# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2006

### done J and K - CET Engineering Solved Paper-2006

• question_answer1) Vector which is perpendicular to $a\,\,\cos \,\theta \,\,\hat{i}+b\,\sin \,\theta \,\,\hat{j}$ is

A) $b\,\sin \,\theta \,\hat{i}-a\,\cos \,\theta \,\hat{j}$

B) $\frac{1}{a}\,\sin \,\theta \,\hat{i}-a\,\cos \,\theta \,\hat{j}$

C) $5\hat{k}$

D) All of the above

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• question_answer2) Which of the following statements is true?

A) When the coordinate axes are translated the component of a vector in a plane changes

B) When the coordinate axes are rotated through some angle components of the vector change but the vector's magnitude remains constant

C) Sum of $\vec{a}$and $\vec{b}$ is $\vec{R}$. If the magnitude of $\vec{a}$alone is increased angle between $\vec{b}$ and $\vec{R}$ decreases

D) The cross product of $3\,\,\hat{i}$ and $4\,\,\hat{j}$ is 12

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• question_answer3) From a balloon rising vertically upwards as $5\text{ }m/s$a stone is thrown up at 10 m/s relative to the balloon. Its velocity with respect to ground after $2\text{ }s$is (assume$g=10\text{ }m/{{s}^{2}}$)

A) zero

B) $5\text{ }m/s$

C) $10\text{ }m/s$

D) $20\text{ }m/s$

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• question_answer4) Two bodies are projected from ground with equal speed $20\text{ }m/s$from the same position in the same vertical plane to have equal range but at different angles above the horizontal. If one of the angle is 30? the sum of their maximum heights is (assume$g=10\text{ }m/{{s}^{2}}$)

A) $400\,\,m$

B) $20\,\,m$

C) $30\,\,m$

D) $40\,\,m$

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• question_answer5) Which of the following quantities measured from different inertial reference frames are same?

A) Force

B) Velocity

C) Displacement

D) Kinetic energy

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• question_answer6) Two particles of equal mass are connected to a rope AB of negligible mass, such that one is at end A and the other dividing the length of the rope in the ratio $1:2$ from B. The rope is rotated about end B in a horizontal plane. Ratio of the tensions in the smaller part to the other is (ignore effect of gravity)

A) $4:3$

B) $1:4$

C) $1:2$

D) $1:3$

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• question_answer7) Angle of banking for a vehicle speed of $10\text{ }m/s$ for a radius of curvature $10\text{ }m$is (assume$g=10\text{ }m/{{s}^{2}}$)

A) ${{30}^{o}}$

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

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

D) ${{45}^{o}}$

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• question_answer8) A body of mass $2\text{ }kg$is projected at $20\text{ }m/s$at an angle ${{60}^{o}}$ above the horizontal. Power due to the gravitational force at its highest point is

A) $200\text{ }W$

B) $100\sqrt{3\,}W$

C) $50\,W$

D) zero

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• question_answer9) A block of mass $2\text{ }kg$rests on a horizontal surface. If a horizontal force of $5\text{ }N$is applied on the block the frictional force on, it is $({{\mu }_{k}}=0.4,\,\,{{\mu }_{s}}=0.5)$

A) $5\,\,N$

B) $10\,\,N$

C) $8\,\,N$

D) zero

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• question_answer10) Three idential spheresof mass M each are placed at the comers of an equilateral triangle of side $2m$. Taking one of the comer as the origin, the position vector of the centre of mass is

A) $\sqrt{3}\,\,(\hat{i}-\hat{j})$

B) $\frac{i}{\sqrt{3}}+\hat{j}$

C) $\frac{\hat{i}+\hat{j}}{3}$

D) $\hat{i}+\frac{{\hat{j}}}{\sqrt{3}}$

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• question_answer11) A shell initially at rest explodes into two pieces of equal mass, the two pieces will

A) move with different velocities in different Directions

B) move with the same velocity in opposite directions

C) move with the same velocity in the same direction

D) be at rest

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• question_answer12) Impulse is

A) a scalar

B) equal to change in the momentum of a body

C) equal to rate of change of momentum of a body

D) a force

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• question_answer13) In a head on elastic collision of a very heavy body moving at V with a light body at rest, velocity of heavy body after collision is

A) $V$

B) $2\,V$

C) zero

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

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• question_answer14) A T Joint is formed by two identical rods A and B each of mass m and length L in the XY plane as shown. Its moment of inertia about axis coinciding with A is A) $\frac{2\,m{{L}^{2}}}{3}$

B) $\frac{\,m{{L}^{2}}}{12}$

C) $\frac{\,m{{L}^{2}}}{6}$

D) None of these

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• question_answer15) A disc of moment of inertia $5\text{ }kg-{{m}^{2}}$is acted upon by a constant torque of$40\text{ }Nm$. Starting from rest the time taken by it to acquire an angular velocity of 24 rad/s is

A) $3\text{ }s$

B) $\text{4 }s$

C) $2.5\,\,s$

D) $120\,\,s$

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• question_answer16) If the angular momentum of a rotating body about a fixed axis is increased by$10%$. Its kinetic energy will be increased by

A) $10%$

B) $20%$

C) $21%$

D) $5%$

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• question_answer17) If the earth were to spin faster, acceleration due to gravity at the poles

A) increases

B) decreases

C) remains the same

D) depends on how fast it spins

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• question_answer18) The time period of an artificial satellite in a circular orbit is independent of

A) the mass of the satellite

B) radius of the orbit

C) mass of the earth and radius of the earth

D) None of the above

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• question_answer19) Angle of contact of a liquid with a solid depends on

A) solid only

B) liquid only

C) both on solid and liquid

D) orientation of the solid surface in liquid

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• question_answer20) If longitudinal strain for a wire is $0.03$ and its Poisson's ratio is $0.5,$ then its lateral strain is

A) $0.003$

B) $0.0075$

C) $0.015$

D) $0.4$

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• question_answer21) When the temperature increases, the viscosity of

A) gas decreases and liquid increases

B) gas increases and liquid decreases

C) gas and liquid increases

D) gas and liquid decreases

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• question_answer22) Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is p at a point where flow speed is v, the pressure at another point where the flow of speed is $2\text{ }v,$is (take density of water as p)

A) $p-\frac{3\,\rho {{v}^{2}}}{2}$

B) $p-\frac{\,\rho {{v}^{2}}}{2}$

C) $p-\frac{3\,\rho {{v}^{2}}}{4}$

D) $p-\rho {{v}^{2}}$

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• question_answer23) Which of the following statements is true?

A) Internal energy of a gas depends only on the state of the gas

B) In an isothermal process change in internal energy is maximum

C) Area under pressure, volume graph equals heat supplied in any process

D) Work done is state dependent but not path dependent

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• question_answer24) A gas $\left( \gamma =\frac{5}{3} \right),$ expands isobaric ally. The percentage, of heat supplied that increases thermal energy and that involved in doing work for expansion is

A) $40:60$

B) $60:40$

C) $50:50$

D) $25:30$

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• question_answer25) A perfect black body is one whose emissive power is

A) maximum

B) zero

C) unity

D) minimum

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• question_answer26) A black body at a temperature T radiates energy at E. If the temperature falls to $\frac{T}{2},$ the radiated energy will be

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

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

C) $2E$

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

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• question_answer27) If the units of mass, length and time are doubled unit of angular momentum will be .

A) doubled

B) tripled

C) quadrupled

D) 8 times the original value

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• question_answer28) Which of the following graphs shows variation of potential energy (U) with position x?

