_{2}}O}$Product

A)  $F{{e}^{2+}}$ion

B)  ${{K}_{3}}[Fe{{(CN)}_{6}}]$

C)  $C{{N}^{-}}$ion

D)  None of these

• question_answer119) According to Pauli exclusion principle, any two electrons in an atom cannot have identical set of ....... quantum number.

A)  1

B)  2

C)  3

D)  4

• question_answer120) Magnetic moment of$C{{u}^{+}}$ion is

A)  1.73

B)  0

C)  2.83

D)  3.95

• question_answer121) Which of the following has$1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},$ $3{{s}^{2}}3{{p}^{6}},3{{d}^{10}}4{{s}^{2}}$electronic configuration?

A)  Zn

B)  $Cu$

C)  $Co$

D)  $Ni$

• question_answer122) Which of the following has zero bond order?

A)  $He_{2}^{+}$

B)  $H{{e}_{2}}$

C)  $H_{2}^{+}$

D)  $H_{2}^{-}$

• question_answer123) An element has the following characters (1) atomic number : 31 (2) with$HN{{O}_{2}}:$no reaction (3) reaction with${{O}_{2}}:$no reaction (4) on heating form a layer of oxide (5) used in transistor then the element will be

A)  Ga

B) $In$

C)  Br

D) $Mg$

• question_answer124) Element$Ca,Sr,Ba$show colours in Bunsen's burner flame due to

A)  low ionization potential value

B)  emission and absorption of energy by electron

C)  high ionization potential value

D)  transfer of energy

• question_answer125) Decreasing order of radius of hydrated ions of $Li,Na,K,Rb$and Cs is

A)  $Li>Na>K>Rb>Cs$

B)  $Cs>Rb>K>Na>Li$

C)  $Cs>Rb>K>Li>Na$

D)  $Cs>K>Rb>Na>Li$

• question_answer126) If the frequency of sodium ion is$5.09\times {{10}^{14}}{{s}^{-1}}$then wavelength will be

A)  5.89nm

B)  589 nm

C)  58.9 nm

D)  5890 nm

• question_answer127) Electron deficient compound is

A)  $PC{{l}_{3}}$

B)  $BC{{l}_{3}}$

C)  $ICl$

D) $PC{{l}_{5}}$

• question_answer128) In the following reaction, $N{{H}_{3}}+B{{F}_{3}}\xrightarrow[{}]{{}}N{{H}_{3}}\to B{{F}_{3}}$ which behaves like Lewis base?

A)  $N{{H}_{3}}$

B)  $B{{F}_{3}}$

C)  $N{{H}_{3}}\to B{{F}_{3}}$

D)  None of these

• question_answer129) For${{H}_{2}}O$and${{D}_{2}}O,$the correct statement is

A)  Both have same boiling point

B)  Surface tension of${{D}_{2}}O$is less than${{H}_{2}}O$

C)  Viscosity of${{H}_{2}}O$is greater than ${{D}_{2}}O$

D)  Solubility of${{D}_{2}}O$is more in ionic compound

• question_answer130) When$BaS$reacts with${{D}_{2}}O$ then products obtained

A)  $BaO+{{D}_{2}}S$

B)  $Ba{{(OD)}_{2}}+{{D}_{2}}S$

C)  $BaS{{O}_{4}}.{{D}_{2}}O+S$

D)  $Ba{{O}_{2}}+{{D}_{2}}O$

• question_answer131) In the reaction,$4LiH+AlC{{l}_{3}}\xrightarrow[{}]{Ether}$Product. The product is

A)  $LiCl$

B)  $L{{i}_{2}}O$

C)  $LiAl{{H}_{4}}$

D)  $Al{{H}_{3}}$

• question_answer132) If mass of$C{{O}_{2}}$molecule is 44u and Avogadro's number is$6.023\times {{10}^{23}}$then mass of one molecule in kg is

A)  $16\times {{10}^{-28}}kg$

B)  $2.16\times {{10}^{-22}}kg$

C)  $3.46\times {{10}^{-28}}kg$

D)  $7.3\times {{10}^{-26}}kg$

• question_answer133) Molecular weight of a compound is 96.5 and has the following characters. (1) poisonous (2) isodiapher (3) finds in cis and trans form (4) hypnotic then the compound is

A)  ${{C}_{2}}HC{{l}_{3}}$

B)  ${{C}_{2}}{{H}_{2}}C{{l}_{2}}$

C)  ${{C}_{2}}{{H}_{3}}Cl$

D)  ${{C}_{2}}C{{l}_{4}}$

• question_answer134) Presence of three unpaired electrons in p-orbital of phosphorus can be explained by

A)  Aufbau rule

B)  Hund's rule

C)  Faults rule

D) $(n+7)$rule

• question_answer135) Colloidal solution is not formed by

A)  precipitation

B)  peptisation

C)  double decomposition

D)  mechanical decomposition

• question_answer136) Formula of bauxite is

A)  $A{{l}_{2}}{{O}_{3}}.2{{H}_{2}}O$

B)  $A{{l}_{2}}{{O}_{3}}.{{H}_{2}}O$

C)  $A{{l}_{2}}{{O}_{3}}$

D)  $A{{l}_{2}}{{O}_{3}}.3{{H}_{2}}O$

• question_answer137) Decrease in oxidation number is called

A)  oxidation

B)  reduction

C)  redox reaction

D)  None of these

• question_answer138) For a buffer solution of$C{{H}_{3}}COOH$and $C{{H}_{3}}COONa$if$[C{{H}_{3}}COOH],[C{{H}_{3}}COONa]=1$ and$p{{K}_{a}}=4.74$the pH value of the solution will be

A)  5.74

B)  6.74

C)  3.74

D)  4.74

• question_answer139) If$pH=8$solution is basic, then the nature of this solution will be corresponding to that solution whose$pH=12$

A)  less basic

B)  more basic

C)  equal

D)  None of these

A) $C{{H}_{4}}$ (84%) + propane + butane + higher alkane

B) $C{{H}_{4}}$(33%) + ethane (33%) + butane (33%)

C)  benzene (10%) + petrol (90%)

D) $C{{H}_{4}}$ (10%) + LPG (90%)

• question_answer141) Which of the following compound is strongly polar and has high dipole moment?

A)  $CHC{{l}_{3}}$

B)  $C{{H}_{2}}C{{l}_{2}}$

C)  $CC{{l}_{4}}$

D)  $C{{O}_{2}}$

• question_answer142) If the hybridization in${{C}_{2}}{{H}_{2}}$is sp, then what will be the bond angle?

