# Solved papers for RAJASTHAN ­ PET Rajasthan PET Solved Paper-2004

### done Rajasthan PET Solved Paper-2004

• question_answer1) F-or a triode amplification factor 20 and ${{g}_{m}}=3\text{ }m\,\Omega ,$If the resistance is$3\times {{10}^{4}}\Omega ,$ the voltage gain will be

A) 16.36

B) 28

C) 78

D) 108

View Answer play_arrow
• question_answer2) Half-life of a radioactive element is T and its decay constant is $\lambda$, then

A) $\lambda T=1$

B) $\lambda T=1/2$

C) $\lambda T={{\log }_{e}}2$

D) $\lambda =-{{\log }_{e}}2T$

View Answer play_arrow
• question_answer3) Internal resistance of cell does not depend upon the

A) current taken by cell

B) distance between the electrode

C) concentration of electrolyte

D) emf of cell

View Answer play_arrow
• question_answer4) Charge is quantized. This prove from

A) experiment of Devisson- Jarmer

B) effect of Compton-scattering

C) Millikans oil drop experiment

D) Raman-scattering

View Answer play_arrow
• question_answer5) The relative permittivity for diamagnetic material is

A) $-1<{{\mu }_{r}}<-10$

B) $1<{{\mu }_{r}}<10$

C) $-1<{{\mu }_{r}}>10$

D) $0<{{\mu }_{r}}>1$

View Answer play_arrow
• question_answer6) In an induction coil with resistance, the induced emf will be maximum when

A) the switch is put on due to high resistance

B) the switch is put off due to high resistance

C) the switch is put on due to low resistance

D) the switch is put off due to low resistance

View Answer play_arrow
• question_answer7) In stationary waves, the nodes have

A) maximum energy

B) maximum change in pressure and density

C) maximum change in distortion

D) All of the above

View Answer play_arrow
• question_answer8) The ratio of diameter of 4th semi-frequency zone to 9th semi-frequency zone will be

A) 2/3

B) 4/9

C) 1/4

D) 16/81

View Answer play_arrow
• question_answer9) If the specific resistance and area of the potential meter wire are$\rho$and A respectively and the current / flows in the wire, then potential gradient will be

A) $I\rho /A$

B) $I/Ap$

C) $IA/\rho$

D) $I/A\rho$

View Answer play_arrow
• question_answer10) The de-Broglie wavelength related to a-particle accelerated by V volt will be

A) $\frac{0.287}{\sqrt{V}}$$\overset{o}{\mathop{\text{A}}}\,$

B) $\frac{12.27}{\sqrt{V}}$$\overset{o}{\mathop{\text{A}}}\,$

C) $\frac{4.34}{\sqrt{V}}$$\overset{o}{\mathop{\text{A}}}\,$

D) $\frac{0.202}{\sqrt{V}}$$\overset{o}{\mathop{\text{A}}}\,$

View Answer play_arrow
• question_answer11) The peak value of AC current is 2$\sqrt{2}$ A. Its apparent value will be

A) 1 A

B) 2 A

C) 4 A

D) zero

View Answer play_arrow
• question_answer12) The wavelength of first line of balmer series is 6563$\overset{o}{\mathop{\text{A}}}\,$. The wavelength of first line of lymen series will be

A) 1215.4$\overset{o}{\mathop{\text{A}}}\,$

B) 2500$\overset{o}{\mathop{\text{A}}}\,$

C) 7500$\overset{o}{\mathop{\text{A}}}\,$

D) 600$\overset{o}{\mathop{\text{A}}}\,$

View Answer play_arrow
• question_answer13) The nature of circuit is antiresonant of maximum frequency from resonant frequency will be

A) resistance

B) capacitance

C) inductance

D) All of these

View Answer play_arrow
• question_answer14) The reactance of inductance at${{10}^{4}}$Hz is${{10}^{4}}$$\Omega$. Its reactance at $2\times {{10}^{4}}Hz$ will be

A) ${{10}^{4}}\Omega$

B) $2\times {{10}^{4}}\Omega$

C) $3\times {{10}^{4}}\Omega$

D) $4\times {{10}^{4}}\Omega$

View Answer play_arrow
• question_answer15) At NTP for the same volume of two gases of constant unit will be

A) the total number of molecule

B) average kinetic energy

C) square mean root velocity

D) mean free path

View Answer play_arrow
• question_answer16) At normal temperature for the diatomic gas, the number of degree of freedom is

A) 7

B) 6

C) 5

D) 4

View Answer play_arrow
• question_answer17) In capillery, meniscus of mercury is

A) concave

B) convex

C) plane

D) circular

View Answer play_arrow
• question_answer18) A ball is released from height h on the ground level. If the coefficient of restitution is e, then what height will after 2 times jump from ground?

A) $eh/2$

B) $2eh$

C) $eh$

D) ${{e}^{4}}h$

View Answer play_arrow
• question_answer19) The moment of inertia of a straight thin rod of mass M and length L about an axis perpendicular to its length and passing through its one end, is

A) $\frac{M{{L}^{2}}}{3}$

B) $\frac{M{{L}^{2}}}{12}$

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

D) $\frac{M{{L}^{2}}}{13}$

View Answer play_arrow
• question_answer20) If the displacement of simple pendulum at any time is 0.02 m and acceleration is$2\text{ }m/{{s}^{2}},$ then in this time angular velocity will be

A) 100 rad/s

B) 10 rad/s

C) 1 rad/s

D) 0.1 rad/s

View Answer play_arrow
• question_answer21) Which is constant, the earth revolving around the sun?

A) Angular momentum

B) Linear momentum

C) Rotational kinetic energy

D) Kinetic energy

View Answer play_arrow
• question_answer22) Two springs of force constants k and 2k are connected to a mass M as shown below. The time period of oscillation of the mass M is

A) $2\pi \sqrt{\frac{3k}{M}}$

B) $2\pi \sqrt{\frac{k}{M}}$

C) $2\pi \sqrt{\frac{M}{2k}}$

D) $2\pi \sqrt{\frac{M}{3k}}$

View Answer play_arrow
• question_answer23) Two spheres each of mass M and radius R/2 are connected with a massless rod of length 2R as shown in the figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod?

A) $pV$

B) $2pV$

C) $3pV$

D) $4pV$

View Answer play_arrow
• question_answer24) In non- elastic collision

A) momentum is conserved

B) energy is conserved

C) momentum and energy are conserved

D) momentum and energy are non conserved

View Answer play_arrow
• question_answer25) In adiabatic process, the work done by system is 50 J, then

A) the temperature of the system will be increase 50 J

B) the temperature of the system will be constant

C) the internal energy of the system will be increase 50 J

D) the internal energy of the system will be decrease 50 J

View Answer play_arrow
• question_answer26) An ideal monoatomic gas is taken round the cycle LMNO as shown in following diagram. The work done during the cycle is

A) pV

B) 2pV

C) 3pV

D) 4pV

View Answer play_arrow
• question_answer27) Water rise upto 5 cm in a straight capillary tube when its one end is dipped vertically in water. If it is bent according to the diagram, then the length of water column will be

A) 5 cm

B) less than 5 cm

C) more than 5 cm

D) 5 cos $\alpha$

View Answer play_arrow
• question_answer28) The requirement in phase relative source that those

A) amplitudes are same

B) wavelengths are same

C) frequencies are same

D) first phase difference are same

View Answer play_arrow
• question_answer29) In the Young's double slit experiment, intensities of black and bright fringes are 1 and 4 respectively, the ratio of amplitudes of sources will be

A) 1 : 1

B) 1 : 2

C) 3 : 1

D) 1 : 4

View Answer play_arrow
• question_answer30) The primary reason of generation of Frounhofer line is

A) reflection of radiations by chromosphere

B) absorption of radiation by chromosphere

C) emittion of radiation by chromosphere

D) transmission of radiation by chromospheres

View Answer play_arrow
• question_answer31) The emf and current in an AC circuit are given by $E=200\text{ }sin\text{ }314t$volt and $I=\,100\,\sin \,\left( 314+\frac{\pi }{3} \right)A,$ the coefficient of power will be

A) 1/2

B) 1/4

C) 1

D) $-1$

View Answer play_arrow
• question_answer32) A pure resistance is attached as shown in figure. The phase difference between the emf and flowing current will be

A) zero

B) $\pi$/2

C) $-\pi$/2

D) $\pi /4$

View Answer play_arrow
• question_answer33) If inductance and resistance of chocke coil are${{X}_{L}}$ and R respectively, then

A) ${{X}_{L}}=r$

B) ${{X}_{L}}>>R$

C) ${{X}_{L}}<<R$

D) ${{X}_{L}}=\infty$

View Answer play_arrow
• question_answer34) The path difference, time difference and phase difference between two successive zones will be

A) $\frac{\lambda }{2},\frac{T}{2}and\pi$

B) $\lambda ,T\,and\,\pi$

C) $\frac{\lambda }{2},\frac{T}{2}and\,\frac{\pi }{2}$

D) $\frac{\lambda }{2},\frac{T}{2}and\,2\pi$

View Answer play_arrow
• question_answer35) The ozone layer is important because

A) it prevents the cooling of each at night

B) it prevents the IR rays coming from the space

C) it prevents UV rays from the meteors coming from the space

D) it prevents the UV rays and micro rays the coming from the space

View Answer play_arrow
• question_answer36) The number of zones for achieving the first minima on the screen due to circular gate will be

A) 4

B) 6

C) 3

D) 2

View Answer play_arrow
• question_answer37) In India for the use the fixed value of voltage and frequency of electricity are

A) 200 V, 60 Hz

B) 220 V. 50 Hz

C) 220 V, 60 Hz

D) 220 V, 50 Hz

View Answer play_arrow
• question_answer38) If resonant frequency is $f$and capacity become 4 times, then resonant frequency will be

A) $f/2$

B) $2f$

C) $f$

D) $f/4$

View Answer play_arrow
• question_answer39) The forbidden energy gap in the intrinsic semiconductor is

A) 0.1 eV

B) 1 eV

C) 5 eV

D) 10 eV

View Answer play_arrow
• question_answer40) How much kinetic energy will be gained by an $\alpha$ -particle in going from a point at 70 V to another point at 50 V?

A) 40 eV

B) 40 keV

C) 40 MeV

D) Zero

View Answer play_arrow
• question_answer41) The relation among magnetic induction B, magnetic field H and magnetic intensity $I$is

A) $B={{\mu }_{0}}H+I$

B) $B=~{{\mu }_{0}}I+H$

C) $B={{\mu }_{0}}(H+I)$

D) $B+{{\mu }_{0}}(H-I)$

View Answer play_arrow
• question_answer42) The velocity of sound in air is 333 m/s and the fundamental frequency of open pipe is 333 Hz. The length of pipe to produced second overtones will be

A) 0.5 m

B) 1.0 m

C) 1.5 m

D) 2 m

View Answer play_arrow
• question_answer43) If the length of sonometer wire is to be half, the value of resonance frequency will be

A) three times

B) half

C) four times

D) twice

View Answer play_arrow
• question_answer44) At what speed should a source of sound move so that stationary observer finds the apparent frequency equal to half of the original frequency?