A) B) C) D) View Answer play_arrow
• question_answer29) Choose the correct statement

A) Time period of a simple pendulum depends on amplitude

B) Time shown by a spring watch varies with acceleration due to gravity

C) In a simple pendulum time period varies linearly with the length of the pendulum

D) The graph between length of the pendulum and time period is a parabola

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• question_answer30) Time period of a spring mass system is T. If this spring is cut into two parts whose lengths are in the ratio $1:3$ and the same mass is attached to the longer part, the new time period will be

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

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

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

D) $\sqrt{3}T$

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• question_answer31) Equation of progressive wave is $y=A\,\sin \left( 10\,\pi x+11\pi t+\frac{\pi }{3} \right)$

A) its wavelength is $2\text{ }units$

B) it is travelling in the positive x-direction

C) wave velocity is $1.5\text{ }units$

D) time period of SHM is 1 s

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• question_answer32) The phenomenon of sound propagation in air is

A) isothermal process

B) isobaric process

C) adiabatic process

D) None of the above

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• question_answer33) The second overtone of an open pipe is in resonance with the first overtone of a closed pipe of length $2\,m$. Length of the open pipe is

A) $4\,m$

B) $2\,m$

C) $8\,m$

D) $1\,m$

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• question_answer34) Choose the correct statement

A) Beats are due to destructive interference

B) Maximum beat frequency audible to a human being is 20

C) Beats are as a result of Doppler?s effect

D) Beats are due to superposition of two waves of nearly equal frequencies

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• question_answer35) A motor car is approaching towards a crossing with a velocity of$72\text{ }km/h$. The frequency of sound of its horn as heard by a policeman standing on the crossing is$260\text{ }Hz$. The frequency of horn is

A) $200\text{ }Hz$

B) $244\text{ }Hz$

C) $150\text{ }Hz$

D) $80\text{ }Hz$

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• question_answer36) Forces exerted by a uniform electric field on an electron having mass ${{m}_{e}}$ and proton of mass ${{m}_{p}}$are represented as ${{F}_{e}}$ and ${{F}_{p}}$ respectively are related as

A) ${{F}_{p}}={{F}_{e}}$

B) $\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{{{m}_{e}}}{{{m}_{p}}}$

C) $\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{{{m}_{p}}}{{{m}_{e}}}$

D) $\frac{{{F}_{e}}}{{{F}_{p}}}=\frac{m_{e}^{2}}{m_{p}^{2}}$

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• question_answer37) Electric field strength due to a dipole at a point on the axial line of dipole is

A) from positive charge to negative charge

B) from negative charge to positive charge

C) along the equatorial line

D) at an angle to axial line

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• question_answer38) Potential and field strength at a certain distance from a point charge are $600\text{ }V$and$200\text{ }N/C$. Distance of the point from the charge is

A) $2\,m$

B) $4\,m$

C) $8\,m$

D) $3\,m$

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• question_answer39) Two identical spheres with charges $4q,-2q$ kept some distance apart exert a force F on each other. If they are made to touch each other and replaced at their old positions, the force between them will be

A) $\frac{1}{9}F$

B) $\frac{1}{8}F$

C) $\frac{9}{8}F$

D) $\frac{8}{9}F$

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• question_answer40) Two capacitors each of capacity $2\mu F$ are connected in parallel. If they are connected to $100\text{ }V$battery, then energy stored in them is

A) $0.02\text{ }J$

B) $0.04\text{ }J$

C) $0.01\text{ }J$

D) $200\text{ }J$

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• question_answer41) Which factor is immaterial for the wire used in electric fuse?

A) Length

B) Radius

C) Material

D) Current

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• question_answer42) A battery of emf $2\text{ }V$and internal resistance $0.1\Omega$ is being charged by a current of $~5\text{ }A$. The potential difference between the terminals of the battery is

A) $2.5\text{ }V$

B) $1.5\text{ }V$

C) $0.5V$

D) $1\,\,V$

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• question_answer43) An electric bulb is rated at $220\text{ }V,$ $200\text{ }W;$ Power consumed by it when operated at $110\text{ }V$is

A) $25\text{ }W$

B) $50\text{ }W$

C) $75\text{ }W$

D) $90\text{ }W$

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• question_answer44) two cells having emf $4\text{ }V,$ $2\text{ }V$and internal resistances $1\,\Omega ,$ $1\,\,\Omega$ are connected as shown in figure below. Current through $6\,\,\Omega$ resistance is A) $\frac{1}{3}A$

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

C) $1\,\,A$

D) $\frac{2}{9}\,\,A$

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• question_answer45) For a given thermocouple neutral temperature

A) is a constant

B) depends on cold junction temperature

C) depends on inversion temperature

D) double that of cold junction temperature

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• question_answer46) A charged particle enters a uniform magnetic field with a certain speed at right angles to it. In the magnetic field a change could occur in its

A) kinetic energy

B) angular momentum

C) linear momentum

D) speed

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• question_answer47) A coil having 500 turns of square shape each of side $10\text{ }cm$is placed normal to a magnetic field which is increasing at $1\text{ }T/s$. The induced emf is

A) $0.1\text{ }V$

B) $0.5\,\,V$

C) $1\,\,V$

D) $-5\,\,V$

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• question_answer48) A galvanometer has a resistance $50\,\,\Omega$. A resistance of $5\,\,\Omega$ is connected parallel to it. Fraction of the total current flowing through galvanometer is

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

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

C) $\frac{1}{50}$

D) $\frac{2}{15}$

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• question_answer49) A wire oriented in the east-west direction carries a current eastward. Direction of the magnetic field at a point to the south of the wire is

A) vertically down

B) vertically up

C) north-east

D) south-east

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• question_answer50) An inductor is connected to an AC source, When compared to voltage, the current in the lead wires

A) is ahead in phase by n

B) lags in phase by n

C) is ahead in phase by ?

D) lags in phase by ?

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• question_answer51) Curie temperature is the one above which

A) paramagnetic substance changes to ferromagnetic

B) paramagnetic changes to diamagnetic

C) diamagnetic changes to paramagnetic

D) ferromagnetic changes to paramagnetic

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• question_answer52) Energy in a current carrying coil is stored in the form of

A) electric field

B) magnetic field

C) heat

D) None of the above

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• question_answer53) Graph of force per unit length between two long parallel currents carrying conductor and the distance between them is

A) straight line

B) parabola

C) ellipse

D) rectangular hyperbola

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• question_answer54) A bar magnet is held at right angles to a uniform magnetic field. The couple acting on the magnet is to be halved by rotating it from this position. The angle of rotation is

A) ${{60}^{o}}$

B) ${{45}^{o}}$

C) ${{30}^{o}}$

D) ${{75}^{o}}$

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• question_answer55) A point source of light is kept below the surface of water in a pond

A) light emerges from every point of the surface of the pond

B) no light is transmitted from the surface of the pond

C) all the light emitted by the source emerges from a circular region of the pond

D) some of the light emitted by the source emerges from a circular region of the pond

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• question_answer56) If white light is used in Young's double slit experiment

A) no interference pattern is formed

B) white fringes are formed

C) central bright fringe is white

D) central bright fringe is coloured

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• question_answer57) Electromagnetic waves can be deflected by

A) electric fields only

B) magnetic fields only

C) Both [a] and [b]

D) None of the above

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• question_answer58) Maximum lateral displacement of a ray of light incident on a slab of thickness t is

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

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

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

D) $t$

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• question_answer59) Mercury vapour lamp gives

A) continuous spectrum

B) line spectrum

C) band spectrum

D) absorption spectrum

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• question_answer60) Pick the correct statement from the following

A) Primary rainbow is a virtual image and secondary rainbow is a real image

B) Primary rainbow is a real image and secondary rainbow is a virtual image

C) Both primary and secondary rainbows are virtual images

D) Both primary and secondary rainbows are real images

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• question_answer61) The refractive index of water, glass and diamond are $1.33,1.50,\text{ }2.40$respectively. The refractive index of diamond relative to water and of glass relative to diamond, respectively are nearly

A) $1.80,0.625$

B) $0.554,\text{ }0.625$

C) $1.80,\text{ }1.6$

D) $0.554,\text{ }1.6$

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• question_answer62) In the diffraction pattern of a single slit

A) all bands are uniformly bright

B) all bands are uniformly wide

C) central band is narrower

D) central band is wider

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• question_answer63) A radioactive substance has a half-life of four months. Three-fourth of the substance will decay in

A) $3\text{ }months$

B) $4\text{ }months$

C) $~8\text{ }months$

D) $\text{12 }months$

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• question_answer64) Electrons in the atom are held to the nucleus by

A)  Coulomb's forces

B)  nuclear forces

C)  van der Waals' forces

D)  gravitational forces

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• question_answer65) Mass of the nucleons together in a heavy nucleus is

A) greater than mass of nucleus

B) equal to mass of nucleus

C) same as mass of nucleus

D) None of the above

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• question_answer66) Ratio of the radii of the nuclei with mass numbers 8 and 27 would be

A) $27/8$

B) $8/27$

C) $2/3$

D) $3/2$

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• question_answer67) Stopping potential required to reduce the photoelectric current to zero

