# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2003

### done J and K - CET Engineering Solved Paper-2003

• question_answer1) The following is the truth table for

 A B Y 0 0 1 1 0 1 0 1 1 1 1 0

A) NAND

B) AND

C) XOR

D) NOT

• question_answer2) In a full wave rectifier circuit operating from $50\text{ }Hz$main frequency, the fundamental frequency in the ripple would be

A) $\text{25 }Hz$

B) $50\text{ }Hz$

C) $70.7\text{ }Hz$

D) $100\text{ }Hz$

• question_answer3) The current gain a of a transistor is 0.9. The transistor is connected to common base configuration. What would be the change in collector current when base current changes by $4mA$?

A) $1.2\,\,mA$

B) $12\,\,mA$

C) $24\,\,mA$

D) $36\,\,mA$

• question_answer4) What is the name of the level formed due to impurity atom in p-type in the forbidden gap?

A) Donor level

B) Acceptor level

C) Conduction level

D) Forbidden level

• question_answer5) Which of the following is not true?

A) All unit cells are primitive

B) FCC structure is a closed packed structure

C) A unit cell is primitive if it contains lattice points only at its corner

D) A lattice does not contain any atom or molecule

• question_answer6) A radioactive element A decays into B with a half-life of 2 days. A fresh prepared sample of A has a mass of $12\text{ }g$. What mass of A and B are there in the sample after 4 days?

A) $~A=3g,B=9g$

B) $A=6g,B=6g$

C) $A=12g,B=0g$

D) $A=9g,B=3g$

• question_answer7) How many $\alpha$-particle and $\beta$-particles are emitted when uranium nucleus $_{92}^{238}U$ decays to lead nucleus $_{82}^{206}Pb$?

A) $\alpha =6,\beta =8$

B) $\alpha =10,\beta =8$

C) $\alpha =8,\beta =10$

D) $\alpha =8,\beta =6$

• question_answer8) The angular speed of the electric in the nth orbit of Bohr hydrogen atom is

A) directly proportional to n

B) inversely proportional to $\sqrt{n}$

C) inversely proportional to ${{n}^{2}}$

D) inversely proportional to ${{n}^{3}}$

• question_answer9) If the electron in hydrogen atom jumps from the third to second orbit, the wavelength of the emitted radiation in terms of Rydberg constant R is given by

A) $\lambda =\frac{36}{5R}$

B) $\lambda =\frac{5R}{36}$

C) $\lambda =\frac{5}{R}$

D) $\lambda =\frac{R}{6}$

• question_answer10) When a monochromatic point source of light is at a distance of $0.2\text{ }m$from a photocell, the cut-off voltage and the saturation current are respectively ${{\text{V}}_{0}}=0.6$volt and${{I}_{s}}=18.0\,mA$. If the same source is placed 0.6 m away from the photocell, then

A) stopping potential ${{V}_{0}}\text{=}0.2$volt and saturation current ${{I}_{s}}=18.0\text{ }mA$

B) stopping potential ${{V}_{0}}=0.6$volt and saturation current ${{I}_{s}}=18.0\text{ }mA$

C) stopping potential ${{V}_{0}}=0.6$ volt and saturation current ${{I}_{s}}=2.0\,mA$

D) stopping potential ${{V}_{0}}=2.0$ volt and saturation current ${{I}_{s}}=2.0\,mA$

• question_answer11) When light of wavelength $300~nm$(nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of $600\text{ }nm$wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters?

A) $1:2$

B) $2:1$

C) $4:1$

D) $1:4$

• question_answer12) In Millikan's oil drop experiment, a charged drop of mass $1.8\times {{10}^{-14}}\text{ }kg$ is stationary between the plates. The distance between the plates $0.9\text{ }cm$and potential difference between the plates is$2000\text{ }V$. The number of electons on the oil drop is

A) $10$

B) $5$

C) $50$

D) $20$

• question_answer13) In the experiment for the determination of $\frac{e}{m}$of electrons by the Thomson method, electric and magnetic fields are

A) parallel and both are perpendicular to the motion of the electron

B) both mutually perpendicular and parallel to the motion of electron

C) both mutually perpendicular and also perpendicular to the motion of electron

D) both mutually perpendicular and have no relation with motion of the electron

• question_answer14) Blue colour of sky is due to

A) interference

B) scattering of light

C) dispersion of light

D) sun emits more of blue light

• question_answer15) In Young's double slit experiment distance between source is 1 mm and distance between the screen and source is 1 m. If the fringe width on the screen is 0.06 cm, then K is

A) $6000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $4000\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $1200\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $2400\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer16) Angle of minimum deviation for a prism of refractive index $1.5$ is equal to the angle of the prism. The angle of the prism is (given $\cos \,{{41}^{o}}-24'-36''=0.75$)

A) ${{82}^{o}}-49'-12''$

B) ${{72}^{o}}-48'-30''$

C) ${{41}^{o}}-24'-36''$

D) ${{31}^{o}}-49'-30''$

• question_answer17) Two media having speeds of light $2\times {{10}^{8}}\text{ }m/s$ and $2.4\times {{10}^{8}}\text{ }m/s,$ are separated by a plane surface. What is the critical angle for a ray going from medium I to medium II ?

A) ${{\sin }^{-1}}\left( \frac{5}{6} \right)$

B) ${{\sin }^{-1}}\left( \frac{5}{12} \right)$

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

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

• question_answer18) When sunlight is incident son a prism, it produces a spectrum due to

A) interference of light

B) diffraction of light

C) total internal reflection

D) variation in speeds of different colours of light in the prism

• question_answer19) The transverse nature of light is shown by

A) interference of light

B) diffraction of light

C) polarization

D) radiation spectrum of black body

• question_answer20) An electromagnetic radiation of wavelength $\lambda ,$ frequency v and propagating in air with velocity v is incident on a glass plate and is transmitted through. Which of the following statement is true for the wave inside the glass plate?