A)  $180{}^\circ$

B)  $120{}^\circ$

C)  $150{}^\circ$

D)  $90{}^\circ$

• question_answer143) Isoelectronic for${{K}^{+}}$ is

A)  $Ar$

B)  $Cl$

C)  S

D)  $Ca$

• question_answer144) When ${{H}_{2}}$reacts with$C{{l}_{2}}$ in presence of sunlight to form $HCl$then order of reaction will be (unit of$K=mol\,{{L}^{-1}}{{S}^{-1}}$)

A)  2

B)  3

C)  0

D)  4

• question_answer145) Correct order of ionization potential is

A)  $B>Be$

B)  $Be>B$

C)  $Be=B$

D)  None of these

• question_answer146) According to the reaction, $Cu+N{{H}_{3}}\xrightarrow[{}]{Air}$ Product;, The product is

A)  $C{{u}^{2+}}$

B)  $C{{u}^{2+}}.NO$

C)  $[Cu{{(N{{H}_{3}})}_{4}}]{{(OH)}_{2}}$

D)  $Cu{{(OH)}_{2}}$

• question_answer147) Main ore of an iron is

A)  $F{{e}_{3}}{{O}_{4}}$

B)  $FeC{{O}_{3}}$

C)  $F{{e}_{2}}{{O}_{3}}$

D)  $Fe{{S}_{2}}$

A) $Ca$and Ba

B)  Be and Mg

C)  $Na$and K

D)  Li and Be

• question_answer149) Number of crand n bonds in$A-N=N-B$

A)  $3\sigma ,1\pi$

B)  $2\sigma ,0\pi$

C)  $2\sigma ,2\pi$

D)  $4\sigma ,0\pi$

• question_answer150) Which of the following compound has zero dipole moment?

A)  $C{{O}_{2}}$

B)  $S{{O}_{2}}$

C)  $N{{H}_{3}}$

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

• question_answer151) If the value of velocity indices are 2 a, 3b and 1c then the value of Miller's indices will be

A)  3, 2, 6

B)  2, 3, 1

C)  1, 2, 3

D)  1, 1, 1

• question_answer152) Radius of$_{6}{{C}^{12}}$nucleus will be

A)  $3.2\times {{10}^{-13}}cm$

B)  $1.6\times {{10}^{-13}}cm$

C)  $4.8\times {{10}^{-13}}cm$

D)  $6.4\times {{10}^{-3}}cm$

• question_answer153) Electron affinity of nitrogen is

A)  0.2

B)  0.002

C)  0.6

D)  2

• question_answer154) If the dissociation constant of two acids are $2.7\times {{10}^{-4}}$and$3\times {{10}^{-5}}$then the ratio of their relative strength will be

A)  $9:1$

B)  $3:1$

C)  $3:2$

D)  $9:2$

• question_answer155) Colour of$ZnS{{O}_{4}}$is white. It is due to

A)  completely filled${{d}^{10}}$orbitals

B)  magnetic moment$\mu =0$

C)  coupling of spin and transfer of electron

D)  pseudo inert configuration

• question_answer156) Solution of$C{{H}_{3}}COON{{H}_{4}}$is

A)  amphoteric

B)  neutral

C)  basic

D)  acidic

• question_answer157) At 373K value of${{K}_{sp}}$of$AgCl$is$1.44\times {{10}^{-4}},$ then the solubility will be

A)  $1.2\times {{10}^{-2}}$

B)  $1.2\times {{10}^{-4}}$

C)  $72\times {{10}^{-2}}$

D)  $72\times {{10}^{-4}}$

• question_answer158) Alcohol does not completely neutralize with which of the following?

A)  Vitamin

B)  Amyi alcohol

C)  Castrol oil

D)  Aniline

• question_answer159) On heating$N{{H}_{3}}$with ethyl acetate, then the product obtained will be will obtain

A)  ethyl amine

B)  ethanamide

C)  ammonium acetate

D)  acetic acid

• question_answer160) For the polymerization of ethylene, the suitable condition is

A)  only high temperature

B)  only catalyst

C)  only high pressure

D)  high temperature and high pressure

A)  ${{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$

B)  ${{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-{{C}_{6}}{{H}_{5}}$

C)  ${{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{(C{{H}_{3}})}_{3}}$

D)  ${{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-H$

• question_answer162) In the presence of KOH, phenol reacts with${{K}_{2}}{{S}_{2}}{{O}_{8}}$to form the product

A)  benzene

B)  1, 4-dihydroxy benzene

C)  benzoic acid

D)  4-hydroxy benzoic acid

A)  in the formation of medicine

B)  in the formation of solid fuel

C)  in the formation of insecticide

D)  it is not possible

• question_answer164) On the reaction of acetone and phenyl hydrazine the product will form

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

B)  $C{{H}_{3}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,=N-\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{N}}\,-{{C}_{6}}{{H}_{5}}$

C)  $C{{H}_{3}}-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,=N-N{{H}_{2}}$

D)  None of the above

• question_answer165) On the reaction of butyric acid with${{H}_{2}}{{O}_{2}},$the product will form

A)  $C{{H}_{3}}C{{H}_{2}}CHO$

B)  $\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{2}}-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-OH$

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

D)  $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-OH$

• question_answer166) Acid in which$COOH$group is not present is

A)  aspirin

B)  anthranilic acid

C)  picric acid

D)  amino acid

• question_answer167) Sodium lauryl sulphate is

A)  cationic detergent

B)  anionic detergent

C)  foam active

D)  neutral detergent

• question_answer168) $2{{C}_{6}}{{H}_{5}}N{{H}_{2}}+C{{S}_{2}}+2KOH\xrightarrow[{}]{{}}$ Main product, the main product will be

A)  ${{C}_{6}}{{H}_{5}}-N=C=S$

B)

C)  ${{C}_{6}}{{H}_{5}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-N{{H}_{2}}$

D)  None of these

• question_answer169) In the reaction, $6C{{H}_{2}}=C{{H}_{2}}+{{B}_{2}}{{H}_{6}}\xrightarrow[{}]{{}}2\left( H-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{C}}}\,-\underset{\begin{smallmatrix} | \\ H \end{smallmatrix}}{\overset{\begin{smallmatrix} H \\ | \end{smallmatrix}}{\mathop{C}}}\, \right)-B$ the carb-boron product known as alkyl borane, on oxidation gives alcohols. This was made by which scientist?