A) is directly proportional to the wavelength of the incident radiation

B) increases uniformly with wavelength of the incident radiation

C) is directly proportional to the frequency of the incident radiation

D) decreases uniformly with the frequency of the incident radiation

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• question_answer68) The first member of the Ballmer?s series of the hydrogen has a wavelength $\lambda ,$ the wavelength of the second member of its series is

A) $\frac{27}{20}\lambda$

B) $\frac{20}{27}\lambda$

C) $\frac{27}{20}\lambda$

D) None of these

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• question_answer69) The photoelectric threshold frequency of a metal is v. When light of frequency $4v$ is incident on the metal. The maximum kinetic energy of the emitted photoelectrons is

A) $4\,\,hv$

B) $3\,\,hv$

C) $5\,\,hv$

D) $\frac{5}{2}\,\,hv$

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• question_answer70) The shortest wavelength in Lyman series is$91.2\text{ }nm$. The longest wavelength of the series is

A) $121.6\text{ }nm$

B) $182.4\text{ }nm$

C) $243.4\text{ }nm$

D) $364.8\text{ }nm$

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• question_answer71) Energy gap of a semiconductor is of the order of

A) $1\,\,eV$

B) $10\,\,eV$

C) $0.1\text{ }eV$

D) None of these

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• question_answer72) Majority charge carriers in p-type material are

A) holes

B) electrons

C) Both and

D) None of the above

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• question_answer73) Resistance of a semiconductor

A) increases with increase in temperature

B) decreases with increase in temperature

C) is not affected by change in temperature

D) increases for germanium and decreases for silicon

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• question_answer74) Semiconductor material having fewer free electrons than pure germanium or silicon is

A) p-type

B) n-type

C) Both [a] and [b]

D) None of the above

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• question_answer75) The concentrations of impurities in a transistor are

A) equal for the emitter, base and collector regions

B) least for the emitter region

C) largest for the emitter region

D) least for the base region

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• question_answer76) At $\text{25}{{\,}^{\text{o}}}\text{C}$, the total pressure of an ideal solution obtained by mixing 3 moles of 'A? and 2 moles of 'B? is 184 Ton". What is the vapour pressure (in Torr) of pure 'B' at the same temperature? (vapour pressure of pure 'A? at $25{{\,}^{o}}C,$ is 200 Torr)

A) 180

B) 160

C) 16

D) 100

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• question_answer77) Relative lowering of vapour pressure of a dilute solution is 0.2. What is the mole fraction of the non-volatile solute?

A) 0.8

B) 0.5

C) 0.3

D) 0.2

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• question_answer78) Match the following List ?A? List ?B? (1) $PhC{{O}_{2}}C{{H}_{3}}$ [A]$2,4-\text{DNP}$ (2) ${{C}_{6}}{{H}_{5}}C{{H}_{2}}C{{O}_{2}}H$ [B] Arndt-Eistert synthesis (3)${{C}_{6}}{{H}_{5}}CHO$ [C] Hydrolysis Correct answer is

A) $1-A,\,2-B,\,3-C$

B) $1-B,\,2-C,\,3-A$

C) $1-C,\,2-B,\,3-A$

D) $1-B,\,2-A,\,3-C$

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• question_answer79) 2-pentanone and 3-methyl-2-butanone are a pair of....... isomers.

A) functional

B) chain

C) positional

D) stereo

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• question_answer80) What are the units of entropy?

A) $\text{cal K}$

B) $\text{Cal}\,{{\text{K}}^{-1}}$

C) $\text{cm}\,{{\text{K}}^{-1}}$

D) $\text{ }\!\!~\!\!\text{ cmK}$

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• question_answer81) Calculate $\Delta H$(in Joules) for, C (graphite) $\to C$(diamond), from the following data C(graphite)$+\,{{O}_{2}}(g)\to C{{O}_{2}}(g);$ $\Delta H=-393.5\,kJ$ C (diamond)$+\,{{O}_{2}}(g)\to C{{O}_{2}}(g);$ $\Delta H=-395.4\,kJ$

A) $1,900$

B) $~-788.9\times {{10}^{3}}$

C) $1,90,000$

D) $~+\,788.9\times \,{{10}^{3}}$

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• question_answer82) $C{{H}_{2}}Br+\bar{O}H\xrightarrow{{}}C{{H}_{3}}OH+B{{r}^{-}}$reaction proceeds by${{S}_{N}}2-$mechanism. Its rate is dependent on the concentration of

A) $C{{H}_{3}}Br,\bar{O}H$

B) $C{{H}_{3}}Br$only

C) $~\bar{O}H$ only

D) $~C{{H}_{3}}Br,C{{H}_{3}}OH$

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• question_answer83) The end products in the Cannizaro reaction of benzaldehyde is

A) $~PhC{{O}_{2}}H,PhC{{H}_{2}}OH$

B) $~PhC{{O}_{2}}H,PhC{{H}_{2}}C{{O}_{2}}H$

C) $PhC{{H}_{2}}OH,PhCOC{{H}_{3}}$

D) $PhCO{{}_{2}}H,PhCOC{{H}_{3}}$

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• question_answer84) For a chemicalreaction, the free energy change $(\Delta G)$ is negative. The reaction is

A) a spontaneous reaction

B) an equilibrium reaction

C) a non-spontaneous reaction

D) characterised by${{r}_{f}}-{{r}_{b}}$ (where${{r}_{f}}$and${{r}_{b}}$ are rates of forward and backward reactions respectively)

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• question_answer85) In which of the following reactions, the heat liberated is known as "heat of combustion"?

A) ${{H}^{+}}(aq)+O{{H}^{-}}(aq)\to {{H}_{2}}O(l)+heat$

B) $C\text{(graphite)}+\frac{1}{2}{{O}_{2}}(g)\to CO(g)+\text{heat}$

C) $C{{H}_{4}}(g)+2{{O}_{2}}(g)\to C{{O}_{2}}(g)+2{{H}_{2}}O(l)+\,heat$

D) ${{H}_{2}}S{{O}_{4}}(aq)+{{H}_{2}}O(l)\to {{H}_{2}}S{{O}_{4}}(aq)+heat$

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• question_answer86) The number of chiral centres in $(+)-$glucose

A) 4

B) 3

C) 2

D) 1

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• question_answer87) Aniline on oxidation with $\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{r}}_{\text{2}}}{{\text{O}}_{\text{7}}}$and ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$gives

A) benzoic acid

B) $m-$ amino benzoic acid

C) Schiff?s base

D) $~p-$ benzoquinone

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• question_answer88) What are the units of equivalent conductivity of a solution?

A) $\text{mho c}{{\text{m}}^{-1}}$

B) $\text{ohm c}{{\text{m}}^{-1}}\text{ g equi}{{\text{v}}^{-1}}$

C) $\text{mho c}{{\text{m}}^{-2}}\text{ g equi}{{\text{v}}^{-1}}$

D) $\text{mho c}{{\text{m}}^{2}}\text{ g equi}{{\text{v}}^{-1}}$

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• question_answer89) What is the cell reaction occurring in Daniel cell (Galvanic cell)?

A) $Cu(s)+ZnS{{O}_{4}}(aq)\to CuS{{O}_{4}}(aq)+Zn(s)$

B) $Zn(s)+CuS{{O}_{4}}(aq)\to Cu(s)+ZnS{{O}_{4}}(aq)$

C) $Ni(s)+ZnS{{O}_{4}}(aq)\to NiS{{O}_{4}}(aq)+Zn(s)$

D) $2Na(s)+CdS{{O}_{4}}(aq)\to N{{a}_{2}}S{{O}_{4}}(aq)$$+\,Cd(s)$

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• question_answer90) $n-$propylamine yields a volatile compound X on warming with ale. alkali and chloroform. X has an offensive odour. The structure of X is

A) $~C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}CN$

B) $~{{(C{{H}_{3}})}_{2}}CHCN$

C) $~C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}NC$

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

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• question_answer91) The molecular formula of benzonitrile is

A) ${{C}_{6}}{{H}_{5}}CN$

B) ${{C}_{6}}{{H}_{5}}NC$

C) ${{C}_{6}}{{H}_{5}}CNO$

D) ${{C}_{6}}{{H}_{5}}NCO$

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• question_answer92) Which of the following statements (or equation) is correct?

A) The units of cell emf are$\text{V}\text{.c}{{\text{m}}^{-1}}$

B) $\Delta G=-\frac{nF}{{{E}_{cell}}}$

C) In Galvanic cell, chemical energy is transformed into electrical energy

D) Oxidation state of Mn in potassium permanganate is + 6

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• question_answer93) Which of the following metal can be obtained by the electrolysis of the aqueous solution of its salts?