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

B) $2v$

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

D) $v$

View Answer play_arrow
• question_answer45) The intensity of the X-rays in coolidge tube control

A) by the current flowing in the filament

B) by potential between the cathode and anti- cathode

C) Both [a] and [b]

D) None of the above

View Answer play_arrow
• question_answer46) Which of the following is correct in terms of increasing work done for the same initial and final states?

A) Adiabatic < Isothermal < Isobaric

B) Isobaric < Adiabatic < Isothermal

C) Adiabatic < Isobaric < Isothermal

D) None of the above

View Answer play_arrow
• question_answer47) A mica slit of thickness t and refractive index $\mu$ is introduced in the ray from the first source${{S}_{1}}$. By how much distance of fringes pattern will be displaced?

A) $\frac{d}{D}(\mu -1)t$

B) $\frac{D}{d}(\mu -1)t$

C) $\frac{d}{(\mu -1)D}$

D) $\frac{D}{d}(\mu -1)$

View Answer play_arrow
• question_answer48) The degree of air pressure in coolidge tube

A) zero

B) ${{10}^{-6}}$mm (mercury)

C) ${{10}^{-3}}$mm (mercury)

D) 1 mm (mercury)

View Answer play_arrow
• question_answer49) The fundamental frequency of open pipe is n. The tube is immersed in water by placing in a vertical position so that its half part remain in the water. Now the fundamental frequency of air column will be

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

B) $\frac{2n}{4}$

C) $n$

D) $2n$

View Answer play_arrow
• question_answer50) The refractive index of water is 4/3 and that of glass is 5/3. What will be the critical angle for the ray of light entering water from the glass?

A) ${{\sin }^{-1}}\left( \frac{4}{5} \right)$

B) ${{\sin }^{-1}}\left( \frac{5}{4} \right)$

C) ${{\sin }^{-1}}\left( \frac{1}{2} \right)$

D) ${{\sin }^{-1}}\left( \frac{2}{1} \right)$

View Answer play_arrow
• question_answer51) A rocket emitting sound of frequency$4\times {{10}^{7}}Hz$is going away from the earth with a speed of 0.2 c, frequency of sound to be heard by the listener is

A) $4\times {{10}^{6}}Hz$

B) $3.3\times {{10}^{7}}Hz$

C) $3\times {{10}^{6}}Hz$

D) $5\times {{10}^{7}}Hz$

View Answer play_arrow
• question_answer52) The radius of fourth zone at observation point present at a distance of 4 m from the plane wave front of wavelength 6400$\overset{o}{\mathop{\text{A}}}\,$ is

A) $32\times {{10}^{-4}}$

B) $32\times {{10}^{-4}}cm$

C) $32\times {{10}^{-4}}mm$

D) $16\times {{10}^{-2}}m$

View Answer play_arrow
• question_answer53) A normally incident ray reflected at angle of$90{}^\circ$. The value of critical angle is

A) $45{}^\circ$

B) $90{}^\circ$

C) $64{}^\circ$

D) $43.5{}^\circ$

View Answer play_arrow
• question_answer54) The produced rays in sonography are

A) microwaves

B) infrared waves

C) sound waves

D) ultra sound

View Answer play_arrow
• question_answer55) The ratio of secondary of primary turns of step up transformer is 4: 1. If a current of 4 A is applied to the primary, the induced current in secondary will be

A) 8 A

B) 2 A

C) 1 A

D) 0.5 A

View Answer play_arrow
• question_answer56) Two waves are represent by ${{y}_{1}}=\alpha \sin \left( \omega t+\frac{\pi }{6} \right),{{y}_{2}}=a\cos \,\omega t,$the resultant amplitude will be

A) $a$

B) $a\sqrt{2}$

C) $a\sqrt{3}$

D) $2a$

View Answer play_arrow
• question_answer57) The plate resistance of a triode is 15 k $\Omega$ and voltage gain is 50. If load resistance is 100 k $\Omega$ the amplification factor will be

A) 5

B) 50

C) 57.5

D) 75.5

View Answer play_arrow
• question_answer58) The relation between magnetic susceptibility$\chi$ and temperature T of paramagnetic materials is

A) $\chi$$=C/T$

B) $\chi$$=CT$

C) $\chi$$=T/C$

D) $\chi$$=C{{T}^{2}}$

View Answer play_arrow
• question_answer59) At the plate voltage of 400 V and 200 V respectively the currents are${{i}_{{{p}_{1}}}}$and${{i}_{{{p}_{2}}}}$respectively. The ratio${{i}_{{{p}_{1}}}}/{{i}_{{{p}_{2}}}}$will be

A) $1:2$

B) $2:1$

C) $1:2\sqrt{2}$

D) $2\sqrt{2}:1$

View Answer play_arrow
• question_answer60) At any instant the ratio of the amount of radioactive substances is 2:1. If their half lives be respectively 12 and 16 hours, then after two days, what will be the ratio of the substances?

A) 4 : 1

B) 2 : 1

C) 1 : 2

D) 1 : 4

View Answer play_arrow
• question_answer61) Moseley's law is

A) $v={{a}^{2}}(Z-b)$

B) $v=\frac{a}{(Z-b)}$

C) $v={{a}^{2}}{{(Z-b)}^{2}}$

D) $v=a\sqrt{(Z-b)}$

View Answer play_arrow
• question_answer62) Two bulbs of wattage 25 and 100 respectively are connected in series, which bulbs will fuse?

A) 25 W bulb

B) 100 W bulb

C) Both [a] and [b]

D) None of them

View Answer play_arrow
• question_answer63) The hardness of X-rays by coolidge tube depends upon

A) filament current

B) air pressure in tube

C) material of target

D) potential between target and cathode

View Answer play_arrow
• question_answer64) In the circuit shown below, what will be the readings of the voltmeter and ammeter?

A) 800 V, 2A

B) 300 V, 2A

C) 220V, 2.2 A

D) 100V, 2A

View Answer play_arrow
• question_answer65) If the pressure of an ideal gas contained in a closed vessel is increased by 0.4%, the increases in temperature is$1{}^\circ C$. The initial temperature of the gas is

A) $25{}^\circ C$

B) $250{}^\circ C$

C) 250 K

D) $2500{}^\circ C$

View Answer play_arrow
• question_answer66) If a van der Waal's gas expands freely, then final temperature is

A) less than the initial temperature

B) equal to the initial temperature

C) more than the initial temperature

D) less or more than the initial temperature depending on the nature of the gas

View Answer play_arrow
• question_answer67) The required mechanical work to increase in per unit surface area of liquid is called surface tension of the liquid. When liquid is in

A) isothermal condition

B) isobaric condition

C) isochoric condition

D) adiabatic condition

View Answer play_arrow
• question_answer68) A person will get more quantity of matter in 1 kg-wt at

A) poles

B) moon

C) equator

D) satellite

View Answer play_arrow
• question_answer69) A sphere of mass m moving with a constant velocity u hits another stationary sphere of the same mass. Ife is the coefficient of restitution, then the ratio of the velocity of two spheres after collision will be

A) $\frac{1-e}{1+e}$

B) $\frac{e-1}{e+1}$

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

D) $\frac{e+1}{e-1}$

View Answer play_arrow
• question_answer70) The moment of inertia of anybody about an its axis is equal to moment of inertia about its perpendicular axis, body is

A) disc

B) solid cylinder

C) ring

D) spherical shell

View Answer play_arrow
• question_answer71) A clocks is based on oscillation of a spring and a clock P is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

A) S will run faster than P

B) P will run faster than S

C) They will both run at the same rate as on the earth

D) None of the above

View Answer play_arrow
• question_answer72) The angular speed of minute needle in a watch

A) $\frac{\pi }{21600}rad/s$

B) $\frac{\pi }{12}rad/s$

C) $\frac{\pi }{3600}rad/s$

D) $\frac{\pi }{1800}rad/s$

View Answer play_arrow
• question_answer73) A body is rolling without slipping on a horizontal surface and its rotational kinetic energy is equal to the translational kinetic energy. The body is

A) disc

B) sphere

C) cylinder

D) ring

View Answer play_arrow
• question_answer74) An inelastic ball is dropped from a height of 100 m. Due to collision with earth, 20% of its energy is lost. To what height the ball will rise?

A) 80 m

B) 40 m

C) 60 m

D) 20 m

View Answer play_arrow
• question_answer75) If two soap bubbles of equal radii R coalesce then the radius of curvature of interface between two bubbles will be

A) infinity

B) R

C) R/2

D) zero

View Answer play_arrow
• question_answer76) In the two vessels of same volume, atomic hydrogen and helium at pressures 1 atm and 2 atm are filled. If temperature of both the samples is same, then average speed of hydrogen atoms $<{{c}_{H}}>$will be related to that of helium$<{{c}_{He}}>$as

A) $<{{c}_{H}}>=\sqrt{2}~<{{c}_{He}}>$

B) $<{{c}_{H}}>=<{{c}_{He}}>$

C) $<{{c}_{H}}>=2<{{c}_{He}}>$

D) $<{{c}_{H}}>=\frac{<{{c}_{He}}>}{2}$

View Answer play_arrow
• question_answer77) Presence of the atmosphere at any planet means

A) ${{V}_{rms}}<<{{v}_{e}}$

B) ${{V}_{rms}}>{{v}_{e}}$

C) the mass and density of planet is less

D) ${{V}_{rms}}=0$

View Answer play_arrow
• question_answer78) An astronaut orbiting the earth in a circular orbit 120 km above the surface of earth , gently drops a pen out of space ship. The pen will

A) move towards the moon

B) fall vertically down to the earth

C) move along with space-ship

D) move opposite direction of space-ship

View Answer play_arrow
• question_answer79) An amplitude of motion represent by displacement equation $y=\frac{1}{\sqrt{a}}\sin \,\omega t\pm \frac{1}{\sqrt{b}}\,\cos \,\omega t,$

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

B) $\frac{\sqrt{a}+\sqrt{b}}{ab}$

C) $\frac{\sqrt{a}\pm \sqrt{b}}{ab}$

D) $\sqrt{\frac{a+b}{ab}}$

View Answer play_arrow
• question_answer80) In sky, a liquid is heated in weightlessness, the heat is transmitted through

A) conduction

B) convection

C) radiation

D) Neither, because the liquid cannot be heated in weightlessness

View Answer play_arrow
• question_answer81) In Young's double slit experiment the type of diffraction is

A) Fresnel

B) Fraunhoffer

C) Both [a] and [b]

D) None of these

View Answer play_arrow
• question_answer82) Positive rays are beam of

A) Positrons

B) Protons

C) $\alpha -$particles

D) Positive-ions

View Answer play_arrow
• question_answer83) Which one is the minimum inresonancing position of series L-C-R circuit?