A)  Brown and Benzamine

B)  Jvifail

C)  Methason

D)  Suberao

• question_answer170) In the presence of sunlight, when hot toluene reacts with excess of$C{{l}_{2}},$the product will be

A)  chloro benzene

B)  benzal chloride

C)  benzyl chloride

D)  benzo trichloride

• question_answer171) Monomer of natural rubber is

A)  $C{{H}_{2}}=C=C{{H}_{2}}$

B)  $C{{H}_{2}}=CH-Cl$

C)  $C{{H}_{2}}=\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,-CH=C{{H}_{2}}$

D)  None of the above

• question_answer172) Monomers of nylon-6 6 are

A)  isoprene + chloroprene

B)  adipic acid + ethylene glycol

C)  adipic acid + hexamethylene diamine

D)  None of the above

• question_answer173) Nylon-6 is formed from caprolactum. Formula of caprolactum is

A)

B)

C)

D) $COOH{{(C{{H}_{2}})}_{6}}COOH$

• question_answer174) In the esterification of alcohol, the order of reactivity is

A)  $2{}^\circ >3{}^\circ >1{}^\circ$

B)  $3{}^\circ >2{}^\circ >1{}^\circ$

C)  $1{}^\circ >2{}^\circ >3{}^\circ$

D)  $1{}^\circ >2{}^\circ >3{}^\circ$

A)  it is a conjugated diene

B)  its dipole moment is more

C)  Both are functional and position isomers

D)  None of the above

• question_answer176) On complete oxidation ether gives

A)  ${{C}_{2}}H.pH$

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

C)  $C{{O}_{2}}+{{H}_{2}}O$

D)  $C{{H}_{3}}COOH$

• question_answer177) In the electrolysis of sodium acetate,${{H}_{2}}$gas releases at cathode and${{C}_{2}}{{H}_{6}}$gas at anode. This reaction is known as

A)  Frenkland

B)  Kolbe

C)  Clemmensen

D)  Wolff-Kishner

• question_answer178) Reactivity order of HX with alcohol is

A)  $HCl>HBr>HI>HF$

B)  $HF>HCl>HBr>HI$

C)  $HI>HCl>HBr>HF$

D)  $HI>HBr>HCl>HF$

• question_answer179) Anhydrous formic acid cannot be obtained from fractional distillation of aqueous HCOOH because

A)  it forms complex with water

B)  its boiling point is 373.4 K

C)  it is soluble in water

D)  None of the above

A)  it reduces heat

B)  it reduces coolness

C)  it reduces pressure

D)  it reduces knocking property

• question_answer181) Which of the following shows optical isomerism?

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

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

C)  $H-\underset{\begin{smallmatrix} | \\ Cl \end{smallmatrix}}{\overset{\begin{smallmatrix} Br \\ | \end{smallmatrix}}{\mathop{C}}}\,-H$

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

• question_answer182) Which of the following reagent used in the formation of ethane amine from propanamide?

A)  $B{{r}_{2}}+KOH$

B)  $Na+{{C}_{2}}{{H}_{5}}OH$

C)  $LiAl{{H}_{4}}$

D)  $AlC{{l}_{3}}$

• question_answer183) In the reaction. $HCOOH+C{{H}_{3}}COOH\xrightarrow[\Delta ]{MnO}X;$ Product X is

A)  $HCHO$

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

C)  $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-O-{{C}_{2}}{{H}_{5}}$

D)  $H-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-O-{{C}_{2}}{{H}_{5}}$

• question_answer184) ${{C}_{6}}{{H}_{5}}OH$and${{C}_{6}}{{H}_{5}}COOH$can be distinguished by

A)  $FeC{{l}_{3}}$

B)  Na metal

C)  $NaOH$

D)  litmus

• question_answer185) For increase in strong basic nature of aniline, which group should attach on para position?

A)  $-OC{{H}_{3}}$

B)  $-C{{H}_{3}}$

C)  $-N{{O}_{2}}$

D)  $-Cl$

• question_answer186) Which of the following alkene gives acetone on ozonolysis?

A)  2-methyl propene

B)  2-methyl-l-butene

C)  2-butene

D)  Ethene

• question_answer187) Which of the following cannot be obtained by$CHC{{l}_{3}}$?

A)  Freon

B)  Chloropicrin

C)  Chloretone

D)  Salicyldehyde

• question_answer188) Which of the following doesn't show Friedel-Craft reaction?

A)  Nitrobenzene

B)  Toluene

C)  Benzene

D)  All of these

• question_answer189) Increasing reactivity order of nucleophilic addition reaction of $H-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-H;C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-H$ and$C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}$will be

A)  $HCHO>C{{H}_{3}}CHO>C{{H}_{3}}COC{{H}_{3}}$

B)  $C{{H}_{3}}CHO>HCHO>C{{H}_{3}}COC{{H}_{3}}$

C)  $C{{H}_{3}}COC{{H}_{3}}>C{{H}_{3}}CHO>HCHO$

D)  $C{{H}_{3}}CHO>C{{H}_{3}}COC{{H}_{3}}>HCHO$

• question_answer190) Purity of organic compound is determined by

A)  molecular weight

B)  boiling point

C)  density

D)  solubility in water

• question_answer191) Which of the following reaction is not stereospecific?

A)  Electrophilic substitution

B)  ${{S}_{N}}1$

C)  ${{S}_{N}}2$

D)  Addition of$B{{r}_{2}}$on ethylene

• question_answer192) The product will be obtained from the reaction of${{C}_{2}}{{H}_{2}}$with$AsC{{l}_{3}}$in the presence of$(AlC{{l}_{3}}+HCl)$

A)  Lewisite

B)  Electrophile

C)  Insecticide

D)  Nucleophite

• question_answer193) $R-C\equiv N\xrightarrow[{}]{Sn+HCl}X\xrightarrow[{}]{{{H}_{2}}O}Y$reaction is known as

A)  Rosenmund's reaction

B)  Stephen's reaction

C)  Clemmensen reduction

D)  Cannizaro reaction

• question_answer194) $C{{H}_{3}}-Mg-X+H-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-H\xrightarrow[{}]{{}}X\xrightarrow[{}]{{{H}_{2}}O}Y$ Product is

A)  ${{C}_{2}}{{H}_{5}}OH$

B)  $C{{H}_{3}}CHO$

C)  $C{{H}_{3}}COOH$

D)  $C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-O-{{C}_{2}}{{H}_{5}}$

• question_answer195) $2C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-H\xrightarrow[{}]{Dil.base}X\xrightarrow[{}]{\Delta }Y$ Product ?Y? is

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

B)  $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-H$

C)  $C{{H}_{3}}-CH=CH-COOH$

D)  $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{2}}-COOH$

• question_answer196) $2Cr{{(OH)}_{3}}+4O{{H}^{-}}+KI{{O}_{3}}\to 2CrO_{4}^{2-}$$+5{{H}_{2}}O+KI$ Equivalent weight of$KI{{O}_{3}}$in the above reaction is

A)  molecular weight

B)  $\frac{molecular\text{ }weight}{3}$

C)  $\frac{molecular\text{ }weight}{6}$

D)  $\frac{molecular\text{ }weight}{2}$

• question_answer197) Which metal is present in chlorophyll?