A) Cu

B) Na

C) Mg

D) K

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• question_answer94) The magnetic moment (in BM) of $\text{Z}{{\text{n}}^{\text{2+}}}$ion according to spin-only formula is

A) zero

B) 1.73

C) 2.84

D) 3.87

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• question_answer95) The 3d-block element that exhibits maximum number of oxidation states is

A) Sc

B) Ti

C) Mn

D) Zn

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• question_answer96) Which of the following molecule in its valence shell has three bond pairs of electrons and one lone pair of electrons?

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

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

C) $~B{{F}_{3}}$

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

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• question_answer97) Which of the following set of properties belong to$PC{{l}_{5}}$?

A) $s{{p}^{3}},$ tetrahedral, 4 valence shell pairs of electrons

B) trigonal bipyramidal, 5 valence shell pairs of electrons

C) $s{{p}^{3}}{{d}^{2}},$octahedral, 6 valence shell pairs of electrons

D) $s{{p}^{3}}d,$square planar, 4 valence shell pairs of electrons

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• question_answer98) The metal ion in complex $\underset{\scriptscriptstyle-}{A}$has BAN identical to the atomic number of krypton. $\underset{\scriptscriptstyle-}{A}$is (At. no. of$Cr=24,\,Fe=26,\,Pd=46$)

A) $[Pd{{(N{{H}_{3}})}_{6}}]C{{l}_{4}}$

B) $[Cr{{(N{{H}_{3}})}_{5}}Cl]S{{O}_{4}}$

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

D) ${{K}_{3}}[Fe{{(CN)}_{6}}]$

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• question_answer99) The complex that does not give a precipitate wit$\text{ }\!\!~\!\!\text{ AgN}{{\text{O}}_{\text{3}}}$solution

A) $[Co{{(N{{H}_{3}})}_{3}}C{{l}_{3}}]$

B) $[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}$

C) $\text{ }\!\![\!\!\text{ Ag(N}{{\text{H}}_{\text{3}}}{{\text{)}}_{\text{2}}}\text{ }\!\!]\!\!\text{ Cl}$

D) $[Cr{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]Cl$

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• question_answer100) According to bond order concept, the correct order of stability of${{\text{O}}_{\text{2}}}\text{,O}_{\text{2}}^{\text{+}}$ and $\text{O}_{2}^{-}$ is

A) ${{O}_{2}}>O_{2}^{+}>O_{2}^{-}$

B) $O_{2}^{-}>{{O}_{2}}>O_{2}^{+}$

C) ${{O}_{2}}>O_{2}^{-}>O_{2}^{+}$

D) $O_{2}^{+}>{{O}_{2}}<O_{2}^{-}$

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• question_answer101) Zero dipole moment is possessed by

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

B) $~B{{F}_{3}}$

C) $Cl{{F}_{3}}$

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

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• question_answer102) The number of moles of ions given on complete ionisation of one mole of $[Co{{(N{{H}_{3}})}_{6}}]C{{l}_{3}}$ is/are

A) 4

B) 3

C) 2

D) 1

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• question_answer103) The coordination number in a/an........ complex may increase to 8.

A) cobalt

B) osmium

C) nickel

D) iron

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• question_answer104) The radius ratio $\left( \frac{{{r}^{+}}}{{{r}^{-}}} \right)$ of an ionic solid$({{A}^{+}}{{B}^{-}})$is 0.69. What is the coordination number of${{B}^{-}}$?

A) 6

B) 8

C) 2

D) 10

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• question_answer105) A, B and C are ideal gases. Their molecular weights are 2, 4 and 28 respectively. The ran of diffusion of these gases follow the order

A) $C>A>B$

B) $~C>B>A$

C) $A=B=C$

D) $~A>B>C$

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• question_answer106) Among the following ions (hydrated), the colourless metal ion is

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

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

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

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

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• question_answer107) German silver is an alloy of

A) $Cu,Zn$

B) $~Cu,Ni,\,Zn$

C) $~Cu,Sn,Zn$

D) $~Cu,Zn$

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• question_answer108) Which of the following Statements is not correct?

A) The units of surface tension are dynes $c{{m}^{-1}}$

B) The units of viscosity coefficient of a liquid are "poise"

C) $\text{CsCl}$crystallizes in body centred cubic type of lattice

D) The coordination number of ${{\text{S}}^{2-}}$in ZnS is 6

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• question_answer109) Which of the following is not a method of preparation of colloidal solution?

A) Electrical dispersion

B) Peptization

C) Coagulation

D) Mechanical dispersion

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• question_answer110) Pauling's equation for determining the electronegativity of an element, is

A) ${{X}_{A}}-{{X}_{B}}=0.208\sqrt{\Delta }$

B) ${{X}_{A}}+{{X}_{B}}=0.208\sqrt{\Delta }$

C) ${{X}_{A}}-{{X}_{B}}=0.208{{\Delta }^{2}}$

D) ${{X}_{A}}-{{X}_{B}}=\sqrt{\Delta }$ ${{X}_{A}},{{X}_{B}}=$electronegativity values of elements AandB $\Delta =$represents polarity of $A-B$bond

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• question_answer111) The ionic radii$(\overset{\text{o}}{\mathop{A}}\,)$of ${{C}^{4-}}$and${{O}^{2-}}$respectively are 2.60 and 1.40. The ionic radius of th6 isoelectronic ion ${{N}^{3-}}$would be

A) 2.6

B) 1.71

C) 1.4

D) 0.95

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• question_answer112) The gold numbers of some colloidal solution are given below Colloidal solution Gold number A 0.01 B 2.5 C 20 The protective nature of these colloidal solutions follow the order

A) $~C>B>A$

B) $~A>B>C$

C) $~A=B=C$

D) $~B>A>C$

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• question_answer113) Which of the following reaction is an example for homogeneous catalysis?

A) $2{{H}_{2}}{{O}_{2}}(l)\xrightarrow{Mn{{O}_{2}}(s)}2{{H}_{2}}O(l)+{{O}_{2}}(g)$

B) $2S{{O}_{2}}(g)+{{O}_{2}}(g)2S{{O}_{3}}(g)$

C) $2CO(g)+{{O}_{2}}(g)\xrightarrow{NO(g)}2C{{O}_{2}}(g)$

D) ${{H}_{2}}(g)+{{C}_{2}}{{H}_{4}}(g)\xrightarrow{Ni(s)}{{C}_{3}}{{H}_{6}}(g)$

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• question_answer114) Consider the following abbreviations for hydrated alkali ions $X={{[Li{{({{H}_{2}}O)}_{n}}]}^{+}}$ $X={{[K{{({{H}_{2}}O)}_{n}}]}^{+}}$ $Z={{[Cs{{({{H}_{2}}O)}_{n}}]}^{+}}$ What is the correct order of size of these hydrated alkali ions?

A) $~X>Y>Z$

B) $~Z>Y>X$

C) $~X=Y=Z$

D) $~Z>X>Y$

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• question_answer115) What is the product formed when phosphorus trioxide is dissolved in water?

A) $~HP{{O}_{3}}$

B) $~{{H}_{3}}P{{O}_{4}}$

C) $~{{H}_{3}}P{{O}_{3}}$

D) $~HP{{O}_{2}}$

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• question_answer116) The molecular formula of dithionic acid is

A) $~{{H}_{2}}{{S}_{2}}{{O}_{4}}$

B) $~{{H}_{2}}{{S}_{2}}{{O}_{6}}$

C) $~{{H}_{2}}{{S}_{2}}{{O}_{5}}$

D) ${{H}_{2}}{{S}_{2}}{{O}_{7}}$

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• question_answer117) The bond dissociation energy of $\text{C}{{\text{l}}_{\text{2}}}\text{, B}{{\text{r}}_{\text{2}}}$and ${{\text{I}}_{\text{2}}}$follow the order

A) $~C{{l}_{2}}>{{I}_{2}}>B{{r}_{2}}$

B) ${{I}_{2}}>B{{r}_{2}}>C{{l}_{2}}$

C) ${{I}_{2}}=C{{l}_{2}}=B{{r}_{2}}$

D) $C{{l}_{2}}>B{{r}_{2}}>{{I}_{2}}$

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• question_answer118) During the extraction of copper, the impurity $(FeS)$is removed as slag by mixing the contaminated copper ore with silica and coke. The molecular formula of slag is

A) $~FeSi{{O}_{3}}$

B) $~F{{e}_{2}}{{O}_{3}}$

C) $FeSi$(solid)

D) $~FeSi$ (vapour)

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• question_answer119) Which of the following is used as indelible ink?