A) Current

B) Impedence

C) Reactance

D) Power factor

View Answer play_arrow
• question_answer84) Which of the following curves correctly represents the variation of capacitive reactance${{X}_{C}}$with frequency of

A)

B)

C)

D)

View Answer play_arrow
• question_answer85) The curve${{v}_{m}}T$ for a ideal black body is

A) A

B) B

C) C

D) D

View Answer play_arrow
• question_answer86) If light to be polarized by reflection then the angle between reflected and refracted rays is

A) $\pi$

B) $\pi /2$

C) $2\pi$

D) $\pi /4$

View Answer play_arrow
• question_answer87) During mean life of a radioactive element, the fraction that disintegrates is

A) $e$

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

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

D) $\frac{e}{e-1}$

View Answer play_arrow
• question_answer88) The order of wavelength of X-rays are

A) ${{10}^{-10}}m$

B) ${{10}^{-10}}cm$

C) ${{10}^{10}}m$

D) ${{10}^{10}}cm$

View Answer play_arrow
• question_answer89) The alternating currents respectively are ${{I}_{1}}={{I}_{0}}$ and and${{I}_{2}}={{I}_{0}}$$\cos (\omega +\phi ).$of its root mean square is

A) 1 : 1

B) 1 : $\phi$

C) 1 : 2

D) None of these

View Answer play_arrow
• question_answer90) What will be the percentage of radioactive material after 5 half- life?

A) 31%

B) 3.125%

C) 0.3%

D) 1%

View Answer play_arrow
• question_answer91) A star of velocity ${{10}^{6}}m/s$ is going away from earth. If the wavelength of its spectrum line is 5700 $\overset{o}{\mathop{\text{A}}}\,$, Dopper displacement will be

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

B) 19$\overset{o}{\mathop{\text{A}}}\,$

C) 20 $\overset{o}{\mathop{\text{A}}}\,$

D) 0.2 $\overset{o}{\mathop{\text{A}}}\,$

View Answer play_arrow
• question_answer92) If x = $\alpha$sin $\left( \omega t+\frac{\pi }{6} \right)$and$x'=\alpha \,cos\omega t,$then the resultant phase difference between both will be

A) $\pi /3$

B) $\pi /6$

C) $\pi /2$

D) $\pi$

View Answer play_arrow
• question_answer93) A rocket is moving towards the moon with velocity v. Rocket captain sends the electro- magnetic signal of frequency v towards the moon. After reflection from moon, captain receive the signal, the change of apparent frequency will be

A) $\frac{cv}{c-v}$

B) $\frac{cv}{c-2v}$

C) $\frac{2vv}{c}$

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

View Answer play_arrow
• question_answer94) The displacement of interference waves respectively are${{y}_{1}}=4sin$$\omega t$and ${{y}_{2}}=3\,\sin \left( \omega t+\frac{\pi }{2} \right).$ The amplitude of resultant wave will be

A) 5

B) 7

C) 1

D) zero

View Answer play_arrow
• question_answer95) An iron rod of length L and magnetic moment M is bent in form of a semicircle. Now its magnetic moment will be

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

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

C) $M$

D) $M\pi$

View Answer play_arrow
• question_answer96) A light wave of speed v is incidence on plane surface, after reflection its speed will be

A) v

B) $v/2$

C) $v/3$

D) $v/4$

View Answer play_arrow
• question_answer97) General isotope in treatment of cancer is

A) ${{K}^{40}}$

B) $C{{o}^{60}}$

C) $S{{r}^{70}}$

D) ${{I}^{131}}$

View Answer play_arrow
• question_answer98) 1 volt is equal to

A) 1 eV

B) $\frac{Joule}{Coulomb}$

C) $Joule\,\times \,Coulomb$

D) $\frac{Erg}{Coulomb}$

View Answer play_arrow
• question_answer99) If the distance between a point light source and screen is decrease one-third, then the relation between intensity of light $\left( I \right)$ and initial light$({{I}_{0}})$ will be

A) $I=\frac{{{I}_{0}}}{3}$

B) $I=\frac{{{I}_{0}}}{9}$

C) $I={{I}_{0}}$

D) $I=9{{I}_{0}}$

View Answer play_arrow
• question_answer100) Two siren situated one kilometer apart are producing sound of frequency 330 Hz. An observer starts moving from one siren to the other with a speed of 2 m/s. If the speed of sound be 330 m/s, what will be the beat frequency heard by the observer?

A) 8

B) 4

C) 6

D) 1

View Answer play_arrow
• question_answer101) The central atom of which molecule has different hybridization from the following similar structure molecules?

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

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

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

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

View Answer play_arrow
• question_answer102) The solubility product of calcium sulphate is$1\times {{10}^{-10}}$. What will be the concentration of calcium ions in its saturated solution?

A) $1\times {{10}^{5}}$

B) $1\times {{10}^{-10}}$

C) $1\times {{10}^{-5}}$

D) $1\times {{10}^{-10}}$

View Answer play_arrow
• question_answer103) Hydrogen halide reacts with unsymmetrical alkene to form

A) a primary alkyl halide

B) a gem dihalide

C) a primary or secondary alkyl halide

D) a secondary or tertiary alkyl halide

View Answer play_arrow
• question_answer104) Which of the following is not matching? [a] Methane nitrile HCN [b] Iso-butyric acid ${{(C{{H}_{3}})}_{3}}C-COOH$ [c] Acetonitrile$C{{H}_{3}}-C-N$ [d] Crotonic acid $C{{H}_{3}}-CH=CH-COOH$

A) A and B

B) A and C

C) A and D

D) B and C

View Answer play_arrow
• question_answer105) Which of the following is favourable condition for the formation of ammonia in equilibrium reaction ${{N}_{2}}+3{{H}_{2}}2N{{H}_{3}}+22\,kcal?$

A) increase in pressure

B) increase in temperature

C) decrease in pressure

D) increase in the concentration of ammonia

View Answer play_arrow
• question_answer106) For the complete reduction of a molecule of ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$the number of electrons are required

A) 3

B) 4

C) 5

D) 6

View Answer play_arrow
• question_answer107) $23.0g$ethanol vapours are passed on hot alumina. If 50% change is completed then the quantity of organic product (molecular weight = 28) in gram will be

A) 14 g

B) 7.0 g

C) 11 g

D) 11.5 g

View Answer play_arrow
• question_answer108) Which of the following pair has the 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) $S{{O}_{2}},C{{r}_{2}}O_{7}^{2-}$

View Answer play_arrow
• question_answer109) Which of the following sodium acetate solution will show minimum pH?

A) 0.01 M

B) 0.001 M

C) 0.0001 M

D) 0.1 M

View Answer play_arrow
• question_answer110) Which of the following is not matching?

A) Isoprene $C{{H}_{2}}=CH-CH=C{{H}_{2}}$

B) Diacetoneamine

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

D) Chloretone $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}}\,-CC{{l}_{3}}$

View Answer play_arrow
• question_answer111) Which is suitable for the test of primary amine?

A) Chlorine

B) Acetyl chloride

C) Chloroform and alkali

D) Alkyl chloride

View Answer play_arrow
• question_answer112) The IUPAC name of $HO{{H}_{2}}C-C{{H}_{2}}-CH-{{(C{{H}_{2}}OH)}_{2}}$

A) 3-hydroxy methyl-1, 4-butane diol

B) 2-hydroxy methyl-1, 4-butane diol

C) 2-hydroxy methyl-4-hydroxy butanol

D) 3-hydroxy methyl-4-hydroxy butanol

View Answer play_arrow
• question_answer113) Which reagent is used for distinguishing in methanol and ethanol?

A) Schiff reagent

B) Lucas reagent

C) ${{I}_{2}}+NaOH$

D) Chromic acid

View Answer play_arrow
• question_answer114) Ethene and ethyne can be distinguished by the reaction of

A) dil. alkaline $KMn{{O}_{4}}$

B) ${{I}_{2}}$and$NaOH$

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

D) anhydrous$ZnC{{l}_{2}}+$cone.${{H}_{2}}S{{O}_{4}}$

View Answer play_arrow
• question_answer115) The structure of$PC{{l}_{5}}$and number of o-bonds in it are

A) square planar, 5

B) distorted tetrahedral, 4

C) trigonal bipyramidal, 5

D) trigonal pyramidal, 4

View Answer play_arrow
• question_answer116) Which compound has octane number 100?

A) 2, 2, 4-trimethyl pentane

B) iso-heptane

C) n-heptane

D) n-octane

View Answer play_arrow
• question_answer117) Which of the following gives haloform reaction?

A) Acetaldehyde

B) Propionaldehyde

C) iso-butyraldehyde

D) All of the above

View Answer play_arrow
• question_answer118) A carbonyl compound [A] forms compound [B] on reaction with HCN. By the hydrolysis of compound [B], compound [C] is obtained. The compound [C] shows optical isomerism and give iodoform test. Compound [A], is

A) formaldehyde

B) acetaldehyde

C) acetone

D) None of these

View Answer play_arrow
• question_answer119) The percentage of nitrogen will be equal in oximes of which of the following compound pairs?

A) Acetone and acetaldehyde

B) Acetone and propionaldehyde

C) Acetone and acraldehyde

D) Acetaldehyde and acraldehyde

View Answer play_arrow
• question_answer120) Benzene reacts with chlorine in the presence of UV-light to give

A) chlorobenzene

B) hexachlorocyclohexane

C) hexachlorobenzene

D) 1, 3, 5-trichlorobenzene

View Answer play_arrow
• question_answer121) Which of the following is not matching?

A) Fool's gold $Fe{{S}_{2}}$

B) Philosopher's wool $ZnO$

C) Calomel $H{{g}_{2}}C{{l}_{2}}$

D) Lunar caustic $AgCl$

View Answer play_arrow
• question_answer122) Match the list-I with list-II and choose the correct set from the sets, which are given below

 List-I List-II [A] Number of sub-energy levels in a energy level 1. ${{n}^{2}}$ [B] Number of orbitals in a sub-energy level 2. $3d$ [C] Number of orbitals in a energy level 3. $2l+1$ [D] $n=3,l=2,\text{ }m=0$ 4. $n$

A) Codes A-4 B-3 C-1 D-2

B) A-3 B-1 C-2 D-4

C) A- 1 B- 2 C-3 D-4

D) A- 3 B-4 C-1 D-2

View Answer play_arrow
• question_answer123) Which of the following compound is colourless and odourless?