A) The velocity v remains unchanged but $\lambda$changes

B) The frequency v and wavelength remain unchanged but v changes

C) The wavelength $\lambda$ remains unchanged but velocity v changes

D) The frequency v remains unchanged but $\lambda$changes

• question_answer21) The oscillating electric and magnetic vectors of an electromagnetic wave in vacuum are oriented along

A) the same direction but differ in phase by ${{90}^{o}}$

B) the same direction and are in phase

C) mutually perpendicular directions and differ in phase by ${{90}^{o}}$

D) mutually perpendicular directions and are in phase

• question_answer22) In an AC circuit the instantaneous values of emf and current are $e=200\text{ }sin\text{ }300\,t\text{ }volt$ and $i=2\,\sin \left( 300t+\frac{\pi }{3} \right)amp$ the average power consumed in watts is

A) $200$

B) $100$

C) $50$

D) $400$

• question_answer23) A transformer is used to light a 140 W, $24\text{ }V$ lamp from $240\text{ }VAC$mains. The current in the mains cable of $0.7\text{ }A$. The efficiency of the transformer is

A) $48%$

B) $63.8%$

C) $83.3%~$

D) $90%$

• question_answer24) A solenoid has 2000 turns wound over a length of $0.30\text{ }m$. The area of its cross-section is $1.2\times {{10}^{-3}}{{m}^{2}}$. Around its central section a coil of 300 turns is wound. If an initial current of 2 A in the solenoid is reversed in $0.25\text{ }s,$ the emf induced in the coil is

A) $48\text{ }V$

B) $4.8\text{ }V$

C) $4.8\times {{10}^{-1}}\,V$

D) $4.8\times {{10}^{-2}}\,V$

• question_answer25) A copper ring is held horizontally and a bar magnet with its length along the axis of the ring is dropped through the ring. The acceleration of the falling magnet is

A) less than that due to gravity

B) equal to that due to gravity

C) more than that due to gravity

D) depends on the length of the magnet and diameter of the ring

• question_answer26) The dimensional formula of Planck's constant (h) is

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

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

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

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

• question_answer27) A particle starts from rest and experiences constant acceleration for 6 s. If it travels a distance d-^ in the first two seconds, a distance ${{d}_{2}}$ in the next two seconds and a distance ${{d}_{3}}$ in the last two seconds, then

A) ${{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:1:1$

B) ${{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:2:3$

C) ${{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:3:5$

D) ${{d}_{1}}:{{d}_{2}}:{{d}_{3}}=1:5:9$

• question_answer28) A particle originally at rest at the highest point of a smooth circle in a vertical plane, is gently pushed and starts sliding/along the circle. It will leave the circle at a' vertical distance h. below the highest point such that

A) $h=2R$

B) $h=\frac{R}{2}$

C) $h=R$

D) $h=\frac{R}{3}$

• question_answer29) An inclined plane has an inclination $\theta$ with horizontal. A body of mass m rests on it. If the coefficient of friction between the body and the plane is $\mu ,$ then the minimum force that needs to be applied parallel to the inclined plane is

A) $mg\,\,\sin \,\theta$

B) $\mu mg\,\,\cos \,\theta$

C) $\mu mg\,\,\cos \,\theta +mg\,\,\sin \,\theta$

D) $\mu mg\,\,\cos \,\theta -mg\,\,\sin \,\theta$

• question_answer30) A $60\text{ }kg$man stands on a spring scale in a lift. At some instant he finds that the scale reading has changed from $60\text{ }kg$ to $50\text{ }kg$ for a while and then comes again to $60\text{ }kg$ mark. What should he conclude?

A) The lift was in constant motion upwards

B) The lift was in constant motion downwards

C) The lift while in motion suddenly stopped

D) The lift while in motion upwards suddenly' stopped

• question_answer31) A diatomic molecule is formed by two atoms which may be treated as mass points ${{m}_{1}}$ and ${{m}_{2}},$ joined by a massless rod of length r. Then the moment of inertia of the molecule about an axis passing through the centre of mass and perpendicular to rod is

A) zero

B) $({{m}_{1}}+{{m}_{2}}){{r}^{2}}$

C) $\left( \frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}{{m}_{2}}} \right){{r}^{2}}$

D) $\left( \frac{{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{r}^{2}}$

• question_answer32) If the polar ice caps of earth melt, how long it affect the length of day?

A) Length of day would remain unchanged

B) Length of day would increase

C) Length of day would decrease

D) None of the above

• question_answer33) A planet revolves in an elliptical orbit around the sun. The semi-major and semi-minor axes are a and b, their the period is given by

A) ${{T}^{2}}\propto {{b}^{3}}$

B) ${{T}^{2}}\propto {{\left( \frac{a+b}{2} \right)}^{3}}$

C) ${{T}^{2}}\propto {{a}^{3}}$

D) ${{T}^{2}}\propto {{\left( \frac{a-b}{2} \right)}^{3}}$

• question_answer34) In a capillary tube of which the lower end dips in a liquid, the liquid rises to a height of$10\text{ }cm$If a capillary of the same bore is taken, whose length is 5 cm and dipped in liquid, then

A) a fountain of liquid will be obtain

B) the liquid will not rise in the tube at all

C) the liquid will rise upto the top and slowly ooze out of it

D) the liquid will rise to the top and will stay there

• question_answer35) There relation between Y (Young's modulus), K (bulk modulus) and $\eta$ (shear modulus) is

A) $\frac{9}{Y}=\frac{1}{K}+\frac{3}{\eta }$

B) $\frac{1}{Y}=\frac{1}{3\lambda }+\frac{1}{9K}$

C) $\frac{9}{Y}=\frac{1}{\eta }+\frac{3}{K}$

D) $\frac{1}{\eta }=\frac{1}{K}+\frac{1}{Y}$

• question_answer36) Solar radiation emitted by sun correspond to that emitted by black body at a temperature of $6000\text{ }K$. Maximum intensity is emitted at wavelength of$4800\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$. If the sun was to cool down from $6000\text{ }K$to $3000\text{ }K,$ then the peak intensity of emitted radiation would occur at a wavelength

A) $4800\overset{\text{o}}{\mathop{\text{A}}}\,$

B) $9600\overset{\text{o}}{\mathop{\text{A}}}\,$

C) $2400\overset{\text{o}}{\mathop{\text{A}}}\,$

D) $19200\overset{\text{o}}{\mathop{\text{A}}}\,$

• question_answer37) An ideal gas heat engine operates in a Carnot cycle between ${{227}^{o}}C$and${{127}^{o}}C$. It absorbs $6\times {{10}^{4}}cal$ at the higher temperature. The amount of heat converted into work is