A) Aqueous $\text{CuS}{{\text{O}}_{\text{4}}}$solution

B) Aqueous $\text{AgN}{{\text{O}}_{\text{3}}}$solution

C) Aqueous $\text{NaCl}$solution

D) Aqueous $\text{NaOH}$solution

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• question_answer120) Which of the following ore is an ore of copper?

A) Argentite

B) Haematite

C) Malachite

D) Calamine

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• question_answer121) $\text{KMn}{{\text{O}}_{\text{4}}}(mol\,wt.=158)$oxidizes oxalic acid in acid medium to $\text{C}{{\text{O}}_{\text{2}}}$and water as follows $5{{C}_{2}}O_{4}^{2-}+2MnO_{4}^{-}+16{{H}^{+}}\to 10C{{O}_{2}}+2M{{n}^{2+}}$$\text{+}\,\,\text{8}{{\text{H}}_{\text{2}}}\text{O}$ What is the equivalent weight of$\text{KMn}{{\text{O}}_{\text{4}}}$?

A) 158

B) 31.6

C) 39.5

D) 79

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• question_answer122) Sodium bicarbonate on heating decomposes to form sodium carbonate, $\text{C}{{\text{O}}_{\text{2}}}$and water. If 0.2 moles of sodium bicarbonate is completely decomposed, how many moles of sodium carbonate is formed?

A) 0.1

B) 0.2

C) 0.05

D) 0.025

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• question_answer123) What is the energy (in eV) required to excite the electron from$n=1$to$n=2$state in hydrogen atom? ($n=$principal quantum number)

A) 13.6

B) 3.4

C) 17.0

D) 10.2

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• question_answer124) According to aufbau principle, the correct order of energy of 3d, 4s and 4p orbitals is

A) $~4p<3d<4s$

B) $~4s<4p<3d$

C) $~4s<3d<4p$

D) $~3d<4s<4p$

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• question_answer125) $n-$pentane and 2-methylbutane are a pair of

A) enantiomers

B) stereoisomers

C) diastereomers

D) constitutional isomers

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• question_answer126) Compound can exhibit

A) geometrical isomerism

B) tautomerism

C) optical isomerism

D) geometrical and optical isomerism

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• question_answer127) The activity of a radioactive nuclide is $2\times {{10}^{7}}$ disintegrations per minute (dpm). After 23.03 min, its activity is reduced to$2\times {{10}^{6}}\text{ dpm}\text{.}$ What is the average life (in min) of this nuclide?

A) 100

B) 10

C) 1

D) 0.1

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• question_answer128) What' is the correct order of velocity of alpha $(\alpha ),$beta $(\beta )$and gamma$(\gamma )$rays?

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

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

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

D) $\gamma >\beta >\alpha$

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• question_answer129) The isomers which are interconverted through rotation around a single bond are

A) conformers

B) diastereomers

C) enantiomers

D) position isomers

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• question_answer130) The major product in the reaction of 2-butyne with $\text{Li/liq}\text{.N}{{\text{H}}_{\text{3}}}$is

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

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

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• question_answer131) What is X in the following nuclear reaction? $_{11}N{{a}^{23}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{11}}N{{a}^{24}}+X$

A) ${{\,}_{1}}{{H}^{1}}$

B) ${{\,}_{2}}H{{e}^{4}}$

C) ${{\,}_{1}}{{H}^{2}}$

D) $\gamma -$ray (gamma ray)

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• question_answer132) HA is a weak acid. The pH of 0.1 M HA solution is 2. What is the degree of dissociation $(\alpha )$of HA?

A) 0.5

B) 0.2

C) 0.1

D) 0.301

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• question_answer133) In the following reaction, A and B, respectively are $A\xrightarrow{\text{HBr}}{{C}_{2}}{{H}_{5}}Br\xrightarrow{B}A$

A) ${{C}_{2}}{{H}_{4}},alc\,KOH/\Delta$

B) ${{C}_{2}}{{H}_{5}}Cl,aq\,KOH/\Delta$

C) $C{{H}_{3}}OH,aq\,KOH/\Delta$

D) ${{C}_{2}}{{H}_{2}},PB{{r}_{3}}$

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• question_answer134) The reagent(s) used in the preparation of aspirin from salicylic acid

A) $\text{SOC}{{\text{l}}_{\text{2}}}\text{,}$pyridine

B) ${{\text{(C}{{\text{H}}_{3}}\text{CO)}}_{2}}O,{{H}^{+}}$

C) $C{{H}_{3}}C{{O}_{2}}H,HCl$

D) $C{{H}_{3}}Cl,AlC{{l}_{3}}$

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• question_answer135) The equilibrium reaction that is not influenced by volume change at constant temperature is

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

B) ${{N}_{2}}(g)+3{{H}_{2}}(g)2N{{H}_{3}}(g)$

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

D) $2NO(g)+{{O}_{2}}2N{{O}_{2}}(g)$

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• question_answer136) Consider the following solutions of equal concentrations $A=N{{H}_{4}}Cl$ $B=C{{H}_{3}}COONa$ $C=N{{H}_{2}}OH$ $D=C{{H}_{2}}COOH$ A buffer solution can be obtained by mixing equal volumes of

A) C and D

B) A and B

C) A and C

D) C and D

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• question_answer137) In the following reaction, X and Y respectively are ${{C}_{2}}{{H}_{5}}OH\xrightarrow{KMn{{O}_{4}}/{{H}^{+}}}X\frac{Y}{{{H}_{2}}S{{O}_{4}}/\Delta }C{{H}_{3}}C{{O}_{2}}{{C}_{2}}{{H}_{5}}$

A) $C{{H}_{3}}OH,{{C}_{2}}{{H}_{5}}OH$

B) $~C{{H}_{3}}CHO,C{{H}_{3}}OH$

C) $~C{{H}_{3}}C{{O}_{2}}H,\text{ }{{C}_{2}}{{H}_{5}}OH$

D) $~{{C}_{2}}{{H}_{4}},C{{H}_{3}}CO{{}_{2}}H$

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• question_answer138) The reaction conditions used for converting 1, 2-dibromopropane to propylene are

A) $KOH,alcohol/\Delta$

B) $KOH,\text{ }water/\Delta$

C) $~Zn,\text{ }alcohol/\Delta$

D) $~Na,\text{ }alcohol/\Delta$

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• question_answer139) Which of the following's a Lewis acid?

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

B) $C{{l}^{-}}$

C) $CO$

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

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• question_answer140) If "a" and$''{{t}_{1/2}}''$ are initial concentration of reactant and half-life of a zero order reaction respectively, which of the following is correct?

A) ${{t}_{1/2}}\propto \frac{1}{a}$

B) ${{t}_{1/2}}\propto a$

C) ${{t}_{1/2}}\propto \frac{1}{{{a}^{2}}}$

D) ${{t}_{1/2}}\propto {{a}^{2}}$

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• question_answer141) All monosaccharides ....... Tollen's reagent.