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

B) $CH{{I}_{3}}$

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

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

View Answer play_arrow
• question_answer124) Electron affinity is the characteristic of an

A) isolated atom

B) combined atom

C) gaseous isolated atom in ground state

D) gaseous isolated atom in excited state

View Answer play_arrow
• question_answer125) The highest atomic number radioactive element in p-block element is

A) $Pb$

B) $Te$

C) $Rn$

D) $Po$

View Answer play_arrow
• question_answer126) From the following ores, the set of sulphide and carbonate ores is

 I. Cinnabar II. Calamine III. Copper glance IV. Siderite V. Corundum VI. Magnatite

A) I, III, V, VI

B) I, II, III, IV

C) I, II, V, VI

D) II, III, IV, V

View Answer play_arrow
• question_answer127) Which of the following statement is false?

A) All methyl ketones give iodoform test

B) All secondary alcohols give iodoform test

C) Methanol forms from the catalytic oxidation of methane

D) Rate of esterification of alcohol $1{}^\circ >2{}^\circ >3{}^\circ$

View Answer play_arrow
• question_answer128) Which of the following is correctly matched?

A) Maximum electronegativity element$-Cl$

B) Number of d-electrons in chromium$-6$

C) Cation with pseudo inert gas structure$-Z{{n}^{2+}}$

D) Number of unpaired electrons in$F{{e}^{3+}}$ ion-4

View Answer play_arrow
• question_answer129) Acetaldehyde changes to a sweet-smell liquid on reaction with aluminium ethoxide. This liquid is

A) $C{{H}_{3}}COO{{C}_{2}}{{H}_{5}}$

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

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

D) ${{(C{{H}_{3}}O)}_{3}}Al$

View Answer play_arrow
• question_answer130) Which of the following is obtained from the reaction of formaldehyde with dil. alkali?

A) A polymer

B) Salt of formic acid

C) Methyl alcohol

D) Methyl alcohol and salt of formic acid

View Answer play_arrow
• question_answer131) Which of the following reagent releases nitrogen, on reaction with ethyl amine?

A) Nitrosyi chloride

B) Acetyl chloride

C) Carbon disulphide

D) Benzoyl chloride

View Answer play_arrow
• question_answer132) Which of the following is correctly matched? [a]${{C}_{6}}{{H}_{6}}$(Benzene) : All C-atom are$s{{p}^{2}}$ hybridized [b]${{(C{{H}_{3}})}_{4}}C:$All C-atom are$s{{p}^{3}}$hybridized [c]$HC=C-CH=C{{H}_{2}}$: Four C-atom are sp-hybridized [d] ${{(C{{H}_{3}})}_{2}}C=C{{H}_{2}}$: Three C-atom are$s{{p}^{2}}$hybridized

A) A, B

B) A, C

C) A, D

D) B, C

View Answer play_arrow
• question_answer133) The equilibrium of aqueous solution of${{H}_{2}}S$is as ${{H}_{2}}S{{H}^{+}}+H{{S}^{-}}$ On adding$HCl$at equilibrium

A) concentration of$H{{S}^{-}}$will increase

B) concentration of$H{{S}^{-}}$will decrease

C) dissociation of${{H}_{2}}S$will increase

D) dissociation of${{H}_{2}}S$will stop

View Answer play_arrow
• question_answer134) 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

View Answer play_arrow
• question_answer135) Which of the following is not correctly matched?

A) $CHC{{l}_{3}}+C{{H}_{3}}-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-C{{H}_{3}}\xrightarrow[{}]{{}}$a solvent

B) ${{C}_{2}}{{H}_{5}}OH+CaOC{{l}_{2}}\xrightarrow[{}]{{}}$a anaesthetic

C) $C{{H}_{3}}COH+{{I}_{2}}+NaOH\xrightarrow[{}]{{}}$a yellow colour precipitate

D) $CHC{{l}_{3}}+HN{{O}_{3}}\xrightarrow[{}]{{}}$a war gas

View Answer play_arrow
• question_answer136) Which of the following set is correctly matched?

A)

 $n=3,$ $l=3,m=0,$ $s=+\frac{1}{2}$

B)

 $n=3,$ $l=2,m=-3,$ $s=+\frac{1}{2}$

C)

 $n=3,$ $l=3,m=-3,$ $s=-\frac{1}{2}$

D)

 $n=3,$ $l=2,m=-1,$ $s=-\frac{1}{2}$

View Answer play_arrow
• question_answer137) Which of the following is deposited as thin layer in galvanised iron?

A) Aluminium

B) Zinc

C) Tin

D) White lead

View Answer play_arrow
• question_answer138) The value of energy will increase in sub-energy level

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

View Answer play_arrow
• question_answer139) The outermost structure of an atom A is$n{{s}^{2}},n{{p}^{3}}$. This compound does not form$A{{F}_{5}}.$ Which of the following statement is false in the given reference?

A) A is element of second period

B) d-electron is not in A

C) The value of n is less than three

D) A cannot form tetrahedral compound

View Answer play_arrow
• question_answer140) Which forms on the reaction of propyne with dil.${{H}_{2}}S{{O}_{4}}$ in the presence of mercuric ion?

A) 2-propanol

B) Propanone

C) Propanal

D) 1, 2-propane diol

View Answer play_arrow
• question_answer141) Which alkene forms only ethanal on ozonolysis?

A) 1-butene

B) 2-butene

C) Propene

D) iso-butylene

View Answer play_arrow
• question_answer142) Which of the following is correct order of radius?

A) ${{K}^{+}}>C{{a}^{2+}}>S{{c}^{3+}}<T{{i}^{4+}}$

B) ${{S}^{2-}}>C{{l}^{-}}>Ar<{{K}^{+}}$

C) ${{O}^{2-}}>{{F}^{-}}>Ne>N{{a}^{+}}>M{{g}^{2+}}$

D) $N{{a}^{+}}>M{{g}^{2+}}>Ne>A{{l}^{3+}}$

View Answer play_arrow
• question_answer143) The intermediates are formed in this reaction are

A) phenoxide ion and dichlorocarbene

B) ${{C}_{6}}{{H}_{5}}{{O}^{-}}$ and ${}_{\bullet }^{\bullet }C{{l}_{2}}$

C) ${{C}_{6}}{{H}_{5}}{{O}^{-}}$ and ${}_{\bullet }^{\bullet }CC{{l}_{3}}$

D) ${{C}_{6}}{{H}_{5}}{{O}^{-}}$ and ${}_{\bullet }^{\bullet }CHCl$

View Answer play_arrow
• question_answer144) The colour of methyl orange in basic medium is

A) red

B) colourless

C) yellow

D) orange

View Answer play_arrow
• question_answer145) The stability order of carbonium ion is

A) $3{}^\circ >2{}^\circ >1{}^\circ >C{{H}_{3}}$

B) $3{}^\circ <2{}^\circ >1{}^\circ <C{{H}_{3}}$

C) $3{}^\circ <2{}^\circ >1{}^\circ >C{{H}_{3}}$

D) $3{}^\circ <2{}^\circ <1{}^\circ <C{{H}_{3}}$

View Answer play_arrow
• question_answer146) The density of Na is higher than K because

A) ionisation 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

View Answer play_arrow
• question_answer147) ${{C}_{6}}{{H}_{5}}N{{O}_{2}}\xrightarrow[{}]{Zn/N{{H}_{4}}Cl}A$ Compound A, is

A) phenyl hydroxyl amine

B) nitrosobenzene

C) azobenzene

D) p-aminophenol

View Answer play_arrow
• question_answer148) $Ar-CON{{H}_{2}}\xrightarrow[{}]{B{{r}_{2}}+KOH}Ar-N{{H}_{2}}$ This reaction is

A) Hofmann mustard oil reaction

B) Hofmann bromamide reaction

C) Hofmann martius rearrangement

D) Hofmann carbylamme reaction

View Answer play_arrow
• question_answer149) $C{{H}_{3}}MgX+A\xrightarrow[{}]{{}}B\xrightarrow[{}]{{{H}_{3}}{{O}^{\oplus }}}C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}OH$ Compound A, in the above reaction is

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

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

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

D) ${{(C{{H}_{3}})}_{2}}CO$

View Answer play_arrow
• question_answer150) The 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) $M{{n}^{2+}},T{{i}^{2+}}$

View Answer play_arrow
• question_answer151) Which of the following presents in sapphine?

A) $A{{l}_{2}}{{O}_{3}}$

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

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

D) $MnO$

View Answer play_arrow
• question_answer152) The set of oxidation numbers of nitrogen in ammonium nitrate is

A) $-3,+3$

B) $-1,+1$

C) $+1,-1$

D) $-3,+5$

View Answer play_arrow
• question_answer153) The formula of microcosmic salt is

A) $N{{a}_{2}}HP{{O}_{4}}.2{{H}_{2}}O$

B) $NaN{{H}_{4}}HP{{O}_{4}}.4{{H}_{2}}O$

C) ${{(N{{H}_{4}})}_{2}}HP{{O}_{4}}$

D) $N{{a}_{2}}N{{H}_{4}}P{{O}_{4}}.2{{H}_{2}}O$

View Answer play_arrow
• question_answer154) Which of the following set is correct on the basis of following lists? List-I List-II [A] $N{{H}_{2}}CONHN{{O}_{2}}$ 1. Biuret [B] ${{({{C}_{6}}{{H}_{5}}NH)}_{2}}CO$ 2. Semicarbazide [C] $N{{H}_{2}}CONHN{{H}_{2}}$ 3. Nitrourea [D] $N{{H}_{2}}CONHCON{{H}_{2}}$ 4. Diphenyl urea

A) Codes A-3 B-4 C-2 D-1

B) A-3 B-1 C-2 D-4

C) A- 3 B- 2 C-1 D-4

D) A-3 B- 1 C-4 D-2

View Answer play_arrow
• question_answer155) For equilibrium reaction,${{N}_{2}}+{{O}_{2}}2NO$at definite temperature${{K}_{c}}=121$. What will be the value of ${{K}_{c}}$for following equilibrium reaction $NO\frac{1}{2}{{N}_{2}}+\frac{1}{2}{{O}_{2}}?$

A) $11$

B) $\frac{1}{121}$

C) $\frac{1}{11}$

D) $121$

View Answer play_arrow
• question_answer156) Molten$NaCl$conducts the electricity because it contains

A) free atom

B) free molecule

C) free ion

D) free electron

View Answer play_arrow
• question_answer157) The vapour density of$PC{{l}_{5}}$at$300{}^\circ C$is 60. Its dissociation percentage will be at this temperature

A) 73

B) 77

C) 83

D) 87

View Answer play_arrow
• question_answer158) Starch$\xrightarrow[{}]{A}$Maltose$\xrightarrow[{}]{B}$ Glucose$\xrightarrow[{}]{C}$ Ethyl alcohol In this reaction A, B, C are respectively

A) Invertase, zymase, maltase

B) Diastase, maltase, zymase

C) Invertase, maltase, zymase

D) Zymase, maltase, invertase

View Answer play_arrow
• question_answer159) The pair of isoelectronic species is

A) ${{N}_{2}},CO$

B) $CO_{3}^{2-},NO_{3}^{-}$

C) $NO_{3}^{-},HCO_{3}^{-}$

D) All of these

View Answer play_arrow
• question_answer160) Which alcohol gives blue colour in Victor Meyer's test?