A) $4.8\times {{10}^{4}}\text{ }cal$

B) $1.2\times {{10}^{4}}\text{ }cal$

C) $3.5\times {{10}^{4}}\text{ }cal$

D) $1.6\times {{10}^{4}}\text{ }cal$

• question_answer38) A certain mass of gas at NTP is expanded to three times its volume under adiabatic conditions. The resulting temperature of gas ,' will be (7 for gas is $1.40$)

A) $273\times {{\left( \frac{1}{3} \right)}^{1.4}}$

B) $273\times {{(3)}^{0.4}}$

C) $273\times {{\left( \frac{1}{3} \right)}^{0.4}}$

D) $273\times {{(3)}^{1.4}}$

• question_answer39) If for a gas $\frac{R}{{{C}_{V}}}=0.67,$ this gas is made up of molecules which "are

A) monoatomic

B) diatomic

C) polyatomic

D) mixture of diatomic and polyatomic molecules

• question_answer40) The velocity of a small ball of mass M and density ${{d}_{1}}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is ${{d}_{2}},$ the viscous force acting on the ball is

A) $Mg\left( 1-\frac{{{d}_{2}}}{{{d}_{1}}} \right)$

B) $Mg\frac{{{d}_{1}}}{{{d}_{2}}}$

C) $Mg({{d}_{1}}-{{d}_{2}})$

D) $Mg{{d}_{1}}{{d}_{2}}$

• question_answer41) The length of an elastic spring is a meters when a force of $4\text{ }N$is applied, and b meters when the $\text{5 }N$ force is applied. Then the length of the spring when the $9N$ force is applied is

A) $a+b$

B) $~9b-9a$

C) $5b-4a$

D) $4a-5b$

• question_answer42) Moment of inertia of a uniform disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

A) $5I$

B) $3I$

C) $4I$

D) $6I$

• question_answer43) The escape velocity of a body from the surface of earth is $11.2\text{ }km/s$. It is thrown up with a velocity 4 times this velocity of escape. The velocity of the body when it has escaped the gravitational pull of earth (neglecting presence of all other heavenly bodies) is

A) $4\times 11.2\text{ }km/s$

B) $\sqrt{15}\times 11.2\text{ }km/s$

C) zero

D) $3\times 11.2\text{ }km/s$

• question_answer44) If a planet of given density were made larger (keeping its density unchanged) its force of attraction for an object on its surface would increase because of increased mass of the planet but would decrease because of larger separation between the centre of the planet and its surface. Which effect would dominate?

A) Increase in mass

C) Both affect the attraction equally

D) None of the above

• question_answer45) Two balls each of mass m are placed on the vertices A and B of an equilateral triangle ABC of side$1\text{ }m$. A ball of mass $2m$ is placed at vertex C. The centre of mass of this system from vertex A (located at origin) is

A) $\left( \frac{1}{2}m,\,\frac{1}{2}m \right)$

B) $\left( \frac{1}{2}m,\sqrt{3}m \right)$

C) $\left( \frac{1}{2}m,\frac{\sqrt{3}}{4}m \right)$

D) $\left( \frac{\sqrt{3}}{4}m,\frac{\sqrt{3}}{4}m \right)$

• question_answer46) A particle moves along the x-axis from $x={{x}_{1}}$ to $x={{x}_{2}}$ under the action of a force given by$F=2\text{ }x$. Then the work done in the process is

A) zero

B) ${{x}_{2}}^{2}-{{x}_{1}}^{2}$

C) $2{{x}_{2}}({{x}_{2}}-{{x}_{1}})$

D) $2{{x}_{1}}({{x}_{1}}-{{x}_{2}})$

• question_answer47) A body of mass 5 kg strikes another body of mass $2.5\text{ }kg$initially at rest. The bodies after collision coalesce and begin to move as whole with a kinetic energy of$5\text{ }J$. The kinetic energy of the first body before collision is

A) $7.5\text{ }J$

B) $5\text{ }J$

C) $2.5\text{ }J$

D) $10\text{ }J$

• question_answer48) For traffic moving at $60\text{ }km/h$along a circular track of radius $0.1\text{ }km,$the correct angle of banking is

A) ${{\tan }^{-1}}\left( \frac{{{60}^{2}}}{0.1} \right)$

B) ${{\tan }^{-1}}\left( \frac{{{(50/3)}^{2}}}{100\times 9.8} \right)$

C) ${{\tan }^{-1}}{{(60\times 0.1\times 9.8)}^{1/2}}$

D) ${{\tan }^{-1}}\left( \frac{100\times 9.8}{{{(50/3)}^{2}}} \right)$

• question_answer49) Two projectiles are fired at different angles with the same magnitude of velocity, such that they have the same range. At what angles they might have been projected?

A) ${{25}^{o}}$ and ${{65}^{o}}$

B) ${{35}^{o}}$ and ${{75}^{o}}$

C) ${{10}^{o}}$ and ${{50}^{o}}$

D) None of these

• question_answer50) If two non-zero vectors obey the relation $|\vec{P}+\vec{Q}|=|\vec{P}-\vec{Q}|$.then the angle between the vectors $\vec{P},$ $\vec{Q}$ is

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

B) $\pi$

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

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

• question_answer51) A weightless spring which has a force constant k oscillates with a frequency r% when a mass m is suspended from it. The spring is cut into two equal halves and a mass 2m is attached to one of the halves. The frequency of oscillation will not become

A) $\sqrt{2n}$

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

C) $2n$

D) $n$

• question_answer52) A particle moves so that its acceleration a is given by $a=-bx,$ where x is displacement from equilibrium position and b is a non-negative real constant. The time period of oscillation of the particle is

A) $2\pi \sqrt{b}$

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

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

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

• question_answer53) A tuning fork of frequency $500\text{ }cycles/s$is sounded on a resonance tube. The first and second resonance is obtained at $17\text{ }cm$and$52\text{ }cm$. The velocity of sound in m/s is

A) $175$

B) $350$

C) $525$

D) $700$

• question_answer54) Which of the following characteristics does not change due to the damping of simple harmonic motion?