A) oxidises

B) condense with

C) reduces

D) add to

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• question_answer142) The product formed in the reaction of glycine with benzoyl chloride $\text{+ aq NaOH}$is

A) $~PhCOC{{H}_{2}}N{{H}_{2}}$

B) $~PhC{{H}_{2}}N{{H}_{2}}$

C) $~PhCONHC{{H}_{3}}$

D) $~PhCONHC{{H}_{2}}C{{O}_{2}}H$

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• question_answer143) The rate constant of a reaction is found to be $3\times {{10}^{-3}}\,mol\,{{L}^{-1}}\,{{\min }^{-1}}.$The order of the reaction is

A) zero

B) 1

C) 2

D) 1.5

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• question_answer144) What is the two third life of a first order reaction having $k=5.48\times {{10}^{-14}}{{s}^{-1}}$

A) $2.01\times {{10}^{11}}s$

B) $2.01\times {{10}^{13}}s$

C) $8.08\times {{10}^{13}}\,s$

D) $16.04\times {{10}^{11}}\,s$

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• question_answer145) Which of the following solvents are aprotic? [A]$N{{H}_{3}}$ [B]$S{{O}_{2}}$ [C] $C{{H}_{3}}CN$ [D] $C{{H}_{3}}C{{O}_{2}}H$

A) $A,B,C$

B) $A,C,D$

C) $B,C$

D) $A,C$

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• question_answer146) Chlorobenzene is o, p -directing in electrophilic substitution reaction. The directing influence is explained by

A) $+\text{ }M$of$Ph$

B) $+\,I$of $Cl$

C) $+\text{ }M$of$Cl$

D) $-I$of $Ph$

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• question_answer147) 5 L of a solution contains$\text{25}\,\text{mg}$ of $\text{CaC}{{\text{O}}_{3}}.$What is its concentration in ppm? (mol. wt. of $\text{CaC}{{\text{O}}_{\text{3}}}$is 100)

A) 25

B) 1

C) 5

D) 2500

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• question_answer148) Observe the following abbrevations ${{\pi }_{obs}}=$observed colligative property ${{\pi }_{cal}}=$theoretical colligative property assuming normal behaviour of solute. van't Hoff factor $(i)$is given by

A) $i={{\pi }_{obs}}\times {{\pi }_{cal}}$

B) $i={{\pi }_{obs}}+{{\pi }_{cal}}$

C) $i={{\pi }_{obs}}-{{\pi }_{cal}}$

D) $i=\frac{{{\pi }_{obs}}}{{{\pi }_{cal}}}$

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• question_answer149) The correct order for homolytic bond dissociation energies ($\Delta H$in kcal/mol) for $C{{H}_{4}}(A),{{C}_{2}}{{H}_{6}}(B)$and$C{{H}_{3}}Br(C),$under identical experimental conditions

A) $C>B>A$

B) $B>C>A$

C) $~C>A>B$

D) $~A>B>C$

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• question_answer150) $RX+{{I}^{-}}\xrightarrow{{}}R-I+X$is an example of....... reaction.

A) nucleophilic addition

B) nucleophilic substitution

C) electrophilic addition

D) elimination

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• question_answer151) If $a{{x}^{3}}+b{{x}^{2}}+ex+d=0$has a repeated root $\alpha ,$ then a is also a root of

A) $3a{{x}^{2}}+2bx+d=0$

B) $a{{x}^{2}}+b\,x+c=0$

C) $3a{{x}^{2}}+2bx+c=0$

D) $6ax+2b=0$

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• question_answer152) If the roots of ${{x}^{3}}-3{{x}^{2}}-6x+8=0$ are in arithmetic progression, then the roots of the equation are

A) $3,4,5$

B) $4,7,10$

C) $-2,1,4$

D) $1,4,7$

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• question_answer153) If $\alpha ,\beta ,\gamma$ are the roots of the cubic equation ${{x}^{3}}-{{x}^{2}}+x-1=0,$then ${{\alpha }^{-3}}+{{\beta }^{-3}}+{{\gamma }^{-3}}$ is equal to

A) $1$

B) $2$

C) $3$

D) $4$

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• question_answer154) If $\alpha ,\beta ,\gamma$ are the roots of ${{x}^{3}}+bx+c=0,$then ${{\alpha }^{2}}\beta +\alpha {{\beta }^{2}}+{{\beta }^{2}}\gamma +{{\gamma }^{2}}\alpha +\gamma {{\alpha }^{2}}$ is equal to

A) $c$

B) $-c$

C) $-3c$

D) $3c$

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• question_answer155) $\underset{x\to \infty }{\mathop{\lim }}\,(\sqrt{x+\sqrt{x}}-\sqrt{x})$

A) $-1/2$

B) $1/2$

C) $1$

D) $0$

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• question_answer156) $\underset{x\to 1}{\mathop{\lim }}\,\frac{2{{x}^{2}}+x-3}{3{{x}^{2}}+2x-2}$is equal to

A) $1$

B) $2$

C) $-1$

D) $-2$

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• question_answer157) $\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\sin }^{-1}}x-x}{{{x}^{3}}\,\cos x}$is equal to

A) $1/2$

B) $1/3$

C) $1/6$

D) $1/12$

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• question_answer158) If $f:R\to R$ given by $f(x)=\left\{ \begin{matrix} 2\,\cos x, & if & x\le -\frac{\pi }{2} \\ a\,\sin \,x+b, & if & -\frac{\pi }{2}<x<\frac{\pi }{2} \\ 1+{{\cos }^{2}}x, & if & x\ge \frac{\pi }{2} \\ \end{matrix} \right.$ is a continuous function on R, then (a, b) is equal to

A) $(1/2,\,1/2)$

B) $(0,-1)$

C) $(0,2)$

D) $(1,0)$

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• question_answer159) \frac{d}{dx}\left\{ \begin{align} & {{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)+{{\tan }^{-1}}\left( \frac{3x-{{x}^{2}}}{1-3{{x}^{2}}} \right) \\ & -{{\tan }^{-1}}\left( \frac{4x-4{{x}^{2}}}{1-6{{x}^{2}}+{{x}^{4}}} \right) \\ \end{align} \right\}equal to

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

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

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

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

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• question_answer160) If $2{{x}^{2}}-3xy+{{y}^{2}}+x-2y-8=0,$then $\frac{dy}{dx}$ is equal to

A) $\frac{3y-4x-1}{2y-3x-2}$

B) $\frac{3y+4x-1}{2y+3x+2}$

C) $\frac{3y+4x+1}{2y-3x+2}$

D) $\frac{3y+4x+1}{2y-3x-2}$

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• question_answer161) The equation of the tangent at $(1,5)$ to the curve $y=5{{x}^{4}}$ is

A) $20x-y=15$

B) $x+20y=101$

C) $20x+y=15$

D) $x-20y=101$

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• question_answer162) The length of the sub tangent at any point $({{x}_{1}},\,{{y}_{1}})$ on the curve $y={{a}^{x}},$$(a>0)$ is

A) $2\,\,\log \,a$

B) $1/\,\,\log \,a$

C) $\log \,a$

D) ${{a}^{{{2}_{{{x}_{1}}}}}}\log \,a$

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• question_answer163) The set $\{{{x}^{3}}-12x:-3\le x\le 3\}$ is equal to

A) $\{x:-16\le x\le 16\}$

B) $\{x:-12\le x\le 12\}$

C) $\{x:-9\le x\le 9\}$

D) $\{x:0\le x\le 10\}$

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• question_answer164) The set of all local maxima for $y=\cos \,\,x$is

A) $\{n\pi :n\in I\}$

B) $\{2n\pi :n\in I\}$

C) $\{n\pi /2:n\in I\}$

D) $\{n\pi /3:n\in I\}$

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• question_answer165) The absolute maximum of ${{x}^{40}}-{{x}^{20}}$on the interval $[0,1]$ is

A) $-1/4$

B) $0$

C) $1/4$

D) $1/2$

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• question_answer166) $\int_{-2}^{2}{(x-|x|)}\,\,dx$ is equal to

A) $0$

B) $2$

C) $4$

D) $-4$

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• question_answer167) If $\int{\frac{dx}{x\,\log \,x}}=f(x)+$ constant, then $f(x)$ is equal to

A) $1/\,\log \,x$

B) $\log \,x$

C) $\log \,\,\log \,x$

D) $x/\,\log \,x$

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• question_answer168) If $\int{\text{cosec x}\,\text{dx =f(x)+}}$ constant, then $f(x)$ is equal to

A) $\tan \,x/2$

B) $\log \,|\tan \,(x/2)|$

C) $\log |\sin \,x|$

D) $\log |cos\,x|$

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• question_answer169) ${{I}_{n}}=\int{{{\tan }^{n}}x}\,\,dx$ for $n\ge 2,$ then ${{I}_{n}}+{{I}_{n-2}}$ is equal to

A) ${{\tan }^{n\,}}x+c$

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

C) $\frac{{{\tan }^{n}}x}{n}+c$

D) $n\,\,{{\tan }^{n}}x+c$

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• question_answer170) $\int_{0}^{\pi /2}{x\,\sin \,x}\,\,dx$is equal to

A) $0$

B) $1$

C) $-1$

D) $2$

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• question_answer171) The area (in square unit) of the region bounded by the y-axis and the curve $2x={{y}^{2}}-1$is

A) $1/3$

B) $2/3$

C) $1$

D) $2$

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• question_answer172) The solution of the differential equation $({{x}^{2}}+{{y}^{2}})dx=2xy\,\,dy$is