A) Butyl alcohol

B) iso-butyl alcohol

C) Secondary butyl alcohol

D) Tertiary butyl alcohol

View Answer play_arrow
• question_answer161) Which of the following functional groups set is deactivating and$m-$directing?

A) $-CN,~-N{{H}_{2}},\,-OH$

B) $-CHO,\,-OC{{H}_{3}},-S{{O}_{3}}H$

C) $-N{{O}_{2}},\,-CHO,\,-S{{O}_{3}}H$

D) $-Cl,~-C{{H}_{3}},\,-NHCOC{{H}_{3}}$

View Answer play_arrow
• question_answer162) The melting point of$SnC{{l}_{4}}$is less than$SnC{{l}_{2}}$ because in comparison of $S{{n}^{2+}}$

A) the size of$S{{n}^{4+}}$is smaller

B) more positive charge on $S{{n}^{4+}}$

C) the ionization potential of$S{{n}^{4+}}$is more

D) the structure of$SnC{{l}_{4}}$is tetrahedral

View Answer play_arrow
• question_answer163) Phenol$\xrightarrow[{}]{NaN{{O}_{2}}+conc.{{H}_{2}}S{{O}_{4}}}$dark colour$\xrightarrow[{}]{alkali}$blue colour This reaction is called

A) Lederer Mannasse reaction

B) Libermann nitroso reaction

C) Coupling reaction

D) Lucas test

View Answer play_arrow
• question_answer164) The atomic number of an element is 20. In which period of Periodic Table it will be placed?

A) 1

B) 2

C) 3

D) 4

View Answer play_arrow
• question_answer165) For the dissociation of formic acid, acetic acid and carbonic acid the value of$p{{K}_{a}}$is 3.62, 4.74 and 6.3 respectively. Which of the following statement is correct?

A) Formic acid is the strongest acid

B) Acetic acid is the weakest acid

C) Carbonic acid is the strongest acid

D) Acetic acid is weaker than carbonic acid

View Answer play_arrow
• question_answer166) Which of the following acid does not contain $-COOH$ group?

A) Lactic acid

B) Barbituric acid

C) Succinic acid

D) Carbonic acid

View Answer play_arrow
• question_answer167) Which of the following statement is false?

A) Electron absorbs energy on transition from lower energy level to higher energy level.

B) Electron cannot fall in nucleus from third energy level.

C) Electron emits energy on transition from higher energy level to lower energy level.

D) Electron emits energy spontaneously in its ground state.

View Answer play_arrow
• question_answer168) For the hydrolysis reaction $C{{N}^{-}}+{{H}_{2}}OHCN+O{{H}^{-}}$ Which of the following relationship is not applicable?

A) ${{K}_{h}}=\frac{{{K}_{w}}}{\sqrt{{{K}_{a}}(HCN)}}$

B) $h=\sqrt{\frac{{{K}_{h}}}{C}}$

C) $pH=\frac{1}{2}p{{K}_{a}}(HCN)$

D) ${{H}^{+}}=\sqrt{\frac{{{K}_{w}}\times {{K}_{a}}}{C}}$

View Answer play_arrow
• question_answer169) Match the given molecule in list-I with given structure in list-II and choose the correct set from the given sets.

 List-I List-II [A] $A{{X}_{3}}{{E}_{2}}$ 1. Trigonal pyramidal [B] $A{{X}_{5}}$ 2. T-structure [C] $A{{X}_{2}}{{E}_{2}}$ 3. Trigonal bipyramidal [D] $A{{X}_{3}}E$ 4. Angular
(A = Central atom and E = number of lone pairs electrons) Codes

A) A-2 B- 3 C-4 D- 1

B) A-1 B-2 C-3 D-4

C) A-3 B-1 C-2 D-4

D) A-4 B-3 C-1 D-2

View Answer play_arrow
• question_answer170) The degree of dissociation of A is a in equilibrium reaction,$A2B+C$. If initially one mole of A is taken then the total number of moles at equilibrium will be

A) $1-\alpha$

B) $1+\alpha$

C) $1-2\alpha$

D) $1+2\alpha$

View Answer play_arrow
• question_answer171) Which of the following has zero dipole moment?

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

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

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

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

View Answer play_arrow
• question_answer172) Carbon tetrachloride is used as

A) anaesthetic and disinfectant

B) coolant and fire extinguisher

C) industrial solvent and fire extinguisher

D) antibiotic and industrial solvent

View Answer play_arrow
• question_answer173) $A+B\xrightarrow[{}]{\Delta }HCOOH\xrightarrow[{}]{{{H}_{2}}S{{O}_{4}}/\Delta }C+D$ A, B, C and D are respectively

A) $CO,{{H}_{2}}O,CO,{{H}_{2}}O$

B) $CO,{{H}_{2}}O,C{{O}_{2}},{{H}_{2}}$

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

D) $C{{O}_{2}},{{H}_{2}}O,CO,{{H}_{2}}O$

View Answer play_arrow
• question_answer174) In the reaction $H{{C}_{2}}O_{4}^{-}+PO_{4}^{3-}HPO_{4}^{2-}+{{C}_{2}}O_{4}^{2-}.$Bronsted base is

A) $PO_{4}^{3-},{{C}_{2}}O_{4}^{2-}$

B) $PO_{4}^{3-},HPO_{4}^{2-}$

C) $H{{C}_{2}}O_{4}^{-},HPO_{4}^{2-}$

D) $H{{C}_{2}}O_{4}^{-},{{C}_{2}}O_{4}^{2-}$

View Answer play_arrow
• question_answer175) Phenol on heating with phthalic anhydride and cone.${{H}_{2}}S{{O}_{4}}$gets converted to

A) phenolphthalein

B) phenetol

C) pinacol

D) o-hydroxy benzoic acid

View Answer play_arrow
• question_answer176) Which of the following compound forms mesitylene on distillation with cone.${{H}_{2}}S{{O}_{4}}$?

A) Acetaldehyde

B) Acetone

C) Acetophenol

D) Acetyl chloride

View Answer play_arrow
• question_answer177) The structure of tetrafluoroborate

A) tetrahedral

B) square planar

C) octahedral

D) trigonal planar

View Answer play_arrow
• question_answer178) Arrange the following acids in decreasing order of their$p{{K}_{a}}$values

 Formic acid (I) Acetic acid (II) Chloro acetic acid (III) Trichloro acetic acid (IV)

A) IV, III, II, I

B) II, I, IV, III

C) II, I, III, IV

D) I, II, IV, III

View Answer play_arrow
• question_answer179) The degree of dissociation of a weak carbonic acid of 0.1 M solution is 10%. The value of dissociation constant of this acid will

A) ${{10}^{-5}}$

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

C) ${{10}^{-3}}$

D) ${{10}^{-2}}$

View Answer play_arrow
• question_answer180) The structure of some complex ions is given in the following list. A. ${{[Ni{{(CN)}_{4}}]}^{2-}}$ : square planar B. ${{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}}$ : linear C. ${{[Fe{{(CN)}_{6}}]}^{4-}}$ : octahedral D. ${{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}$: tetrahedral Which of the above is not matched?

A) A

B) B

C) C

D) D

View Answer play_arrow
• question_answer181) The correct set of number of lattice points present in unit cell of a body centred cubic structure and a face centred cubic structure

A) 2, 4

B) 4, 2

C) 4, 6

D) 2, 6

View Answer play_arrow
• question_answer182) The solubility product of two sparingly soluble electrolyte AX and BX are$1\times {{10}^{-8}}$and$1\times {{10}^{-10}}$ respectively. Which of the following statement is correct?

A) Solubility of AX is 100 times more than BX.

B) Solubility of BX is 100 times more than AX.

C) Solubility of AX is 10 times more than BX.

D) Comparison of solubility cannot done from these data

View Answer play_arrow
• question_answer183) Which of following are correct matched? [a] Position isomer of isopropyi alcohol $C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{CH}}\,-C{{H}_{3}}$ [b] Functional isomer of 1-butadiene $C{{H}_{3}}-C\equiv C-C{{H}_{3}}$ [c] Position isomer of ethylidene chloride $Cl-C{{H}_{2}}-C{{H}_{2}}-Cl$ [d] Metamer of ethyl acetate $H-\underset{\begin{smallmatrix} || \\ O \end{smallmatrix}}{\mathop{C}}\,-O-C{{H}_{2}}-C{{H}_{2}}C{{H}_{3}}$

A) A, B

B) B, C

C) C, D

D) A, D

View Answer play_arrow
• question_answer184) Generally, alkenes and alkynes show the following type of reaction

A) nucleophilic addition

B) electrophilic addition

C) free radical substitution

D) electrophilic substitution

View Answer play_arrow
• question_answer185) Ethyl acetate reacts with hydrazine to give

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

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

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

D) $C{{H}_{3}}CON{{H}_{2}}$

View Answer play_arrow
• question_answer186) The hydrolysis product of which compound form sodium bisulphite addition product but does not give silver mirror with Tollen's reagent?

A) $Cl-C{{H}_{2}}C{{H}_{2}}Cl$

B) $C{{H}_{3}}C{{H}_{2}}CHC{{l}_{2}}$

C) $C{{H}_{3}}C(C{{l}_{2}})C{{H}_{3}}$

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

View Answer play_arrow
• question_answer187) Which of the following reaction is different from other reaction?

A) $2H{{g}^{2+}}\xrightarrow[{}]{{}}Hg_{2}^{2+}$

B) $Mg\xrightarrow[{}]{{}}M{{g}^{2+}}$

C) $2{{I}^{-}}\xrightarrow[{}]{{}}{{I}_{2}}$

D) $Cu_{2}^{2+}\xrightarrow[{}]{{}}2C{{u}^{2+}}$

View Answer play_arrow
• question_answer188) The IUPAC name of $C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{CH}}\,-\underset{\begin{smallmatrix} | \\ {{C}_{2}}{{H}_{5}} \end{smallmatrix}}{\mathop{CH}}\,-{{C}_{2}}{{H}_{5}}$is

A) 3-ethyl-4-methyl hexane

B) 3-methyl-4-ethyl hexane

C) 3-ethyl-l, 2-dimethyl pentane

D) 3-ethyl-4, 5-dimethyl pentane

View Answer play_arrow
• question_answer189) Which of the following statement is false?

A) $\alpha -$butylene and isobutylene are chain isomers.

B) n-propyi alcohol and isopropyi alcohol are not position isomers.

C) Equal molecular weight alcohol and ether are functional isomers.

D) 1-alkyne does not show geometrical isomerism.