A) Angular frequency

B) Time period

C) Initial phase

D) Amplitude

• question_answer55) A hollow charged metal sphere has a radius r. If the potential difference between its surface and a point at a distance $3\text{ }r$from the centre is V, then electrical intensity at distance $3\text{ }r$from the centre is

A) $\frac{V}{2r}$

B) $\frac{V}{3r}$

C) $\frac{V}{4r}$

D) $\frac{V}{6r}$

• question_answer56) Current is flowing with a current density $J=480\,A/c{{m}^{2}}$in a copper wire. Assuming that each copper atom contributes one free electron and given that Avogadro number $=6.0\times {{10}^{23}}\text{ }atoms/mol$ Density of copper $=9.0\text{ }g/c{{m}^{3}}$ Atomic weight of copper $=64\text{ }g/mol$ Electronic charge $=1.6\times {{10}^{-19}}C$ The drift velocity of electrons is

A) $1\text{ }mm/s$

B) $\text{2 }mm/s$

C) $0.5\text{ }mm/s$

D) $0.36\text{ }mm/s$

• question_answer57) A tap supplies water at ${{20}^{o}}C$. A man takes $1\text{ }L$of water per minute at ${{35}^{o}}C$from a geyser connected to the tap. The power of geyser is

A) $1050\text{ }W$

B) $2100\text{ }W$

C) $1500\text{ }W$

D) $3000\text{ }W$

• question_answer58) A charge is fired through a magnetic field. The force acting on the charge is maximum when the angle between the direction of motion of charge and the magnetic field is

A) zero

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

C) $\pi$

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

• question_answer59) At a place the angle of dip is ${{30}^{o}}$. If the horizontal component of earth's magnetic field is H, then the total field intensity is

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

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

C) $H\sqrt{2}$

D) $H\sqrt{3}$

• question_answer60) A particle is vibrating in simple harmonic motion with an amplitude of$4\text{ }cm$. At what displacement from the equilibrium position is its energy half potential and half-kinetic?

A) $2\sqrt{2}cm$

B) $\sqrt{2}cm$

C) $2\,cm$

D) $1\,cm$

• question_answer61) A tuning fork of frequency $480\text{ }Hz$produces 10 beats/s, when sounded with a sonometer string. A slight increase in tension in the sonometer string produces fewer beats/s than before. What was the frequency of sonometer string?

A) $470\text{ }Hz$

B) $490\text{ }Hz$

C) $480\text{ }Hz$

D) $460\text{ }Hz$

• question_answer62) A hollow metal sphere of radius $5\text{ }cm$is charged such that potential at its surface is$10\text{ }V$. The potential at the centre of the sphere is

A) zero volt

B) $10\text{ }V$

C) same as at point $5\text{ }cm$away from the surface

D) same as at point $\text{10 }cm$ away from the surface

• question_answer63) An electric dipole consisting of two opposite charges of $2\times {{10}^{-6}}\text{ }C$each, separated by a distance of $3\text{ }cm$is placed in an electric field of $2\times {{10}^{5}}\text{ }N/C$. The maximum torque on the dipole is

A) $12\times {{10}^{-1}}\text{ }Nm$

B) $12\times {{10}^{-3}}\text{ }Nm$

C) $24\times {{10}^{-1}}Nm$

D) $24\times {{10}^{-3}}\text{ }Nm$

• question_answer64) A given piece of wire of length I and radius r is having a resistance R. This wire is stretched uniformly to a wire of radius $\frac{r}{2}$. What is the new resistance?

A) $4R$

B) $8R$

C) $16R$

D) $2R$

• question_answer65) Two .thin long parallel wires separated by a distance b are carrying current i ampere each. The magnitude of the force per unit length exerted by one wire on the other is

A) $\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}^{2}}}{b}$

B) $\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}^{2}}}{{{b}^{2}}}$

C) $\frac{{{\mu }_{0}}}{2\pi }\frac{i}{b}$

D) $\frac{{{\mu }_{0}}}{2\pi }\frac{i}{{{b}^{2}}}$

• question_answer66) To increase the range of a voltmeter, we need to connect a suitable

A) high resistance in parallel

B) high resistance in series

C) low resistance in series

D) low resistance in parallel

• question_answer67) Two wires made up of the same material are of equal lengths but their radii are in the ratio of$1:2$. On stretching each of these two strings by the same tension, the ratio between the fundamental frequencies is

A) $1:4$

B) 4 : 1

C) $2:1$

D) $1:2$

• question_answer68) An object producing a pitch of $400\text{ }Hz$flies past a stationary person. The object was moving in a straight line with a velocity 200 m/s. The velocity of sound is 300 m/s. What is the change in frequency noted by the person as the object flies past him?

A) $1440\text{ }Hz$

B) $240\text{ }Hz$

C) $1200\text{ }Hz$

D) $960\text{ }Hz$

• question_answer69) Four capacitors each of $1\mu F$ are connected as shown. The equivalent capacitance between P and Q is

A) $4\mu F$

B) $\frac{1}{4}\mu F$

C) $\frac{3}{4}\mu F$

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

• question_answer70) The magnitude of electric field at distance r from an infinitely thin rod having a linear charge density $\lambda ,$is (use Gauss's law)

A) $E=\frac{\lambda }{2\pi {{\varepsilon }_{0}}r}$

B) $E=\frac{2\lambda }{\pi {{\varepsilon }_{0}}r}$

C) $E=\frac{2\lambda }{4\pi {{\varepsilon }_{0}}r}$

D) $E=\frac{4\lambda }{\pi {{\varepsilon }_{0}}r}$

• question_answer71) A $200\text{ }W$and a $100\text{ }W$bulb, both. meant for operation at $220\text{ }V$are connected in series. When connected to a $220\text{ }V$ supply the power consumed by the, combination is

A) $33.3\text{ }W$

B) $66.7\text{ }W$

C) $300W$

D) $100W$

• question_answer72) The sensitivity of a moving coil galvanometer depends on

A) angle of deflection -

B) earth's magnetic field

C) torsional constant of the spring

D) None of the above

• question_answer73) Domain formation is the necessary feature of

A) diamagnetic substances

B) paramagnetic substances

C) ferromagnetic substances

D) All of the above

• question_answer74) In a charged capacitor the energy stored in

A) the positive charges

B) the negative charges

C) the field between the plates

D) None of the above

• question_answer75) For a given temperature difference which of the following pairs will generate maximum thermo-emf?