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

B) $c({{x}^{2}}-{{y}^{2}})=x$

C) ${{x}^{2}}-{{y}^{2}}=cy$

D) ${{x}^{2}}+{{y}^{2}}=cx$ (here c is an arbitrary constant)

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• question_answer173) A number n is chosen at random from the set $\{11,12,13,.....30\}.$The probability that n is neither divisible by 3 nor divisible by 5 is

A) $7/20$

B) $9/20$

C) $11/20$

D) $13/20$

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• question_answer174) The probability that a number n chosen at random from 1 to 30, to satisfy $n+(50/n)>27$is

A) $7/30$

B) $3/10$

C) $3/5$

D) $1/5$

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• question_answer175) If a random variable X has the distribution given below, then the value of c is

 $x=k$ $-2$ $-1$ $0$ $1$ $2$ $3$ $P(X=k)$ $\frac{1}{10}$ $\frac{1}{10}$ $2c$ $\frac{3}{10}$ $\frac{1}{5}$ $c$

A) $1/5$

B) $2/5$

C) $1/10$

D) $3/10$

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• question_answer176) A random variable X can attain only the value 1, 2, 3, 4, 5 with respective probabilities k, 2k, 3k, 2k, k. If m is the mean of the probability distribution, then (k, m) is equal to

A) $(3,\,1/9)$

B) $(\,1/9,3)$

C) $(\,1/8,4)$

D) $(\,1,3)$

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• question_answer177) If $f(x)=\lambda {{e}^{-ax}}\,\,(a>0)$ for $0\le x<\infty$ is a probability density, then 'k is equal to

A) $a$

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

C) $1/a$

D) ${{a}^{2}}$

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• question_answer178) Two unbiased dice are thrown simultaneously- The probability to get a sum more than 8 is

A) $5/36$

B) $5/18$

C) $5/12$

D) $2/9$

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• question_answer179) The moment generating function of a random variable X is

A) $E({{e}^{-1X}})$

B) $E({{e}^{itX}})$

C) $E({{e}^{tX}})$

D) $E({{e}^{-it\,X}})$

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• question_answer180) It $\sigma$ is the standard deviation of a random variable X, then the standard deviation of the random variable $aX+b,$where $a,\text{ }b\in R$is

A) $a\sigma +b$

B) $|a|\sigma$

C) $|a|\sigma +b$

D) ${{a}^{2}}\sigma$

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• question_answer181) If A and B are two sets, then $A-(A-B)$is equal to

A) $B$

B) $A\cup B$

C) $A\cap B$

D) $B-A$

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• question_answer182) For any real number y the greatest integers not exceeding y is denoted by [y]. If $f:R\to R$ is defined by $f(x)=[2x]-2[x]$ for $x\in R,$ then the range of f is

A) $\{x\in R:x>0\}$

B) $\{x\in R:x\le 0\}$

C) $\{x\in R:0\le x\le 1\}$

D) $\{0,\,1\}$

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• question_answer183) The argument of $\frac{1+i\sqrt{3}}{1-i\sqrt{3}}$ is

A) $2\pi /3$

B) $\pi /3$

C) $-\pi /3$

D) $-2\pi /3$

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• question_answer184) If $S=\left\{ z\in C:\arg \left( \frac{z-2}{z+2} \right)=\frac{\pi }{3} \right\},$ then S is

A) an ellipse

B) a straight line.

C) a circle

D) a parabola

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• question_answer185) If $ac\ne 0$ and $\alpha ,\beta$ are the roots of the equation $a{{x}^{2}}+bx+c=0,$then the quadratic equation with $1/\alpha$ and $1/\beta$ as its root is

A) ${{x}^{2}}/a+x/b+1/c=0$

B) $c{{x}^{2}}+bx+a=0$

C) $b{{x}^{2}}+cx+a=0$

D) $a{{x}^{2}}+cx+b=0$

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• question_answer186) If $\left\{ {{a}_{n}} \right\}_{n}^{x}$ is a sequence with ${{a}_{0}}=p$ and ${{a}_{n}}-{{a}_{n-1}}=r{{a}_{n-1}}$ for $n\ge 1,$ then the terms of the sequence are in

A) an arithmetic progression

B) a geometric progression

C) a harmonic progression

D) an arithmetico-geometric progression

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• question_answer187) The coefficient of ${{x}^{-17}}$in the expansion of ${{\left( {{x}^{4}}-\frac{1}{{{x}^{3}}} \right)}^{15}}$is

A) $^{15}{{C}_{11}}$

B) $^{15}{{C}_{12}}$

C) $^{-15}{{C}_{11}}$

D) $^{-15}{{C}_{3}}$

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• question_answer188) The term independent of x in the expansion of ${{\left( {{x}^{3}}+\frac{2}{{{x}^{2}}} \right)}^{15}}$ is

A) ${{T}_{7}}$

B) ${{T}_{8}}$

C) ${{T}_{9}}$

D) ${{T}_{10}}$

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• question_answer189) The ortho centre of the $\Delta \,OAB,$where O is the origin,$A(6,0)$ and $B(3,\,3\sqrt{3})$ is

A) $(9/2,\,\sqrt{3}/2)$

B) $(3,\,\sqrt{3})$

C) $(\,\sqrt{3},3)$

D) $(3,-\sqrt{3})$

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• question_answer190) The distance between the pair of parallel lines given by ${{x}^{2}}-1005x+2006=0$is

A) $1001$

B) $1000$

C) $1005$

D) $2006$

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• question_answer191) The radical axis of the coaxial system of circles with limiting points $(1,2)$ and $(-2,1)$ is

A) $x+3y=0$

B) $3x+y=0$

C) $2x+3y=0$

D) $3x+2y=0$

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• question_answer192) The equation of the circle that can be inscribed in the square OABC, where O is the origin $A(-2,0),\,B(-2,2)$ and $C(0,2)$ is

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

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

C) ${{x}^{2}}+{{y}^{2}}+2x-2y-1=0$

D) ${{x}^{2}}+{{y}^{2}}-2x+2y+1=0$

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• question_answer193) The curve with parametric equation $x={{e}^{t}}+{{e}^{-t}}$ and $y={{e}^{t}}-{{e}^{-t}}$ is

A) a circle

B) an ellipse

C) a hyperbola

D) a parabola

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• question_answer194) If $(-1,\,2\sqrt{2})$ is one of extremity of a focal chord of the parabola ${{y}^{2}}=-8x,$ then the other extremity is

A) $(-1,-\sqrt{2})$

B) $(2\sqrt{2},-1)$

C) $(-4,4\sqrt{2})$

D) $(4,4\sqrt{2})$

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• question_answer195) The equation of the pair of straight lines perpendicular to the pair $2{{x}^{2}}+3xy+2{{y}^{2}}+10x+5y=0$ and passing through the origin is

A) $2{{x}^{2}}+5xy+2{{y}^{2}}=0$

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

C) $2{{x}^{2}}+3xy+{{y}^{2}}=0$

D) $2{{x}^{2}}-5xy+2{{y}^{2}}=0$

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• question_answer196) If two angles of a triangle are ${{45}^{o}}$ and ${{\tan }^{-1}}(2),$ then the third angle is

A) ${{60}^{o}}$

B) ${{75}^{o}}$

C) ${{\tan }^{-1}}3$

D) ${{90}^{o}}$

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• question_answer197) $\frac{\tan A}{1+\sec A}+\frac{1+\sec A}{\tan A}$is equal to

A) $2\text{ }sin\text{ }A$

B) $2\text{ }cos\text{ }A$

C) $2\text{ }cosec\text{ }A$

D) $2\text{ }sec\text{ }A$

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• question_answer198) If $\sin \theta +\cos \theta =h,$ then the quadratic equation having $\sin \theta$ and $\cos \theta$ as its roots is

A) ${{x}^{2}}-hx+({{h}^{2}}-1)=0$

B) $2{{x}^{2}}-2hx+({{h}^{2}}-1)=0$

C) ${{x}^{2}}-hx+2({{h}^{2}}-1)=0$

D) ${{x}^{2}}-2hx+({{h}^{2}}-1)=0$

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• question_answer199) In a triangle, if ${{r}_{1}}+{{r}_{3}}=k\,\,{{\cos }^{2}}\,B/2,$then k is equal to

A) $R$

B) $2R$

C) $3R$

D) $4R$

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• question_answer200) If $\tan (k+1)\theta =\tan \theta ,$ then $\theta$ belongs to the set