A)  Cr

B)  Co

C)  Mg

D)  Fe

• question_answer198) Which gas is used for the cutting and welding of metal?

A)  Acetylene

B)  Methane

C)  Carbon dioxide

D)  Neon

• question_answer199) Which of the following will give silver mirror test?

A)  Glucose

B)  Fructose

C)  Starch

D)  Sucrose

• question_answer200) Conjugated acid of$NH_{2}^{-}$is

A)  $NH_{4}^{+}$

B)  $N{{H}_{4}}OH$

C)  $N{{H}_{3}}$

D)  ${{N}_{2}}{{O}_{4}}$

• question_answer201) $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{e}^{\tan x}}-{{e}^{x}}}{\tan x-x}$is equal to

A) 0

B) 1

C) $e$

D) $1/e$

• question_answer202) $\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{\frac{1-\cos 2x}{2}}}{x}$is equal to

A) 1

B) $-1$

C) 0

D) None of these

• question_answer203) $\underset{x\to 0}{\mathop{\lim }}\,\frac{x}{{{\tan }^{-1}}2x}$is equal to

A) 2

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

C) 0

D) None of these

• question_answer204) If$y=a{{x}^{n+1}}+b{{x}^{-n}},$then$\frac{{{x}^{2}}{{d}^{2}}y}{d{{x}^{2}}}$is equal to

A) $ny$

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

C) $n(n-1)y$

D) $n(n+1)y$

• question_answer205) $\frac{d}{dx}\left[ \log \left\{ {{e}^{x}}{{\left( \frac{x-2}{x+2} \right)}^{3/4}} \right\} \right]$is equal to

A) 1

B) $\frac{{{x}^{2}}+1}{{{x}^{2}}-4}$

C) $\frac{{{x}^{2}}-1}{{{x}^{2}}-4}$

D) $\frac{{{x}^{2}}-1}{{{x}^{2}}-4}{{e}^{x}}$

• question_answer206) $\int{\frac{1+{{\tan }^{2}}x}{1-{{\tan }^{2}}x}}dx$is equal to

A) $\log \left( \frac{1-\tan x}{1+\tan x} \right)+c$

B) $\log \left( \frac{1+\tan x}{1-\tan x} \right)+c$

C) $\frac{1}{2}\log \left( \frac{1-\tan x}{1+\tan x} \right)+c$

D) $\frac{1}{2}\log \left( \frac{1+\tan x}{1-\tan x} \right)+c$

• question_answer207) If${{a}^{2}}{{x}^{4}}+{{b}^{2}}{{y}^{4}}={{c}^{6}},$then maximum value of$xy$ is

A) $\frac{{{c}^{3}}}{2ab}$

B) $\frac{{{c}^{3}}}{\sqrt{2ab}}$

C) $\frac{{{c}^{3}}}{ab}$

D) $\frac{{{c}^{3}}}{\sqrt{ab}}$

• question_answer208) Maximum value of$px+qy,$when$xy={{r}^{2}},$is

A) $2r\sqrt{pq}$

B) $2pq\sqrt{r}$

C) $-2r\sqrt{pq}$

D) None of these

• question_answer209) If$f(x)={{x}^{2}}+1,$ then the value of${{f}^{-1}}(17)$and${{f}^{-1}}(-3)$are respectively

A) 4, 1

B) 4, 0

C) 3, 2

D) None of these

• question_answer210) If$a=\cos \alpha +i\sin \alpha ,$$b=\cos \beta +i\sin \beta ,$$c=\cos \gamma +i\sin \gamma$and$\frac{b}{c}+\frac{c}{a}+\frac{a}{b}=1$then $\cos (\beta -\gamma )+\cos (\gamma -\alpha )+\cos (\alpha -\beta )$is equal to

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

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

C) $0$

D) 1

• question_answer211) ${{\left[ \frac{1+\cos \frac{\pi }{8}+i\sin \frac{\pi }{8}}{1+\cos \frac{\pi }{8}-i\sin \frac{\pi }{8}} \right]}^{8}}$is equal to

A) 0

B) 1

C) $-1$

D) 2

• question_answer212) ${{i}^{n}}+{{i}^{n+1}}+{{i}^{n+2}}+{{i}^{n+3}},(n\in N)$is equal to

A) 4

B) 1

C) 0

D) 2

• question_answer213) If$2(y-a)$is the harmonic mean of$y-x$and $y-z,$then$x-a,\text{ }y-a,\text{ }z-a$are in

A) AP

B) GP

C) HP

D) None of these

• question_answer214) If${{a}^{x}}={{b}^{y}}={{c}^{z}}={{d}^{u}}$and a, b, c, d are in GP, then$x,\text{ }y,\text{ }z$are in

A) AP

B) GP

C) HP

D) None of these

• question_answer215) $lo{{g}_{3}}2,\text{ }lo{{g}_{6}}2,\text{ }lo{{g}_{12}}2$are in

A) AP

B) GP

C) HP

D) None of these

• question_answer216) Angle between the planes$2x-y+z=6$and $x+y+2z=3$is

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

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

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

D) 0

• question_answer217) $\int_{0}^{\pi /2}{\frac{\sqrt[3]{{{\sin }^{2}}x}dx}{\sqrt[3]{{{\sin }^{2}}x}\sqrt[3]{{{\cos }^{2}}x}}}$is equal to

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

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

C) $\pi$

D) $2\pi$

• question_answer218) $\int_{-1}^{1}{|1-x|}\,dx$is equal to

A) 0

B) $-2$

C) 4

D) 2

• question_answer219) $\int_{0}^{1}{\frac{{{\tan }^{-1}}xdx}{1+{{x}^{2}}}}$is equal to

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

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

C) $\frac{{{\pi }^{2}}}{16}$

D) $\frac{{{\pi }^{2}}}{32}$

• question_answer220) Area of the region bounded by the curve $y=x,\text{ }x-$axis and abscissas$x=-1$and$x=2$is