B) copper-iron

C) gold-silver

D) antimony-bismuth

• question_answer76) The electrons identified by quantum numbers:

 (I) $n=4,l=1$ (II) $n=4,l=0$ (III) $n=3,l=2$ (IV) $n=2,l=1$
can be placed in order of increasing energy from the lowest to highest as

A) $(IV)<(II)<(III)<(I)$

B) $(II)<(IV)<(I)<(III)$

C) $(I)<(III)<(II)<(IV)$

D) $(III)<(I)<(IV)<(II)$

• question_answer77) Ground state electronic configuration of nitrogen atom can be represented as

A)

B)

C)

D)

• question_answer78) The first emission line in the electronic spectrum of hydrogen in the Balmer series appears at$c{{m}^{-1}}$

A) $\frac{9R}{400}c{{m}^{-1}}$

B) $\frac{7R}{144}c{{m}^{-1}}$

C) $\frac{3R}{4}c{{m}^{-1}}$

D) $\frac{5R}{36}c{{m}^{-1}}$

• question_answer79) $\text{KMn}{{\text{O}}_{\text{4}}}$reacts with oxalic acid according to the equation $2MnO_{4}^{-}+5{{C}_{2}}O_{4}^{2-}+16{{H}^{+}}\xrightarrow{{}}2M{{n}^{2+}}$$+\,10C{{O}_{2}}+8{{H}_{2}}O$ Here, 20 mL of $\text{0}\text{.1}\,\text{M}\,\text{KMn}{{\text{O}}_{\text{4}}}$ is equivalent to

A) $\text{20 mL}$of $\text{0}\text{.5}\,\text{M }{{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}$

B) $\text{50}\,\text{mL}$of $\text{0}\text{.1}\,\text{M}\,{{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}$

C) $\text{ }\!\!~\!\!\text{ 50 mL}$of $\text{0}\text{.01}\,\text{M}\,{{\text{H}}_{2}}{{C}_{2}}{{O}_{4}}$

D) $\text{20}\,\text{mL}$of $\text{0}\text{.1 M}\,{{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}}$

• question_answer80) Half-life of a sample is 160 days. After 800 days, 1 g of the sample shall be reduced to

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

B) $\frac{1}{5}g$

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

D) $\frac{1}{32}g$

A) GN Lewis

B) J Williard Gibbs

C) WF Libby

D) W Nernst

• question_answer82) An aqueous solution of 6.3 g oxalic acid dihydrate is made up to 250 mL. The volume of N sodium hydroxide required to completely neutralise 10 mL of this solution is

A) 40 mL

B) 20 mL

C) 10 mL

D) 4 mL

• question_answer83) How will increase of pressure affect the equation? $C(s)+{{H}_{2}}O(g)CO(g)+{{H}_{2}}(g)$

A) Shift in the forward direction

B) Shift in the reverse direction

C) Increase in the yield of hydrogen

D) No effect

• question_answer84) For which of the following reactions,${{K}_{p}}={{K}_{c}}?$

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

B) ${{N}_{2}}+{{O}_{2}}2NO$

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

D) $2S{{O}_{3}}2S{{O}_{2}}+{{O}_{2}}$

• question_answer85) Which of the following salts is most soluble?

A) $B{{i}_{2}}{{S}_{3}}({{K}_{sp}}=1\times {{10}^{-17}})$

B) $MnS({{K}_{sp}}=7\times {{10}^{-16}})$

C) $CuS({{K}_{sp}}=8\times {{10}^{-37}})$

D) $A{{g}_{2}}S({{K}_{sp}}=6\times {{10}^{-51}})$

• question_answer86) Ostwald dilution law is applicable to

A) strong electrolytes only

B) weak electrolytes only

C) non-electrolytes only

D) strong as well as weak electrolytes

• question_answer87) In the reaction $2A+B\xrightarrow{{}}{{A}_{2}}B,$ if the concentration of A is doubled and that of B is halved, then the rate of reaction will

A) increase by 4 times

B) decrease by 2 times

C) increase by 2 times

D) remains the same

• question_answer88) The Arrhenius equation expressing the effect of temperature on the rate constant of a reaction is

A) $k={{e}^{-E/RT}}$

B) $k=\ln \frac{E}{RT}$

C) $k=\frac{A.E}{RT}$

D) $k=A.{{e}^{-{{E}_{a}}/RT}}$

• question_answer89) If the half-time for a particular reaction is found to be constant and independent of the initial concentration of the reactants, then the reaction is of

A) first order

B) zero order

C) second order

D) none of these

• question_answer90) Normality of $\text{2}\,\text{M}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}$ is

A) $\text{2N}$

B) $\text{4}\,\text{N}$

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

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

• question_answer91) Which of the following is a non-colligative property?

A) Elevation in boiling point

B) Osmotic pressure

C) Optical activity

D) Depression in freezing point

• question_answer92) The freezing point of equimolal aqueous solution will be highest for

A) ${{C}_{6}}{{H}_{5}}N{{H}_{3}}Cl$

B) $La{{(N{{O}_{3}})}_{3}}$

C) glucose

D) $Ca{{(N{{O}_{3}})}_{2}}$

• question_answer93) The van't Hoff factor for $\text{0}\text{.1}\,\text{M}\,\text{Ba(N}{{\text{O}}_{\text{3}}}{{\text{)}}_{\text{2}}}$ solution is 2.74. The degree of dissociation is

A) 91.3%

B) 87%

C) 100%

D) 74%

• question_answer94) The enthalpy of vaporisation of liquid water using the data ${{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l)$ $\Delta H=-285.77\,kJ/mol$ ${{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(g);$ $\Delta H=-241.84\,kJ/mol$is

A) $+\,43.93\,kJ/mol$

B) $-43.93\,kJ/mol$

C) $527.61\,kJ/mol$

D) $-527.61\,kJ/mol$

• question_answer95) The enthalpy change for the transition of liquid water to steam is $40.8\,kJ\,mo{{l}^{-1}}$at $373\,K.$ Calculate the entropy of vaporisation of water.