A) $\{n\pi :n\in I\}$

B) $\{n\pi /2:n\in I\}$

C) $\{n\pi /k:n\in I\}$

D) $\{n\pi /2k:n\in I\}$

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• question_answer201) ${{\tan }^{-1}}\left( \frac{3x-{{x}^{3}}}{1-3{{x}^{2}}} \right)-{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)$ is equal to

A) $0$

B) $1$

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

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

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• question_answer202) If $sin\text{ }A:sin\text{ }B:sin\text{ }C=3:4:5,$ then $cos\text{ }A:cos\text{ }B$is equal to

A) $4:3$

B) $5:3$

C) $3:4$

D) $3:5$

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• question_answer203) If A is a matrix such that ${{A}^{2}}=A+I,$where I is the unit matrix, then ${{A}^{5}}$is equal to

A) $5A+I$

B) 5A + 21

C) $5A+3I$

D) $5A+4I$

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• question_answer204) The inverse of $\left[ \begin{matrix} 0 & 0 & 2 \\ 0 & 2 & 0 \\ 2 & 0 & 0 \\ \end{matrix} \right]$ is

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

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

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

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

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• question_answer205) $\left| \begin{matrix} 1 & 2 & 3 \\ {{1}^{3}} & {{2}^{3}} & {{3}^{3}} \\ {{1}^{5}} & {{2}^{5}} & {{3}^{5}} \\ \end{matrix} \right|$ equal to

A) $1!\,\,2\,\,1\,\,\,3$

B) $1\,\,!\,\,\,3\,\,!\,\,\,5\,\,!$

C) $6\,\,!$

D) $9\,\,!$

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• question_answer206) $\left| \begin{matrix} a & b & a+b \\ b & a+b & a \\ a+b & a & b \\ \end{matrix} \right|$ is equal to

A) ${{a}^{3}}+{{b}^{3}}$

B) $-({{a}^{3}}+{{b}^{3}})$

C) $2\,({{a}^{3}}+{{b}^{3}})$

D) $-2\,({{a}^{3}}+{{b}^{3}})$

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• question_answer207) If $A\left[ \begin{matrix} a & b & 0 \\ -b & a & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right],$ where ${{a}^{2}}+{{b}^{2}}=1,$ then adj is equal to

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

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

C) $A$

D) $-A$ (Here, ${{A}^{T}}$ is the transpose of A)

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• question_answer208) If A is a non-singular matrix such that ${{A}^{3}}=A+I,$ then the inverse of $B={{A}^{6}}-{{A}^{5}}$is

A) $A$

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

C) $-A$

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

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• question_answer209) The value of $\lambda$ such that $x+3y+\lambda z=0,$$2x+4y-z=0,\,\,\,\,\,\,\,x+5y-2z=0$has a non-trivial solution is

A) $-1$

B) $0$

C) $1$

D) $2$

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• question_answer210) If $A=\left[ \begin{matrix} 0 & -3 & -4/3 \\ 3 & 0 & -1/4 \\ 4/3 & 1/4 & 0 \\ \end{matrix} \right],$ then det $(A+{{A}^{T}})$ is equal to

A) $0$

B) $1$

C) $2$

D) $3$

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• question_answer211) If the position vector of A with respect to O is $3\hat{i}-2\hat{j}+4\hat{k}$and $\overrightarrow{AB}=3\hat{i}-\hat{j}+\hat{k},$ then the position vector of B with respect to 0 is

A) $-\hat{j}+3\hat{k}$

B) $6\hat{i}-3\hat{j}+5\hat{k}$

C) $\hat{j}-3\hat{k}$

D) $\hat{i}-3\hat{j}+5\hat{k}$

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• question_answer212) If $|\vec{a}|=|\vec{b}|=|\vec{a}-\vec{b}|=1,$ then $|\vec{a}+\vec{b}|$is equal to

A) $1$

B) $2$

C) $\sqrt{2}$

D) $\sqrt{3}$

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• question_answer213) If the vectors $2\hat{i}-3\hat{j}+4\hat{k},\,\,\hat{i}+2\hat{j}-\hat{k}$ and $\lambda \hat{i}-\hat{j}+2\hat{k}$are coplanar, then X is equal to

A) $0$

B) $5/8$

C) $8/5$

D) $1$

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• question_answer214) If $\vec{a}=2\hat{i}+2\hat{j}+\hat{k},\,\vec{a}.\vec{b}=14$ and $\vec{a}\times \vec{b}=3\hat{i}+\hat{j}-8\hat{k},$ then $\vec{b}$ equals

A) $\hat{i}+5\hat{j}+2\hat{k}$

B) $\hat{i}-2\hat{j}+16\hat{k}$

C) $5\hat{i}+\hat{j}+2\hat{k}$

D) $5\hat{i}-\hat{j}+2\hat{k}$

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• question_answer215) If $\vec{a},\vec{b},\vec{c}$ are non-coplanar vectors and $(\vec{a}-\lambda \vec{b}).(\vec{b}-2\vec{c})\times (\vec{c}+2\vec{a})=0,$ then $\lambda$ is equal to

A) $1$

B) $1/4$

C) $0$

D) $-1/4$

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• question_answer216) If $\vec{a},\vec{b},\vec{c}$ are non-coplanar and $[\vec{a}+\vec{b}\,\,\,\vec{b}+\vec{c}\,\,\,\,\vec{c}+\vec{a}]=k[\vec{a}\vec{b}\vec{c}],$then k is equal to

A) $0$

B) $1$

C) $2$

D) $3$

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• question_answer217) If $\vec{a}+2\vec{b}+2\vec{c}=\vec{0}$ and $(\vec{a}\times \vec{b})+(\vec{b}\times \vec{c})+(\vec{c}\times \vec{a})=\lambda (\vec{b}\times \vec{c}),$ then $\lambda$ is equal to

A) $4$

B) $7$

C) $8$

D) $9$

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• question_answer218) The line segment adjoining the points A , B makes projection 1,4,3 on X,Y,Z axis respectively. Then the direction cosines of AB are

A) $1,4,3$

B) $1/\sqrt{26},\,\,4/\sqrt{26},\,\,3/\sqrt{26}$

C) $-1/\sqrt{26},\,\,4/\sqrt{26},\,\,3/\sqrt{26}$

D) $1/\sqrt{26},-\,\,4/\sqrt{26},\,\,3/\sqrt{26}$

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• question_answer219) The length of the projection of the line segment joining $(3,-1,0)$ and $(-3,5,\sqrt{2})$ on a line with direction cosines $1/2,\,\,1/2,\,\,1/\sqrt{2}$ is

A) $1$

B) $2$

C) $3$

D) $4$

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• question_answer220) The line perpendicular to the plane s$2x-y+5z=4$ passing through the point $(-1,0,1)$ is

A) $\frac{x+1}{2}=-y=\frac{z-1}{-5}$

B) $\frac{x+1}{2}=-y=\frac{z-1}{-5}$

C) $\frac{x+1}{2}=-y=\frac{z-1}{5}$

D) $\frac{x+1}{2}=y=\frac{z-1}{5}$

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• question_answer221) The shortest distance between the lines $\frac{x-2}{3}=\frac{y+3}{4}=\frac{z-1}{5}$ and $\frac{x-5}{1}=\frac{y-1}{2}=\frac{z-6}{3}$ is

A) $3$

B) $2$

C) $1$

D) $0$

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• question_answer222) Angle between the line $\frac{x+1}{1}=\frac{y}{2}=\frac{z-1}{1}$ and a normal to the plane $x-y+z=0$ is

A) ${{0}^{o}}$

B) ${{30}^{o}}$

C) ${{45}^{o}}$

D) ${{90}^{o}}$

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• question_answer223) A point on x-axis which is equidistant from both the points $(1,\,2,3)$ and $(3,5,-2)$ is

A) $(-6,0,0)$

B) $(5,0,0)$

C) $(-5,0,0)$

D) $(6,0,0)$

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• question_answer224) Foot of the perpendicular from $(-2,1,4)$ to a plane is $(3,1,2)$, then the equation of the plane is

A) $4x-2y=11$

B) $5x-2y=10$

C) $5x-2z=11$

D) $5x+2z=11$

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• question_answer225) If $\theta$ is the angle between the planes $2x-y+z-1=0$ and $x-2y+z+2=0,$ then $\cos \,\theta$ is equal to

A) $2/3$

B) $3/4$

C) $4/5$

D) $5/6$s

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