View Answer play_arrow
• question_answer190) After calcination, metal is obtained in the form of

A) oxide

B) hydrated oxide

C) sulphide

D) carbonate

View Answer play_arrow
• question_answer191) The reaction of ether with cold HI is called

A) Williamson's synthesis

B) Zeravitinof method

C) Zeisel method

D) None of the above

View Answer play_arrow
• question_answer192) Which gas is evolved on heating acetamide with aqueous alkali?

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

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

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

D) $NO$

View Answer play_arrow
• question_answer193) Which of the following is not a polymer?

A) Teflon

B) Nylon

C) Orion

D) Phorone

View Answer play_arrow
• question_answer194) $PC{{l}_{5}}PC{{l}_{3}}+C{{l}_{2}}$ In this reaction, degree of dissociation of $PC{{l}_{5}}$is proportional to

A) $\sqrt{p}$

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

C) ${{p}^{2}}$

D) $p$

View Answer play_arrow
• question_answer195) Vinegar is

A) 10% formic acid

B) 8-10% acetic acid

C) 6-10% ethyl alcohol

D) glacial acetic acid

View Answer play_arrow
• question_answer196) Water gas is a mixture of

A) 1 mole CO + 1 mole water vapour

B) 1 mole CO + 2 mole${{H}_{2}}$

C) 2 mole CO + 1 mole${{H}_{2}}$

D) 1 mole CO + 1 mole${{H}_{2}}$

View Answer play_arrow
• question_answer197) Aniline reacts with cone.${{H}_{2}}S{{O}_{4}}$at$150{}^\circ C$to form

A) sulphanilic acid

B) sulphonic acid

C) o-amino sulphonic acid

D) aniline sulphate

View Answer play_arrow
• question_answer198) The pH value of${{10}^{-8}}N\,HCl$is

A) less than 7

B) more than 7 but less than 8

C) 8

D) 7

View Answer play_arrow
• question_answer199) 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) $\frac{1}{\lambda }=R{{\left( \frac{1}{{{n}_{2}}}-\frac{1}{{{n}_{1}}} \right)}^{2}}$

View Answer play_arrow
• question_answer200) The relationship between the solubility and solubility product is

A) ${{K}_{sp}}={{x}^{x}}{{y}^{y}}{{x}^{x+y}}$

B) ${{K}_{sp}}={{s}^{x+y}}$

C) ${{K}_{sp}}={{x}^{x}}{{y}^{y}}{{s}^{x-y}}$

D) ${{K}_{sp}}={{x}^{2}}{{y}^{2}}{{s}^{x+y}}$

View Answer play_arrow
• question_answer201) The distance between the lines$7x+24y+3=0$ and$7x+24y+28=0$is

A) 1 unit

B) $1\frac{6}{25}$units

C) 25 units

D) None of these

View Answer play_arrow
• question_answer202) The imaginary part of$sin\text{ }h(x+iy)$is

A) $cos\text{ }x\text{ }sinh\text{ }y$

B) $-cosh\text{ }x\text{ }sin\text{ }y$

C) $cosh\text{ }x\text{ }sin\text{ }y$

D) None of these

View Answer play_arrow
• question_answer203) ${{\left( \frac{1+\sin \theta +i\cos \theta }{1+\sin \theta -i\cos \theta } \right)}^{n}}$is equal to

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

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

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

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

View Answer play_arrow
• question_answer204) $\tanh (x+y)$is equal to

A) $\frac{\tanh x+\tanh y}{1-\tanh x\tan y}$

B) $\frac{\tanh x+\tanh y}{1+\tanh x\tan y}$

C) $\frac{\tanh x-\tanh y}{1-\tanh x\tan y}$

D) $\frac{\tanh x-\tanh y}{1+\tanh x\tan y}$

View Answer play_arrow
• question_answer205) The value of$sinh\text{ }3x$is

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

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

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

D) None of these

View Answer play_arrow
• question_answer206) Line$x+2y-8=0$is the perpendicular bisector of line AB and point B is (3, 5), then coordinates of A are

A) (2, 2)

B) (2, 1)

C) (1, 1)

D) (1, 2)

View Answer play_arrow
• question_answer207) The points A (8,5),$B(-7,-5)$and$C(-5,5)$are the vertices of a parallelogram, then its fourth vertex is

A) (15, 10)

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

C) (10, 15)

D) $(-4,\text{ }5)$

View Answer play_arrow
• question_answer208) $\frac{{{(\cos \theta +i\sin \theta )}^{5}}}{{{(\sin \theta +i\cos \theta )}^{7}}}$is equal to

A) $\sin 12\theta -i\cos 12\theta$

B) $-\sin 12\theta +i\cos 12\theta$

C) $-\sin 12\theta -i\cos 12\theta$

D) $\sin 12\theta +i\cos 12\theta$

View Answer play_arrow
• question_answer209) If$\sin \alpha +\sin \beta +\sin \gamma =0$and $cos\alpha +cos\beta +cos\gamma =0,$then $sin\text{ }2\alpha +sin\text{ }2\beta +sin\text{ }2\gamma$is equal to

A) $sin\text{ }2(\alpha +\beta +\gamma )$

B) $2sin(\alpha +\beta +\gamma )$

C) 1

D) 0

View Answer play_arrow
• question_answer210) If$2\cos \alpha =a+\left( \frac{1}{a} \right)$and$2\cos \beta =b+\left( \frac{1}{b} \right),$then $ab+\left( \frac{1}{ab} \right)$is equal to

A) $2\text{ }cos(\alpha +\beta )$

B) $2\text{ }\sin (\alpha +\beta )$

C) $2\text{ }cos(\alpha -\beta )$

D) $4\cos \alpha \cos \beta$

View Answer play_arrow
• question_answer211) If$A=\left[ \begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix} \right],a,b$are arbitrary scalars and$I$is an unit matrix of order$2\times 2,$then${{(aI+bA)}^{2}}$is equal to

A) ${{a}^{2}}I+{{b}^{2}}{{A}^{2}}$

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

C) ${{a}^{2}}I+2abA+{{b}^{2}}$

D) ${{a}^{2}}I+{{b}^{2}}A$

View Answer play_arrow
• question_answer212) If$A=\left[ \begin{matrix} 2 & -1 \\ 4 & 2 \\ \end{matrix} \right],B=\left[ \begin{matrix} 2 & 3 \\ 1 & 2 \\ \end{matrix} \right]$and$C=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right],$then$A+B-C$is equal to

A) $\left[ \begin{matrix} 3 & 2 \\ 5 & 3 \\ \end{matrix} \right]$

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

C) $\left[ \begin{matrix} 5 & 2 \\ 3 & 5 \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} 3 & 2 \\ 5 & 5 \\ \end{matrix} \right]$

View Answer play_arrow
• question_answer213) If${{A}^{T}}$and${{B}^{T}}$are transpose matrices of two square matrices A and B of order$2\times 2,$then${{(AB)}^{T}}$will be equal to

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

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

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

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

View Answer play_arrow
• question_answer214) ${{\tanh }^{-1}}x$ is equal to

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

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

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

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

View Answer play_arrow
• question_answer215) $cos\,{{h}^{-1}}x$ is equal to

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

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

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

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

View Answer play_arrow
• question_answer216) The real part of${{\cos }^{-1}}(\cos \theta +i\sin \theta )$is

A) ${{\cos }^{-1}}\sqrt{(\sin \theta )}$

B) ${{\sin }^{-1}}\sqrt{(\sin \theta )}$

C) $\sqrt{\theta }$

D) None of these

View Answer play_arrow
• question_answer217) The equation of line passes through the point (1,2) and perpendicular to the line$x+y+1=0,$is

A) $y-x+1=0$

B) $y-x+2=0$

C) $y-x-1=0$

D) $y-x-2=0$

View Answer play_arrow
• question_answer218) The value of the determinant $\left| \begin{matrix} a+1 & 1 & 1 \\ 1 & b+1 & 1 \\ 1 & 1 & c+1 \\ \end{matrix} \right|$is

A) $abc$

B) $ab+bc+ca+abc$

C) $ab+bc+ca$

D) $3(a+b+c)$

View Answer play_arrow
• question_answer219) If${{(1+i\sqrt{3})}^{9}}=a+ib,a,b\in R,$then the value of $b$is

A) 29

B) $-29$

C) 0

D) None of these

View Answer play_arrow
• question_answer220) ${{(1+\cos \theta +i\sin \theta )}^{3}}+{{(1-\cos \theta -i\sin \theta )}^{3}}$is equal to

A) ${{2}^{4}}{{\cos }^{3}}\left( \frac{\theta }{2} \right)\cos \left( \frac{3\theta }{2} \right)$

B) ${{2}^{3}}{{\cos }^{3}}\left( \frac{\theta }{2} \right)\cos \left( \frac{3\theta }{2} \right)$

C) ${{2}^{3}}{{\cos }^{3}}\left( \frac{\theta }{2} \right)\sin \left( \frac{3\theta }{2} \right)$

D) ${{2}^{4}}{{\cos }^{3}}\left( \frac{\theta }{2} \right)\sin \left( \frac{3\theta }{2} \right)$

View Answer play_arrow
• question_answer221) If$A=\left[ \begin{matrix} 1 & -2 & 3 \\ 0 & 2 & -1 \\ -2 & 5 & 2 \\ \end{matrix} \right],$then adj A is

A) $\left[ \begin{matrix} 9 & 19 & -4 \\ -4 & 8 & -1 \\ 4 & -1 & 2 \\ \end{matrix} \right]$

B) $\left[ \begin{matrix} 9 & 19 & 4 \\ -2 & 14 & 1 \\ -4 & 1 & x \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} 9 & 19 & -4 \\ 2 & 8 & 1 \\ 4 & -1 & 2 \\ \end{matrix} \right]$

D) None of these

View Answer play_arrow
• question_answer222) The value of$\left| \begin{matrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \\ \end{matrix} \right|$is

A) abc

B) 2abc

C) 4abc

D) 0

View Answer play_arrow
• question_answer223) How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?