A) $109.4\,J{{K}^{-1}}\,mo{{l}^{-1}}$

B) $-109.4\,J{{K}^{-1}}\,mo{{l}^{-1}}$

C) $218.8\,J{{K}^{-1}}\,mo{{l}^{-1}}$

D) $-218.8\,J{{K}^{-1}}\,mo{{l}^{-1}}$

• question_answer96) The occurrence of the reaction is impossible if

A) $\Delta H$ is$+\,ve;\Delta S$ is also $+\,ve$

B) $\Delta H$is$~-ve;\text{ }\Delta S$ is also $-ve$

C) $\Delta H$is $-ve;\Delta \,S$is $+\,ve$

D) $\Delta H$ is $+\,ve;\Delta S$is $-ve$

• question_answer97) The bond energy of an$O-H$ bond is 109 kcal/mol. When a mole of water is formed, then

A) 109 kcal is released

B) 218 kcal is absorbed

C) 109 kcal is absorbed

D) 218 kcal is released

• question_answer98) Of the following reaction, only one is a redox reaction. Identify this reaction.

A) $Ca{{(OH)}_{2}}+2HCl\xrightarrow{{}}CaC{{l}_{2}}+2{{H}_{2}}O$

B) $2{{S}_{2}}O_{7}^{2-}+2{{H}_{2}}O\xrightarrow{{}}2SO_{4}^{2-}+4{{H}^{+}}$

C) $BaC{{l}_{2}}+MgS{{O}_{4}}\xrightarrow{{}}BaS{{O}_{4}}+MgC{{l}_{2}}$

D) $C{{u}_{2}}S+2FeO\xrightarrow{{}}2Cu+2Fe+S{{O}_{2}}$

• question_answer99) Oxidation number of nitrogen is highest in

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

B) ${{N}_{2}}{{O}_{4}}$

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

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

• question_answer100) Correct order of first ionization potential among the following elements Be, B, C, N, O is

A) $B<Be<C<O<N$

B) $B<Be<C<N<O$

C) $~Be<B<C<N<\text{O}$

D) $~Be<B<C<O<N$

• question_answer101) The unit of equivalent conductivity is

A) ohm cm

B) $~oh{{m}^{-1}}c{{m}^{2}}\text{ }g\text{ }equi{{v}^{-1}}$

C) $oh{{m}^{-2}}c{{m}^{-2}}\text{ }g\text{ }equiv$

D) $oh{{m}^{-2}}c{{m}^{-2}}g\,equiv$

• question_answer102) In which of the following crystals of ionic compounds would you expect maximum distance between the centres of cations and anions?

A) $\text{ }\!\!~\!\!\text{ LiF}$

B) $\text{CsF}$

C) $CsI$

D) $LiI$

• question_answer103) 50 mL of hydrogen diffuses through small hole from a vessel in 20 min time. Time taken for 40 mL of oxygen to diffuse out under similar conditions will be

A) 12 min

B) 32 min

C) 8 min

D) 64 min

• question_answer104) A gas will approach ideal behaviour at

A) low temperature and high pressure

B) low temperature and low pressure

C) high temperature and low pressure

D) high temperature and high pressure

• question_answer105) A colloidal system in which gas bubbles are dispersed in a liquid is known as

A) foam

B) aerosol

C) sol

D) emulsion

• question_answer106) In which of the following, Tyndall effect is not observed?

A) Smoke

B) Emulsions

C) Sugar solution

D) Gold sol

• question_answer107) Which is not correct regarding the adsorption of a gas on surface of a solid?

A) Enthalpy and entropy change is negative

B) Adsorption is more for some specific substance

C) On increasing temperature, adsorption increases progressively

D) It is a reversible reaction

• question_answer108) The ionic radii of isoelectronic species${{N}^{3-}},{{O}^{2-}}$and ${{F}^{-}}$are in the order

A) 1.36, 1.40, 1.71

B) 1.36, 1.71, 1.40

C) 1.71, 1.40, 1.36

D) 1.71, 1.36, 1.40

• question_answer109) Which of the following element is most electropositive?

A) Al

B) Mg

C) P

D) S

• question_answer110) The compound in which carbon atom uses only $s{{p}^{3}}-$hybrid orbitals for bond formation is

A) $HCOOH$

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

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

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

• question_answer111) The only molecule having dipole moment is

A) 2,2-dimethylpropane

B) trans-2-pentene

C) trans-3-hexene

D) 2,2,3,3-tetramethylbutane

• question_answer112) ${{N}_{2}}$and${{O}_{2}}$are converted into$N_{2}^{+}$and $O_{2}^{+}$respectively. Which of the following is .not correct?

A) In ${{N}_{2}}^{+},$the N?N bond weakens

B) In $O_{2}^{+},O-O$ bond order increases

C) ln ${{O}_{2}}^{+},$ paramagnetism decreases

D) ${{\text{N}}_{\text{2}}}^{\text{+}}$becomes diamagnetic

• question_answer113) The hybridisation of carbon atoms in C?C single bond of$HC\equiv C-CH=C{{H}_{2}}$is

A) $s{{p}^{3}}-s{{p}^{3}}$

B) $s{{p}^{2}}-s{{p}^{2}}$

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

D) $s{{p}^{3}}-sp$

• question_answer114) Chemical A is used for water softening to remove temporary hardness. A reacts with sodium carbonate to generate caustic soda. When$\text{C}{{\text{O}}_{\text{2}}}$ is bubbled through A, it turns cloudy. What is A?

A) $\text{CaC}{{\text{O}}_{3}}$

B) $CaO$

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

D) $Ca{{(HC{{O}_{3}})}_{3}}$

• question_answer115) Which of the following pentafluorides can't be formed?