A) 0 sq unit

B) 3/2 sq unit

C) 5/2 sq units

D) - 5/2 sq unit

• question_answer221) The value of $\underset{x\to 1}{\mathop{\lim }}\,(1-x)\tan \frac{\pi x}{2}$is equal to

A) $1$

B) $\infty$

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

D) 0

• question_answer222) If$z=i\log (2-\sqrt{3}),$then$cos\text{ }z$is equal to

A) 0

B) 2

C) 4

D) $-2$

• question_answer223) Tangent and normal at any point P of the parabola meet the axes at T and G respectively, then

A) $ST=SG.SP$

B) $ST\ne SG=SP$

C) $ST=SG\ne SP$

D) $ST=SG=SP$

• question_answer224) Domain of the function$f(x)=\log (\sqrt{x-4}+$$\sqrt{6-x})$is

A) $[4,\infty ]$

B) $(-\infty ,6)$

C) [4, 6]

D) None of these

• question_answer225) Inverse of the function$\frac{{{10}^{x}}-{{10}^{-x}}}{{{10}^{x}}+{{10}^{-x}}}$is

A) ${{\log }_{10}}(2-x)$

B) $\frac{1}{2}{{\log }_{10}}\left( \frac{1+x}{1-x} \right)$

C) $\frac{1}{2}{{\log }_{10}}(2x-1)$

D) $\frac{1}{4}{{\log }_{10}}\left( \frac{2x}{2-x} \right)$

• question_answer226) Domain of the function $f(x)={{\log }_{3+x}}({{x}^{2}}-1)$is

A) $(-3,-1)\cup (1,\infty )$

B) $(-3,-1)\cup [1,\infty )$

C) $(-3,-2)\cup (-2,-1)\cup (1,\infty )$

D) $[-3,-2)\cup (-2,-1)\cup [1,\infty )$

• question_answer227) If$n=3k$and$1,\omega ,{{\omega }^{2}}$are the cube roots of unity, then the value of the determinant $\left| \begin{matrix} 1 & {{\omega }^{n}} & {{\omega }^{2n}} \\ {{\omega }^{2n}} & 1 & {{\omega }^{n}} \\ {{\omega }^{n}} & {{\omega }^{2n}} & 1 \\ \end{matrix} \right|$is

A) 0

B) $\omega$

C) ${{\omega }^{2}}$

D) 1

• question_answer228) One root of the equation $\left| \begin{matrix} 3-x & -6 & 3 \\ -6 & 3-x & 3 \\ 3 & 3 & -6-x \\ \end{matrix} \right|=0$is

A) 6

B) 3

C) 0

D) None of these

• question_answer229) Three coins are tossed together, then the probability of getting atleast one tail is

A) $\frac{1}{8}$

B) $\frac{7}{8}$

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

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

• question_answer230) A card is drawn randomly from a pack of 52 cards, then the probability that the card is king or spade is

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

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

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

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

• question_answer231) Angle between those two lines, in which direction comes are represented by $l+m+n=0$and${{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0$is

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

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

C) $\frac{5\pi }{6}$

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

• question_answer232) If $P(A)=0.25,P(B)=0.50$and $P(B/A)=0.6,$then the value of P(A/B) is

A) 0.3

B) 0.35

C) 0.15

D) 0.5

• question_answer233) If $f(x)=|x{{|}^{3}},$then$f'(0)$is equal to

A) 0

B) 1

C) $f'(1)$

D) $f'\,'(1)$

• question_answer234) ${{\cosh }^{-1}}x$is equal to

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

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

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

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

• question_answer235) There are 16 points in a plane, out of which 6 points are collinear. Then, how many straight lines can be drawn using these lines.

A) 106

B) 105

C) 60

D) 55

• question_answer236) ${{(1+i)}^{8}}+{{(1-i)}^{8}}$is equal to

A) 16

B) $-16$

C) 32

D) $-32$

• question_answer237) $\int{\frac{{{e}^{m{{\tan }^{-1}}x}}}{1+{{x}^{2}}}}dx$is equal to

A) ${{e}^{m+{{\tan }^{-1}}x}}$

B) ${{e}^{{{\tan }^{-1}}x}}$

C) $\frac{1}{m}{{\tan }^{-1}}x$

D) None of these

• question_answer238) The adjoint matrix of the matrix$\left[ \begin{matrix} 1 & 8 \\ 2 & -5 \\ \end{matrix} \right]$is given by

A) $\left[ \begin{matrix} -5 & -8 \\ -2 & 1 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} -5 & -2 \\ -8 & 1 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 5 & -8 \\ -2 & 1 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 5 & -8 \\ -2 & -1 \\ \end{matrix} \right]$

• question_answer239) If p and q are the roots of the equation ${{x}^{2}}+px+q=0,$then

A) $p=1$

B) $p=-2$

C) $p=0$and 1

D) $p=-2$and 0

• question_answer240) Coefficient of${{x}^{4}}$in the expansion of ${{(1+x+{{x}^{2}}+{{x}^{3}})}^{n}}$is

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

B) $^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}$

C) $^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}{{+}^{n}}{{C}_{4}}^{n}{{C}_{2}}$

D) $^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}{{+}^{n}}{{C}_{1}}^{n}{{C}_{2}}$

• question_answer241) $\int_{0}^{\pi /2}{\log \tan xdx}$is equal to

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

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

C) 0

D) None of these

• question_answer242) Focus and directrix of the parabola${{x}^{2}}=-8ay$are

A) $(-2a,0)$and$x=4$

B) $(0,2a)$and$y=-2a$

C) $(0,-2a)$and$y=2a$

D) $[2a,0)$and$x=-2a$

• question_answer243) Coefficient of${{x}^{4}}$in the expansion of ${{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}$is

A) $\frac{504}{259}$

B) $\frac{450}{263}$

C) $\frac{405}{256}$

D) None of these

• question_answer244) Coordinates of that point on$x-$axis which is at a perpendicular distance 'a' from the line $\frac{x}{a}+\frac{y}{b}=1,$are

A) $(\pm a,0)$

B) $\left( a\pm \frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}},0 \right)$

C) $\left( a+\frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}},0 \right)$

D) $\left( a-\frac{a}{b}\sqrt{{{a}^{2}}+{{b}^{2}}},0 \right)$

• question_answer245) Equation of tangent to the circle${{x}^{2}}+{{y}^{2}}={{a}^{2}}$ which is parallel to the line$y=mx+c,$is

A) $my=x\pm a\sqrt{1+{{m}^{2}}}$

B) $y=mx\pm \sqrt{1+{{m}^{2}}}$

C) $y=mx\pm a\sqrt{1+{{m}^{2}}}$

D) None of these

• question_answer246) Which one of the following is correct?