A) 12

B) 24

C) 36

D) 48

View Answer play_arrow
• question_answer224) If sum of n terms of an AP is$2{{n}^{2}}+5n,$then its nth term is

A) $4n+3$

B) $4n+5$

C) $4n+7$

D) $4n+6$

View Answer play_arrow
• question_answer225) Harmonic mean of any two numbers is 4 and relation between their geometric mean and arithmetic mean is${{G}^{2}}+2A=27,$then these numbers are

A) 6, 3

B) 4, 27

C) 6, 7

D) 3, 9

View Answer play_arrow
• question_answer226) In a complex plane, the point z moves such that$|z-3i|=2$then its locus is

A) a straight line

B) a circle

C) y-axis

D) None of these

View Answer play_arrow
• question_answer227) The solutions of$|{{x}^{2}}-x-6|=x+2$are

A) $-2,\text{ }2,\text{ }4$

B) $-2,\text{ }2,-4$

C) 4, 3, 3

D) $3,\text{ }2,-2$

View Answer play_arrow
• question_answer228) The square root of$5-12i$is

A) $\pm (3+2i)$

B) $\pm (3-2i)$

C) $\pm (2+3i)$

D) $\pm (2-3i)$

View Answer play_arrow
• question_answer229) In a GP, second term is 2 and sum of infinite terms is 8, then its first term will be

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

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

C) 2

D) 4

View Answer play_arrow
• question_answer230) The roots of the equations${{x}^{2}}+ax+b=0$and ${{x}^{2}}+bx+a=0$are common and$a\ne b,$then$a+b$is equal to

A) 0

B) 1

C) $-1$

D) None of these

View Answer play_arrow
• question_answer231) In the expansion of${{\left( \frac{2{{x}^{2}}}{3}+\frac{3}{2{{x}^{2}}} \right)}^{10}},$the middle term is

A) 251

B) 252

C) 250

D) None of these

View Answer play_arrow
• question_answer232) The quadratic equation of real coefficients, whose one root is$7+5i,$will be

A) ${{x}^{2}}+14x+74=0$

B) ${{x}^{2}}-14x-74=0$

C) ${{x}^{2}}+14x-74=0$

D) ${{x}^{2}}-14x+74=0$

View Answer play_arrow
• question_answer233) If in the expansion of${{(x+a)}^{n}},$the sum of odd terms is P and sum of even terms is Q, then the value of${{({{x}^{2}}-{{a}^{2}})}^{n}}$is

A) ${{P}^{2}}+{{Q}^{2}}$

B) $4PQ$

C) ${{P}^{2}}-{{Q}^{2}}$

D) $2P-2Q$

View Answer play_arrow
• question_answer234) The value of determinant$\left| \begin{matrix} 4 & -6 & 1 \\ -1 & -1 & 1 \\ -4 & 11 & -1 \\ \end{matrix} \right|$is

A) 25

B) $-25$

C) 0

D) $-75$

View Answer play_arrow
• question_answer235) There are 10 points in a plane. If 4 points are collinear, then the number of straight lines obtained by joining these points is

A) 44

B) 45

C) 46

D) 40

View Answer play_arrow
• question_answer236) The value of$cos\,{{h}^{2}}x-sin\,{{h}^{2}}x$is

A) $cos\,h\text{ }2x$

B) 1

C) 0

D) None of these

View Answer play_arrow
• question_answer237) If${{y}^{2}}+xy-{{x}^{2}}=5,$then$\frac{dy}{dx}$is equal to

A) $\frac{2x+y}{x+2y}$

B) $\frac{2y+x}{2x-y}$

C) $\frac{2x-y}{2y+x}$

D) None of these

View Answer play_arrow
• question_answer238) If$f(x)=\left\{ \begin{matrix} x+1 & when\,x<2 \\ 2x-1, & when\,x\ge 2 \\ \end{matrix} \right.,$then at$a=2,f'(x)$is equal to

A) 10

B) 1

C) 2

D) does not exist

View Answer play_arrow
• question_answer239) $\underset{x\to 0}{\mathop{\lim }}\,\frac{|x|}{x}$is equal to

A) 1

B) $-1$

C) 0

D) does not exist

View Answer play_arrow
• question_answer240) The equation of the normal to the curve${{y}^{2}}=4\text{ }ax$at point$(a{{t}^{2}},2at)$is

A) $y-tx=a{{t}^{3}}+2at$

B) $y+tx=a{{t}^{3}}+2at$

C) $y-tx=a{{t}^{3}}-2at$

D) None of these

View Answer play_arrow
• question_answer241) Function$f(x)=|x|$is

A) discontinuous at$x=0$

B) discontinuous at $x=1$

C) continuous at all points

D) discontinuous at all points

View Answer play_arrow
• question_answer242) Function is defined as$f:x\to \frac{1+x}{1-x},$then$f\{f(x)\}$is equal to

A) $x$

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

C) $-x$

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

View Answer play_arrow
• question_answer243) If$y={{\sec }^{-1}}x,$then$\frac{dy}{dx}$is equal to

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

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

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

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

View Answer play_arrow
• question_answer244) The centroid of the triangle formed by the lines$x=0,x-y=3$and$2x+3y=6$is

A) $(3,-1)$

B) $(1,-3)$

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

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

View Answer play_arrow
• question_answer245) Three lines$3x+4y+6=0,$$\sqrt{2}x+\sqrt{3}y+2\sqrt{2}=0$and$4x+7y+8=0$are

A) sides of a triangle

B) concurrent

C) parallel

D) None of these

View Answer play_arrow
• question_answer246) The equation of circle concentric to the circle ${{x}^{2}}+{{y}^{2}}-3x+4y-2=0$and passes through the point$(-1,-2)$is

A) ${{x}^{2}}+{{y}^{2}}-3x-4y=0$

B) ${{x}^{2}}+{{y}^{2}}+3x-4y=0$

C) ${{x}^{2}}+{{y}^{2}}-3x+4y+\frac{25}{2}=0$

D) None of the above

View Answer play_arrow
• question_answer247) If$f(x)=\left\{ \begin{matrix} x, & x<0 \\ 1, & x=0 \\ {{x}^{2}}, & x>0 \\ \end{matrix} \right.,$then the true statement is

A) $\underset{x\to 0}{\mathop{\lim }}\,f(x)=1$

B) $\underset{x\to 0}{\mathop{\lim }}\,f(x)=0$

C) at$x=0,f(x)$is continuous

D) $\underset{x\to 0}{\mathop{\lim }}\,f(x)$does not exist

View Answer play_arrow
• question_answer248) $\underset{x\to a}{\mathop{\lim }}\,\frac{{{x}^{n}}-{{a}^{n}}}{x-a}$is equal to

A) 0

B) $n{{a}^{n-1}}$

C) $n{{a}^{n}}$

D) $\infty$

View Answer play_arrow
• question_answer249) The polar of the circle ${{x}^{2}}+{{y}^{2}}+2\lambda x+2\mu y+c=0$with respect to origin will touch${{x}^{2}}+{{y}^{2}}={{r}^{2}},$if

A) ${{r}^{2}}={{c}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})$

B) ${{c}^{2}}={{r}^{2}}({{\lambda }^{2}}+{{\mu }^{2}})$

C) $c=r({{\lambda }^{2}}+{{\mu }^{2}})$

D) $r=c({{\lambda }^{2}}+{{\mu }^{2}})$

View Answer play_arrow
• question_answer250) Equation of radical axis of the circles ${{x}^{2}}+{{y}^{2}}+4x+7=0$and$2{{x}^{2}}+2{{y}^{2}}+3x+5y+9=0$is

A) $x+y+1=0$

B) $x+y-1=0$

C) $x-y-1=0$

D) $x-y+1=0$

View Answer play_arrow
• question_answer251) Line$y=mx+\frac{a}{m}$is a tangent to the parabola ${{y}^{2}}=4\text{ }ax,$then the point of contact is

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

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

C) $(a{{m}^{2}},2am)$

D) None of these

View Answer play_arrow
• question_answer252) The coordinates of two points A and B are $(-1,2)$and$(2,-1)$respectively, then equation of circle AB as diameter, is

A) ${{x}^{2}}+{{y}^{2}}-x+y-4=0$

B) ${{x}^{2}}+{{y}^{2}}+x+y-4=0$

C) ${{x}^{2}}+{{y}^{2}}-x-y-4=0$

D) None of the above

View Answer play_arrow
• question_answer253) The equation of line joining the point (2, 3) to the point of intersection$2x+3y+1=0$and $3x-4y=8,$is

A) $3x+y-9=0$

B) $5x-y-7=0$

C) $5x+y-13=0$

D) $3x-y-3=0$

View Answer play_arrow
• question_answer254) The equation of a parabola is${{x}^{2}}=-10y,$then coordinates of focus are

A) $\left( 0,-\frac{5}{2} \right)$

B) $\left( 0,\frac{5}{2} \right)$

C) $\left( \frac{5}{2},0 \right)$

D) $\left( -\frac{5}{2},0 \right)$

View Answer play_arrow
• question_answer255) The equation of tangent to the parabola ${{y}^{2}}=8x$which is perpendicular to the line $2x-y+1=0,$is

A) $x+2y=8$

B) $x+2y+8=0$

C) $2x+y=8$

D) $2x+y+8=0$

View Answer play_arrow
• question_answer256) If vertex and focus of a parabola are (3, 3) and $(-3,3),$then its equation is

A) ${{(y+3)}^{2}}$$~=24(x+3)$

B) ${{(y+3)}^{2}}=-24(x+3)$

C) ${{(y-3)}^{2}}=-24(x-3)$

D) ${{(y-3)}^{2}}=24(x-3)$

View Answer play_arrow
• question_answer257) The equation of normal to the circle ${{x}^{2}}+{{y}^{2}}-4x+6y=0$at point (0, 0) is

A) $3x-2y=0$

B) $3x+2y=0$

C) $2x-3y=0$

D) $2x+3y=0$

View Answer play_arrow
• question_answer258) A circle touches the line$2x-y-1=0$at point (3,5). Its centre lies on the line$x+y=5,$then the coordinates of centre of circle are

A) $(-3,\text{ }8)$

B) (2, 3)

C) (3, 2)

D) None of these

View Answer play_arrow
• question_answer259) If ordinate of a point on the parabola${{y}^{2}}=64x$is 8, then the equation of tangent at this point is

A) $4x-y+4=0$

B) $4x+y+4=0$

C) $x+4y-4=0$

D) None of these

View Answer play_arrow
• question_answer260) The length of the double ordinate of the parabola${{x}^{2}}=8y$is 8. Then, the end points of this double ordinate are

A) $(4,2),(4,-2)$

B) $(2,4),(2,-4)$

C) $(4,2),(-4,2)$

D) $(-2,4),(2,4)$

View Answer play_arrow
• question_answer261) The area of the region bounded by the curve$y=\frac{3}{{{x}^{2}}},$$x-$axis and$x=1,\text{ }x=2$is

A) $1\,sq\,unit$

B) $3\,sq\,unit$

C) $2\,sq\,unit$

D) $\frac{3}{2}\,sq\,unit$

View Answer play_arrow
• question_answer262) The area of the region bounded by the curve $y=4+3x-{{x}^{2}}$and$x-$axis is

A) $\frac{125}{6}$sq units

B) $\frac{125}{3}$sq units

C) $\frac{125}{2}$ sq units

D) None of these

View Answer play_arrow
• question_answer263) $\int_{-1}^{1}{x\,{{\tan }^{-1}}x\,dx}$is equal to

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

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

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

D) None of these

View Answer play_arrow
• question_answer264) The value of$\int{\frac{dx}{\sqrt{(3-5x-{{x}^{2}})}}}$is