A) $P{{F}_{5}}$

B) $As{{F}_{5}}$

C) $Sb{{F}_{5}}$

D) $Bi{{F}_{5}}$

• question_answer116) The correct order of increasing oxidising power is

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

B) $~{{F}_{2}}<B{{r}_{2}}<C{{l}_{2}}<{{I}_{2}}$

C) $~C{{l}_{2}}<B{{r}_{2}}<{{F}_{2}}<{{I}_{2}}$

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

• question_answer117) Amongst $TiF_{6}^{2-},CoF_{6}^{3-},C{{u}_{2}}C{{l}_{2}}$and $NiCl_{4}^{2-}$at. no.$Ti=22,Co=27,Cu=29,Ni=28$). The. colourless species are

A) $CoF_{6}^{3-}$and $NiCl_{4}^{2-}$

B) $TiF_{6}^{2-}$and $CoF_{6}^{3-}$

C) $C{{u}_{2}}C{{l}_{2}}$ and $NiCl_{4}^{2-}$

D) $TiF_{6}^{2-}$ and $C{{u}_{2}}C{{l}_{2}}$

• question_answer118) The number of S?S bonds in sulphur trioxide is

A) three

B) two

C) one

D) zero

• question_answer119) Choose the correct statement.

A) Transition elements have low melting point

B) Transition elements do not have catalytic activity

C) Transition elements exhibit variable oxidation states

D) Transition elements show inert pair effect

• question_answer120) Two of the constituents of German silver are

A) $Ag+Cu$

B) $Ag+Zn$

C) $Cu+Zn$

D) $Cu+Sn$

• question_answer121) Aufbau principle does not Jgrve the correct arrangement of filling Up T of atomic orbitals in

A) Cu and Zn

B) Co and Zn

C) Mn and Cr

D) Cu and Cr

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

B) $[Co{{(en)}_{3}}]C{{l}_{3}}$

C) $[Co{{(en)}_{2}}N{{O}_{2}}Cl]Br$

D) $[Co{{(N{{H}_{3}})}_{5}}Cl]B{{r}_{2}}$

• question_answer123) IUPAC name of$[Pt{{(N{{H}_{3}})}_{3}}Br(N{{O}_{2}})Cl]Cl$

A) triamminechlorobromonitro platinum (IV) chloride

B) triamminebromonitrochloro platinum (IV) chloride

C) triamminebromochloronitro platinum (IV) chloride

D) triamminenitrochlorobromo platinum (IV)chloride

• question_answer124) According to postulates ofWemefs theory for coordination compounds, which of the following is true?

A) Primary valencies are ionisable

B) Secondary valencies are ionisable

C) Only primary valencies are non-ionizable

D) Primary and secondary valencies are non- ionisable

• question_answer125) Ferrocene is an example of

A) sand-wiched complex

B) pi-bonded complex

C) a complex in which all the five carbon atoms of cyclopentadiene anion are bonded to the metal

D) all of the above

• question_answer126) Which form of iron is least ductile?

A) Hard steel

B) Cast iron

C) Mild steel

D) Wrought steel

• question_answer127) Which of the following is known as Lunar caustic when in the fused state?

A) Silver nitrate

B) Silver sulphate

C) Silver chloride

D) Sodium sulphate

• question_answer128) One of the following metals is obtained by leaching its ore with dilute cyanide solution. Identify it.

A) Titanium

C) Silver

D) Zinc

• question_answer129) Which of the following species could be expected to exhibit aromatic character? Select the correct answer from the following

A) I and IV

B) II and IV

C) I and III

D) II and III

• question_answer130) The correct IUPAC name of the following compound is $C{{H}_{3}}C{{H}_{2}}\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C=\underset{{{C}_{2}}{{H}_{5}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-\underset{{{C}_{2}}{{H}_{5}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,HC{{H}_{2}}C{{H}_{2}}C{{H}_{2}}C{{H}_{3}}$

A) 5, 6-dimethyl-8-methyl dec-6-ene

B) 6-butyl-5-ethyl-3-methyl oct-4-ene

C) 5, 6-diethyl-3-methyl dec-4-ene

D) 2, 4, 5-triethyl non-3-ene

• question_answer131) The kind of delocalisation involving sigma bond is called

A) inductive effect

B) hyperconjugation effect

C) electromeric effect

D) mesomeric effect

• question_answer132) Which of the following compounds react with HBr obeying Markownikoff?s rule?

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

B)

C)

D)

• question_answer133) How many cyclic isomers of ${{\text{C}}_{\text{5}}}{{\text{H}}_{\text{10}}}$are possible?

A) Four

B) Three

C) Two

D) Six

• question_answer134) The (R) and (S) enantiomers of an optically active compound differ in

A) their reactivity

B) their optical rotation of plane polarized light

C) their melting point

D) their solubility in achiral reagents

• question_answer135) Which of the following organic compounds exhibit acidic character?

A) ${{H}_{3}}C-C\equiv CH$

B) ${{H}_{3}}C-C\equiv C-C{{H}_{3}}$

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

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

• question_answer136) Methane is produced by the hydrolysis of

A) $A{{l}_{4}}{{C}_{3}}$

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

C) Dry ice

D) $n-{{C}_{3}}{{H}_{7}}MgBr$

• question_answer137) In the reaction of phenol with chloroform and aqueous solution of$\text{NaOH}$at $\text{70}{{\,}^{o}}C,$ the electrophile attacking the ring is

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

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

C) $_{.}^{.}CC{{l}_{2}}$

D) $COC{{l}_{2}}$

• question_answer138) Which of the following compounds can exist in optically active form?

A) 1-butanol

B) 2-butanol

C) 3-pentanol

D) 4-heptanol

• question_answer139) Chloroform is slowly oxidised by air in the presence of light and air to form

A) formyl chloride

B) trichloro methanol

C) phosgene

D) formaldehyde

• question_answer140) Chlorination of toluene in the presence of light and heat followed by treatment with aqueous NaOH solution gives

A) o-cresol

B) p-cresol

C) benzoic acid

D) 2, 4-dihydroxytoluene

• question_answer141) Formation of cyanohydrin from the reaction of acetone with HCN is called

C) electrophilic substitution

D) nucleophilic substitution

• question_answer142) In the following reaction, $C{{H}_{3}}COCl\frac{BaS{{O}_{4}}}{Pd/{{H}_{2}}}X$ Identify X out of the following

A) acetaidehyde

B) propionaldehyde

C) acetone

D) acetic anhydride

• question_answer143) Reaction of t-butyl bromide with sodium methoxide produces

A) isobutane

B) isobutylene

C) sodium-t-butoxide

D) t-butylmethylether

• question_answer144) The acid which does not contain $-\text{COOH}$ group is

A) ethanoic acid

B) picric acid

C) lactic acid

D) palmitic acid

• question_answer145) The decreasing order of basic character of the three amines and ammonia is