A) $cos\text{ }ix=i\text{ }cosh\text{ }x$

B) $\tan ix=tanh\text{ }x$

C) $\sin \text{ }ix=i\text{ }\sin \text{ }x$

D) $cos\text{ }ix=cosh\text{ }x$

• question_answer247) Equation of line perpendicular to$x=c$is

A) $y=0$

B) $x=0$

C) $x=y$

D) $x=d$

• question_answer248) ${{(\sin \theta +i\cos \theta )}^{n}}$ is equal to

A) ${{i}^{n}}(i\sin \theta +\cos \theta )$

B) $(\sin n\theta +i\cos n\theta )$

C) $\cos n\left( \frac{\pi }{2}-\theta \right)+i\sin n\left( \frac{\pi }{2}-\theta \right)$

D) $\cos \theta +i\sin n\theta$

• question_answer249) If A is a square matrix, then$A+{{A}^{T}}$is

A) symmetric matrix

B) anti-symmetric matrix

C) diagonal matrix

D) triangular matrix

• question_answer250) If a, b are two constant positive integers such that$f(a+x)=b+[{{b}^{3}}+1-3{{b}^{2}}f(x)+3b{{\{f(x)\}}^{2}}$$-\{f{{(x)}^{3}}\}{{]}^{1/3}},$for every$x$. Then,$f(x)$is a periodic function with the period

A) $a$

B) $2a$

C) $b$

D) $2b$

• question_answer251) If$\overrightarrow{A}.\overrightarrow{B}=\overrightarrow{A}.\overrightarrow{C},$then difference of$\overrightarrow{B}$and$\overrightarrow{C}$and$\overrightarrow{A}$are

A) parallel

B) perpendicular

C) coplanar

D) None of these

• question_answer252) If$A=\left[ \begin{matrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \\ \end{matrix} \right],$then${{A}^{2}}$is equal to

A) $\left[ \begin{matrix} \cos 2\alpha & \sin 2\alpha \\ -\sin 2\alpha & \cos 2\alpha \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} {{\cos }^{2}}\alpha & -{{\sin }^{2}}\alpha \\ -{{\sin }^{2}}\alpha & {{\cos }^{2}}\alpha \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} {{\sin }^{2}}\alpha & {{\cos }^{2}}\alpha \\ -{{\cos }^{2}}\alpha & {{\sin }^{2}}\alpha \\ \end{matrix} \right]$

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

• question_answer253) Argument of$\frac{1+\sqrt{3}i}{\sqrt{3}+i}$is

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

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

C) $0$

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

• question_answer254) The tangential point, where the line$y=mx+c$touches the parabola${{y}^{2}}=4ax,$is

A) $\left( \frac{a}{{{m}^{2}}},\frac{-2a}{m} \right)$

B) $\left( -\frac{a}{{{m}^{2}}},-\frac{2a}{m} \right)$

C) $\left( -\frac{a}{{{m}^{2}}},-\frac{2a}{m} \right)$

D) $\left( \frac{a}{{{m}^{2}}},\frac{2a}{m} \right)$

• question_answer255) $\frac{(\cos \alpha +i\sin \alpha )(\cos \beta +i\sin \beta )}{(\cos \gamma +i\sin \gamma )(\cos \delta +i\sin \delta )}$is equal to

A) $\cos (\alpha +\beta -\gamma -\delta )-i\sin (\alpha +\beta -\gamma -\delta )$

B) $\cos (\alpha +\beta -\gamma +\delta )+i\sin (\alpha +\beta -\gamma +\delta )$

C) $\sin (\alpha +\beta -\gamma -\delta )+i\cos (\alpha +\beta -\gamma -\delta )$

D) $\cos (\alpha +\beta -\gamma -\delta )+i\sin (\alpha +\beta -\gamma -\delta )$

• question_answer256) $sinh\text{ }3x$ is equal to

A) $4sin{{h}^{3}}x-3sinh\text{ }x$

B) $3\text{ }sin{{h}^{3}}x+4\text{ }sinh\text{ }x$

C) $3\text{ }sinh\text{ }x+4\text{ }sin{{h}^{3}}x$

D) $3\text{ }sin{{h}^{3}}x-4\text{ }sinh\text{ }x$

• question_answer257) If$z=\frac{\sqrt{3}+i}{-2},$then${{z}^{69}}$is equal to

A) 1

B) 2

C) $-i$

D) $-1$

• question_answer258) If$x+\frac{1}{x}=2\cos \theta ,$then$x$is equal to

A) $cos\text{ }\theta +i\text{ }sin\text{ }\theta$

B) $cos\text{ }\theta -i\text{ }sin\text{ }\theta$

C) $cos\text{ }\theta \pm i\text{ }sin\text{ }\theta$

D) None of these

• question_answer259) Projection of a line on the axes are 3, 4, 5 respectively, then its length is

A) 12

B) 50

C) $5\sqrt{2}$

D) None of these

• question_answer260) If$\overrightarrow{a}$and$\overrightarrow{b}$are the adjacent sides of a rhombus, then

A) $\overrightarrow{a}.\overrightarrow{a}=\overrightarrow{b}.\overrightarrow{b}$

B) $\overrightarrow{a}.\overrightarrow{b}=0$

C) $\overrightarrow{a}\times \overrightarrow{b}=0$

D) $\overrightarrow{a}.\overrightarrow{a}=0$

• question_answer261) $\overrightarrow{a}[\overrightarrow{a}\times (\overrightarrow{a}\times \overrightarrow{b})]$is equal to

A) $(\overrightarrow{a}.\overrightarrow{a})(\overrightarrow{a}\times \overrightarrow{b})$

B) $(\overrightarrow{a}.\overrightarrow{a})(\overrightarrow{b}\times \overrightarrow{a})$

C) $(\overrightarrow{b}.\overrightarrow{b})(\overrightarrow{a}\times \overrightarrow{b})$

D) $(\overrightarrow{b}.\overrightarrow{b})(\overrightarrow{b}\times \overrightarrow{a})$

• question_answer262) $\overrightarrow{A}.(\overrightarrow{B}\times \overrightarrow{C})$is equal to