A) ${{\sin }^{-1}}\left( \frac{2x+5}{\sqrt{37}} \right)+c$

B) ${{\sinh }^{-1}}\left( \frac{2x+5}{\sqrt{37}} \right)+c$

C) ${{\sin }^{-1}}\left( \frac{2x+5}{37} \right)+c$

D) None of the above

View Answer play_arrow
• question_answer265) $\int{\frac{{{e}^{x}}}{{{e}^{x}}-1}}dx$is equal to

A) $\log ({{e}^{x}}-1)+c$

B) $-\log ({{e}^{x}}-1)+c$

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

D) None of these

View Answer play_arrow
• question_answer266) The value of $\int_{2}^{4}{\frac{\sqrt{{{x}^{2}}-4}}{x}}dx$ is

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

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

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

D) $2\sqrt{3}-\frac{2\pi }{3}$

View Answer play_arrow
• question_answer267) The value of$\int_{0}^{2/3}{\frac{dx}{4+9{{x}^{2}}}}$is

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

B) $\pi$

C) $0$

D) $\frac{\pi }{24}$

View Answer play_arrow
• question_answer268) $\int{\frac{t}{{{e}^{3{{t}^{2}}}}}}dt$is equal to

A) $\frac{1}{6}{{e}^{3{{t}^{2}}}}+c$

B) $-\frac{1}{5}{{e}^{3{{t}^{2}}}}+c$

C) $\frac{1}{6}{{e}^{-3{{t}^{2}}}}+c$

D) $-\frac{1}{6}{{e}^{-3{{t}^{2}}}}+c$

View Answer play_arrow
• question_answer269) The area of the region bounded by the curve $y=cos\text{ }x$and$x-$axis when$0<x\le 2\pi ,$will be

A) 4 sq units

B) 3 sq units

C) 2 sq units

D) 1 sq unit

View Answer play_arrow
• question_answer270) If$y=log\text{ }{{x}^{10}},$then$\frac{dy}{dx}$is equal to

A) $10{{x}^{2}}$

B) $\frac{10}{x}$

C) $10x$

D) None of these

View Answer play_arrow
• question_answer271) ${{e}^{x}}\sin y-{{e}^{y}}\cos x=1,$then$\frac{dy}{dx}$is equal to

A) $\frac{\sin y+{{e}^{y-x}}\sin x}{\cos y-{{e}^{y-x}}\cos x}$

B) $\frac{\cos y-{{e}^{y-x}}\cos x}{\sin y+{{e}^{y-x}}\sin x}$

C) $\frac{\cos y+{{e}^{y-x}}\cos x}{\sin y-{{e}^{y-x}}\sin x}$

D) $\frac{\sin y+{{e}^{y-x}}\sin x}{{{e}^{y-x}}\cos x-\cos y}$

View Answer play_arrow
• question_answer272) If$y=\frac{\sec x+\tan x}{\sec x-\tan x},$then$\frac{dy}{dx}$is equal to

A) $2\text{ }sec\text{ }x{{(sec\text{ }x+tan\text{ }x)}^{2}}$

B) $2\text{ }sec\text{ }x{{(sec\text{ }x-tan\text{ }x)}^{2}}$

C) $2\,sec\,x$

D) None of the above

View Answer play_arrow
• question_answer273) The equation of the normal to the curve $y=x(2-x)$at point (2, 0) is

A) $x-2y=2$

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

C) $2x+y=0$

D) $2x+y-4=0$

View Answer play_arrow
• question_answer274) The length of subnormal to the curve${{y}^{2}}=4x$ at any point is

A) 2

B) $\frac{{{y}^{2}}}{2}$

C) $2{{y}^{2}}$

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

View Answer play_arrow
• question_answer275) If$x=a{{t}^{2}},\text{ }y=2at,$then the value of$\frac{dy}{dx}$at$t=2$ is

A) 2

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

C) 0

D) None of these

View Answer play_arrow
• question_answer276) If$y=\sqrt{\left( \frac{1+x}{1-x} \right)},$then$\frac{dy}{dx}$is equal to

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

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

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

D) None of these

View Answer play_arrow
• question_answer277) If$y={{(x-2)}^{x}},$then$\frac{dy}{dx}$is equal to

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

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

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

D) None of the above

View Answer play_arrow
• question_answer278) The points on the curve$y=12x-{{x}^{3}}$at which the slope of the tangent will be zero, are

A) $(2,-16),(-2,16)$

B) (3, 10), (0, 10)

C) $(2,16),(-2,-16)$

D) None of these

View Answer play_arrow
• question_answer279) The value of$\int{{{\sec }^{4}}xdx}$is

A) $\tan x+\frac{1}{3}{{\sec }^{3}}x+c$

B) $\frac{1}{6}\tan x+{{\sec }^{3}}x+c$

C) $\tan x-\frac{1}{3}{{\sec }^{3}}x+c$

D) None of these

View Answer play_arrow
• question_answer280) The function$f(x)=\frac{1}{3}{{x}^{3}}+\frac{1}{2}{{x}^{2}}-6x+8$is decreasing in the interval

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

B) $(2,\infty )$

C) $(-3,2)$

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

View Answer play_arrow
• question_answer281) The point of inflexion on the curve$y={{x}^{5/3}}$ will be

A) (0, 0)

B) (1, 0)

C) (0, 1)

D) does not exist

View Answer play_arrow
• question_answer282) The value of$\int{\frac{{{({{x}^{2}}+8)}^{2}}}{{{x}^{4}}}}dx$is equal to

A) $x+\frac{16}{x}+\frac{64}{3{{x}^{2}}}+c$

B) $x-\frac{16}{x}-\frac{64}{3{{x}^{3}}}+c$

C) $x-\frac{32}{{{x}^{3}}}-\frac{256}{3{{x}^{2}}}+c$

D) None of these

View Answer play_arrow
• question_answer283) The value of$\int{\frac{\tan xdx}{\sec x+\cos x}}$is

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

B) $-{{\tan }^{-1}}(\cos x)+c$

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

D) None of these

View Answer play_arrow
• question_answer284) If$x$and y are two variables such that$xy=1,\text{ }x>1,$then the minimum value of$x+y$ will be

A) 1

B) 2

C) 3

D) 4

View Answer play_arrow
• question_answer285) The maximum value of$sin\text{ }x+cos\text{ }x$is

A) $2$

B) $\sqrt{2}$

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

D) 1

View Answer play_arrow
• question_answer286) The value of$\int{{{\sec }^{3}}\theta d\theta }$is

A) $\frac{1}{2}log\text{(}sec\theta +tan\theta )+\frac{1}{2}sec\theta tan\theta +c$

B) $log(sec\theta +tan\theta )+sec\theta tan\theta +c$

C) $log(sec\theta -tan\theta )+\frac{1}{2}sec\theta tan\theta +c$

D) None of the above

View Answer play_arrow
• question_answer287) The value of$\int{\frac{4x-7}{{{x}^{2}}+x-2}}dx$is

A) $\log ({{x}^{2}}+x-2)+3\left( \frac{x-1}{x+2} \right)+c$

B) $2\log ({{x}^{2}}+x-2)-3\log \left( \frac{x+1}{x+2} \right)+c$

C) $2\log ({{x}^{2}}+x-2)-3\log \left( \frac{x-1}{x+2} \right)+c$

D) None of the above

View Answer play_arrow
• question_answer288) A man draws a card from a pack of 52 playing cards, replace it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times, is

A) $\frac{9}{64}$

B) $\frac{1}{64}$

C) $\frac{1}{16}$

D) $\frac{9}{16}$

View Answer play_arrow
• question_answer289) Two dice are thrown together. The probability of getting the sum 7 is

A) $\frac{7}{36}$

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

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

D) None of these

View Answer play_arrow
• question_answer290) The projection of vector$2\hat{i}+3\hat{j}-2\hat{k}$ on the vector $\hat{i}+2\hat{j}+3\hat{k}$is

A) $\frac{1}{\sqrt{14}}$

B) $\frac{2}{\sqrt{14}}$

C) $\frac{2}{\sqrt{17}}$

D) None of these

View Answer play_arrow
• question_answer291) The probability that a leap year will have 53 Sundays, is

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

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

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

D) $\frac{1}{7}$

View Answer play_arrow
• question_answer292) If$[\overrightarrow{a}+\overrightarrow{b}]=[\overrightarrow{a}-\overrightarrow{b}],$then the vectors$\overrightarrow{a}$and$\overrightarrow{b}$are

A) parallel

B) perpendicular

C) collinear

D) coplanar

View Answer play_arrow
• question_answer293) If the adjacent sides of a parallelogram are represented by$\overrightarrow{a}=3\hat{i}+\hat{j}+2\hat{k}$and $\overrightarrow{b}=2\hat{i}-2\hat{j}+4\hat{k},$then its area will be

A) $8\sqrt{3}$ sq units

B) 8 sq units

C) $8\sqrt{2}$sq units

D) None of these

View Answer play_arrow
• question_answer294) If$\overrightarrow{a}=\hat{i}+2\hat{j}-\hat{k}$and$\overrightarrow{b}=2\hat{i}+\hat{j}+\hat{k},$then the angle between 1st and b will be

A) $30{}^\circ$

B) $45{}^\circ$

C) $60{}^\circ$

D) $90{}^\circ$

View Answer play_arrow
• question_answer295) Six boys and six girls are sitting in a row. The probability that all 6 girls sit together, is

A) $\frac{1}{102}$

B) $\frac{1}{112}$

C) $\frac{1}{122}$

D) $\frac{1}{132}$

View Answer play_arrow
• question_answer296) The value of$\underset{x\to 0}{\mathop{\lim }}\,\left[ \frac{{{e}^{x}}-{{e}^{\sin x}}}{x-\sin x} \right]$is

A) $-1$

B) 0

C) 1

D) None of these

View Answer play_arrow
• question_answer297) The number of terms in the expansion of ${{(a+b+c)}^{10}}$is

A) 11

B) 21

C) 55

D) 66

View Answer play_arrow
• question_answer298) The eccentricity of the conjugate hyperbola of the hyperbola${{x}^{2}}-3{{y}^{2}}=1$is

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

B) 4

C) $2$

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

View Answer play_arrow
• question_answer299) The value of$\int_{0}^{\pi }{\frac{x\,dx}{1+\sin x}}$is

A) $-\pi$

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

C) $\pi$

D) None of these

View Answer play_arrow
• question_answer300) Harmonic mean of the two numbers$\frac{a}{1-ab}$and $\frac{a}{1+ab}$is

A) $\frac{1}{1-{{a}^{2}}{{b}^{2}}}$

B) $\frac{a}{1-{{a}^{2}}{{b}^{2}}}$

C) $a$

D) $\frac{a}{\sqrt{1-{{a}^{2}}{{b}^{2}}}}$

View Answer play_arrow

LIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!

You need to login to perform this action.
You will be redirected in 3 sec