A) $\overrightarrow{B}.(\overrightarrow{A}\times \overrightarrow{C})$

B) $\overrightarrow{B}.(\overrightarrow{C}\times \overrightarrow{A})$

C) $\overrightarrow{C}.(\overrightarrow{B}\times \overrightarrow{A})$

D) None of these

• question_answer263) If$O$is the origin and${{P}_{3}}$is the mid point of${{P}_{1}}(2,-1)$and${{P}_{2}}(-4,3),$then${{\overset{\to }{\mathop{OP}}\,}_{3}}$is equal to

A) $(-1,1)$

B) $(1,1)$

C) $(1,-1)$

D) $(-1,-1)$

• question_answer264) $\frac{\cos \sqrt{x}}{\sqrt{x}}$is equal to

A) $\sin \sqrt{x}+c$

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

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

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

• question_answer265) Sum of the infinite terms of the series$1+\frac{4}{5}+\frac{7}{{{5}^{2}}}+\frac{10}{{{5}^{3}}}+....$is

A) $\frac{16}{35}$

B) $\frac{11}{8}$

C) $\frac{35}{16}$

D) $\frac{8}{16}$

• question_answer266) Radical axis of the circles $3{{x}^{2}}+3{{y}^{2}}-7x+8y+11=0$and ${{x}^{2}}+{{y}^{2}}-3x-4y+5=0$is

A) $x+10y=2$

B) $x+10y+2=0$

C) $x+10y=8$

D) $x+10y+8=0$

• question_answer267) $\underset{x\to 0}{\mathop{\lim }}\,\frac{x({{5}^{x}}-1)}{1-\cos x}$is equal to

A) $4\text{ }log\text{ }5$

B) $2\text{ }log\text{ }5$

C) $\frac{1}{2}log\text{ }5$

D) None of these

• question_answer268) If the line$x+2y=1$is the polar of the circle ${{x}^{2}}+{{y}^{2}}=5,$then pole is

A) $(5,10)$

B) $(5,5)$

C) $(-5,10)$

D) $(-5,-10)$

• question_answer269) $\cos (\alpha +i\beta )$is equal to

A) $cos\text{ }\alpha \text{ }coch\text{ }\beta -2\text{ }sin\text{ }\alpha \text{ }sinh\text{ }\beta$

B) $cos\text{ }\alpha \text{ }cosh\text{ }\beta +2\text{ }sin\text{ }\alpha \text{ }sinh\text{ }\beta$

C) $cosh\text{ }\alpha \text{ }cos\text{ }\beta -2\text{ }sinh\text{ }\alpha \text{ }sin\text{ }\beta$

D) None of the above

• question_answer270) If$\overrightarrow{A}=2\hat{i}-2\hat{j}-\hat{k}$and$\overrightarrow{B}=-\hat{i}+3\hat{j}+2\hat{k},$then $A\times B$is equal to

A) $\hat{i}+2\hat{j}-4\hat{k}$

B) $-\hat{i}-3\hat{j}+4\hat{k}$

C) $-\hat{i}-5\hat{j}+4\hat{k}$

D) $-2\hat{i}-\hat{j}+\hat{k}$

• question_answer271) If$\overrightarrow{A}=4\hat{i}+8\hat{j}-\hat{k},\overrightarrow{B}=3\hat{i}+2\hat{j}-\hat{k}$and$\overrightarrow{C}=5\hat{i}+4\hat{j}+\hat{k},$then$\overrightarrow{A}.(\overrightarrow{B}.\overrightarrow{C})$is equal to

A) $88\hat{i}+176\hat{j}-22\hat{k}$

B) $22\hat{i}+44\hat{j}-11\hat{k}$

C) $\hat{i}+4\hat{j}-\hat{k}$

D) None of these

• question_answer272) If A and B are two matrices such that$AB=0,$then

A) $A\ne O$or$B=O$

B) $A=O$and$B=O$

C) it is not necessary that$A=O$or$B=O$

D) all the statements are incorrect

• question_answer273) If$\overrightarrow{a}$and$\overrightarrow{b}$are non-collinear vectors and $x\overrightarrow{a}+y\overrightarrow{b}=0,$then

A) $x=0$but it is not necessary for y to be 0

B) not dependent on$x$and $y$

C) $x=0,y=0$

D) dependent on$x$and y

• question_answer274) A perpendicular to the pont P(1, 0,3) is drawn to the line joining the points A (4,7,1) and B(3,5,3). The foot of perpendicular to the line is

A) $(5,7,1)$

B) $\left( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right)$

C) $\left( \frac{7}{3},\frac{5}{3},\frac{7}{3} \right)$

D) $\left( \frac{5}{2},\frac{2}{3},\frac{7}{3} \right)$

• question_answer275) If the coefficient of${{x}^{7}}$and${{x}^{8}}$in the expansion of${{\left( 2+\frac{x}{3} \right)}^{n}}$are equal, then n is equal to

A) 55

B) 56

C) 45

D) 15

• question_answer276) Sum of the$n$terms of the series $\frac{3}{{{1}^{2}}}+\frac{5}{{{1}^{2}}+{{2}^{2}}}+\frac{7}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+....$is

A) $\frac{4n}{(n+1)}$

B) $\frac{6n}{(n+1)}$

C) $\frac{12n}{(n+1)}$

D) $\frac{9n}{(n+1)}$

• question_answer277) If difference of the roots of the equation ${{x}^{2}}+px+8=0$is 2, then value of p is

A) $\pm 6$

B) $\pm 2$

C) $2,-6$

D) $6,2$

• question_answer278) If the roots of the equation$\frac{{{x}^{2}}-bx}{ax-c}=\frac{\lambda -1}{\lambda +1}$are equal and opposite in sign, then$\lambda$is equal to

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

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

C) 0

D) None of these

• question_answer279) $\int{\left( \frac{a{{x}^{3}}+b{{x}^{2}}+c}{{{x}^{4}}} \right)}dx$is equal to

A) $a\log x+\frac{b}{{{x}^{3}}}+\frac{c}{3{{x}^{3}}}+A$

B) $a\log x+\frac{b}{x}-\frac{c}{3{{x}^{3}}}+A$

C) $a\log x-\frac{b}{x}-\frac{c}{3{{x}^{3}}}+A$

D) $a\log x+\frac{b}{x}+\frac{c}{3{{x}^{3}}}+A$

• question_answer280) $\int{\sqrt{{{x}^{2}}+{{a}^{2}}}}dx$is equal to

A) $\frac{x}{2}\sqrt{{{x}^{2}}+{{a}^{2}}}+\frac{{{a}^{2}}}{2}\log \{x+\sqrt{{{x}^{2}}+{{a}^{2}}}\}+c$

B) $\frac{x}{2}\sqrt{{{x}^{2}}+{{a}^{2}}}-\frac{{{a}^{2}}}{2}\log \{x+\sqrt{{{x}^{2}}+{{a}^{2}}}\}+c$

C) $\frac{x}{2}+\sqrt{{{x}^{2}}+{{a}^{2}}}+\frac{{{a}^{2}}}{2}\log \{x-\sqrt{{{x}^{2}}+{{a}^{2}}}\}+c$

D) $\sqrt{{{x}^{2}}+{{a}^{2}}}+\frac{{{a}^{2}}}{2}\log \{x-\sqrt{{{x}^{2}}+{{a}^{2}}}\}+c$

• question_answer281) If 6 points out of 10 points are collinear, then number of triangles made by using these 10 points is

A) 100

B) 16

C) 12

D) 14

• question_answer282) If${{a}_{ij}}=\frac{1}{2}2i-3j,$then matrix${{A}_{2\times 2}}=[{{a}_{ij}}]$is equal to

A) $\left[ \begin{matrix} 1/2 & 2 \\ 1/2 & 1 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 2 & 2 \\ 1/2 & 1/2 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 1/2 & -2 \\ -1/2 & 1 \\ \end{matrix} \right]$

D) None of these

• question_answer283) If$A=\left[ \begin{matrix} 1 & -2 & 1 \\ 2 & 1 & 3 \\ \end{matrix} \right]$and$B=\left[ \begin{matrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \\ \end{matrix} \right],$then${{(AB)}^{T}}$is equal to

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

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

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

D) $A.B$

• question_answer284) Probabilities to solve a problem by three students A, B and C are 1/2, 1/3 and 1/4, then the probability that the problem will be solved, is

A) 1/2

B) 1/4

C) 3/4

D) 2/3

• question_answer285) Two cards are drawn with replacement from a well shuffled pack of 52 cards. The probability that both are ace, is

A) 4/13

B) 1/169

C) 2/13

D) None of these

• question_answer286) Length of normal at any point of the curve$x=a(t+\sin t),y=a(1-\cos t),$is

A) $a\sin t$

B) $2a\sin {{t}^{3}}\left( \frac{t}{2} \right)\sec \left( \frac{t}{2} \right)$

C) $2a\sin \left( \frac{t}{2} \right)\tan \left( \frac{t}{2} \right)$

D) $2a\sin \left( \frac{t}{2} \right)$

• question_answer287) $\underset{x\to 0}{\mathop{\lim }}\,{{\left[ \tan \left( \frac{\pi }{4}+x \right) \right]}^{1/x}}$is equal to

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

B) e

C) ${{e}^{-1}}$

D) 1

• question_answer288) $^{x}{{C}_{r}}{{+}^{x}}{{C}_{r-1}}^{y}{{C}_{1}}{{+}^{x}}{{C}_{r-2}}^{y}{{C}_{2}}+{{.....}^{y}}{{C}_{r}}$is equal to

A) $\frac{x+y!}{r!}$

B) $^{x+y}{{C}_{r}}^{xy}{{C}_{r}}$

C) $^{x+y}{{C}_{r}}$

D) $^{xy}{{C}_{r}}$

• question_answer289) If $A=\left[ \begin{matrix} 3 & 8 \\ 2 & 1 \\ \end{matrix} \right],$then${{A}^{-1}}$is equal to

A) $-\frac{1}{13}\left[ \begin{matrix} 1 & 7 \\ 8 & 3 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} -1 & 8 \\ 2 & -3 \\ \end{matrix} \right]$

C) $-\frac{1}{13}\left[ \begin{matrix} 1 & -8 \\ -2 & 3 \\ \end{matrix} \right]$

D) does not exist

• question_answer290) Direction ratios of two lines are$5,-12,13$and $-3,4,5,$then angle between the lines is

A) ${{\cos }^{-1}}\left( \frac{2}{65} \right)$

B) ${{\cos }^{-1}}\left( \frac{1}{65} \right)$

C) ${{\cos }^{-1}}\left( \frac{3}{65} \right)$

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

• question_answer291) In a GP, the ratio of the sum of first three terms and first six terms is 125:152, then common ratio is

A) $\frac{1}{5}$

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

C) $\frac{3}{5}$

D) $\frac{4}{5}$

• question_answer292) Triangle made by the points$(0,7,10),(-1,6,6)$and$(-4,9,6)$is

A) right angled

B) isosceles

C) equilateral

D) right angled isosceles

• question_answer293) If the equation$a(b-c){{x}^{2}}+b(c-a)x+$$c(a-b)=0$has equal roots, then a, b, c are in

A) AP

B) HP

C) GP

D) None of these

• question_answer294) If P=0.25, P=0.5 and$P(A\cap B)=0.14,$then$P(\overline{A}\cap \overline{B})$is equal to

A) 0.39

B) 0.61

C) 0.48

D) 0.45

• question_answer295) If$y=\sqrt{\sin x+y},$then$\frac{dy}{dx}$is equal to

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

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

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

D) $\frac{\sin x}{1+xy}$

• question_answer296) Three vertices of a parallelogram are$A(-1,-2),$$B(1,0)$and$C(3,4),$then the fourth vertex is

A) (1, 2)

B) $(-3,-4)$

C) (2, 0)

D) $(-1,2)$

• question_answer297) If$2x-\left[ \begin{matrix} 1 & 2 \\ 7 & 4 \\ \end{matrix} \right]=\left[ \begin{matrix} 3 & 2 \\ 0 & -2 \\ \end{matrix} \right],$then$x$is equal to

A) $\left[ \begin{matrix} 4 & 4 \\ 7 & 2 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 2 & 2 \\ 7/2 & 1 \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 3 & -1 \\ 7/2 & 2 \\ \end{matrix} \right]$

D) None of these

• question_answer298) $\int{\frac{{{x}^{2}}}{{{x}^{2}}+4}}$is equal to

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

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

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

D) None of the above

• question_answer299) The function $f(x)=sin\left( \frac{\pi x}{2} \right)+2cos\left( \frac{\pi x}{3} \right)-\tan \left( \frac{\pi x}{4} \right)$is a periodic function. It's period is

A) 6

B) 3

C) 4

D) 12

• question_answer300) Line$ax+by+c=0$is normal to the circle${{x}^{2}}+{{y}^{2}}={{r}^{2}}$. Length of the intercepts cut by the line on the circle is

A) r

B) ${{r}^{2}}$

C) 2r

D) $\sqrt{r}$