A) $N{{H}_{3}}>C{{H}_{3}}N{{H}_{2}}>{{C}_{2}}{{H}_{5}}N{{H}_{2}}>{{C}_{6}}{{H}_{5}}N{{H}_{2}}$

B) ${{C}_{2}}{{H}_{5}}N{{H}_{2}}>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}>{{C}_{6}}{{H}_{5}}N{{H}_{2}}$

C) ${{C}_{6}}{{H}_{5}}N{{H}_{2}}>{{C}_{2}}{{H}_{5}}N{{H}_{2}}>C{{H}_{3}}N{{H}_{2}}>N{{H}_{3}}$

D) $C{{H}_{3}}N{{H}_{2}}>{{C}_{2}}{{H}_{5}}N{{H}_{2}}>{{C}_{6}}{{H}_{5}}N{{H}_{2}}>N{{H}_{3}}$

• question_answer146) Aniline is treated with a mixture of sodium nitrite and hypophosphorus acid, the product formed is

A) aniline diazonium hypophosphate

B) benzene

C) anilinium hypophosphite

D) aniline diazonium hypophosphite

• question_answer147) Nitrosoamines $({{R}_{2}}N-N=O)$ are soluble in water. On heating them with cone ${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{,}$they give secondary amines. The reaction is called

A) Perkin's reaction

B) Fries reaction

C) Libermann nitroso reaction

D) Etard reaction

• question_answer148) The compound obtained by heating a mixture of${{\text{1}}^{\text{o}}}$amine and chloroform with ethanolic potassium hydroxide is

A) an alkyl isocyanide

B) an alkyl isothiocyanate

C) an amide

D) an amide and nitro compound

• question_answer149) Which of the following is not an amino acid?

A) Glycine

B) Alanine

C) Histidine

D) Benzidine

• question_answer150) Which of the following is a fat soluble vitamin?

A) Vitamin A

B) Riboflavin

C) Pyridoxin

D) Thiamine

• question_answer151) $\int_{0}^{1}{{{\cot }^{-1}}(1-x+{{x}^{2}})dx}$ is equal to

A) $\pi -\log 2$

B) $\pi +\log 2$

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

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

• question_answer152) $\int_{0}^{1}{\log \,\left\{ \sin \left( \frac{\pi \,\,x}{2} \right) \right\}}\,\,dx$ is equal to

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

B) $-\,\log \,\,\,2$

C) $-\frac{\pi }{2}\,\log \,2$

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

• question_answer153) The value of $2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}$ is

A) $-1$

B) $0$

C) $1$

D) None of these

• question_answer154) In a triangle ABC, $a=5,$ $b=4$ and $\cos (A+B)=\frac{31}{32}$ In this triangle, c is equal to

A) $\sqrt{6}$

B) $36$

C) $6$

D) None of these

• question_answer155) The locus of the centre of a circle of radius 2 which rolls on the outside of the circle ${{x}^{2}}+{{y}^{2}}+3x-6y-9=0$is

A) ${{x}^{2}}+{{y}^{2}}+3x-6y+5=0$

B) ${{x}^{2}}+{{y}^{2}}+3x-6y-31=0$

C) ${{x}^{2}}+{{y}^{2}}+3x-6y+\frac{29}{4}=0$

D) None of these

• question_answer156) $\int{x|x|\,dx}$ is

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

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

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

D) None of these

• question_answer157) The solution set of the equation $\sqrt{3{{x}^{2}}-7x-30}-\sqrt{2{{x}^{2}}-7x-5}=x-5$ is

A) $\{6\}$

B) $\left\{ 6,-\frac{5}{2} \right\}$

C) $\{5,6\}$

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

• question_answer158) If one root of the equation ${{x}^{2}}+px+q=0$is $2+\sqrt{3},$ then the value of p and q are

A) $-4,1$

B) $4,-1$

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

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

• question_answer159) In an AP the sum of any two terms, such that the distance of one of them from the beginning is same as that of the other from the end, is

A) first term

B) sum of first and last terms

C) last term

D) half of the sum of the series

• question_answer160) If $x,\,2x+2,\,\,3x+3,.....$ are in GP, then the fourth term is

A) $27.5$

B) $4x+5$

C) $-13.5$

D) $4x+4$

• question_answer161) The third term of a GP is 4. The product of its first five terms is

A) ${{4}^{5/2}}$

B) ${{4}^{5}}$

C) ${{4}^{3}}$

D) None of these

• question_answer162) The number of terms in the expansion of ${{[{{(a+4b)}^{3}}{{(-4b+a)}^{3}}]}^{2}}$are

A) $6$

B) $7$

C) $8$

D) $18$

• question_answer163) The coefficient of ${{x}^{4}}$ in ${{\left( \frac{x}{2}-\frac{3}{{{x}^{2}}} \right)}^{10}}$is

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

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

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

D) None of these

• question_answer164) Let A and B be two events such that $P(A)=0.3,$$P(A\cup B)=0.8,$if A and B are independent events, then $P(B)$ is equal to

A) $5/7$

B) $5/13$

C) $1/3$

D) $1/2$

• question_answer165) If for some real number k $\underset{x\to 0}{\mathop{\lim }}\,kx\,\,\text{cosec (x) =}\underset{x\to 0}{\mathop{\text{lim}}}\,\,\,x\,\,\text{cosec}\,\,(kx),$ then the possible values of k are

A) $1,-1$

B) $0,\,\,\,1$

C) $1,\,\,\,2$

D) $0,\,\,\,\pi$

• question_answer166) If ${{\log }_{2}}[{{\log }_{3}}\{lo{{g}_{4}}({{\log }_{5}}x)\}]=0,$then the value of x is

A) ${{5}^{24}}$

B) $1$

C) ${{2}^{25}}$

D) ${{5}^{64}}$

• question_answer167) The tangent to the curve $y=2{{x}^{2}}-x+1$is parallel to the line $y=3x+9$at the point

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

B) $(2,\,\,-1)$

C) $(2,\,1)$

D) $(1,\,2)$

• question_answer168) The system of equations $x+3y+2z=0$ $3x+y+z=0$ and $2x-2y-z=0$

A) possesses a trivial solution only

B) possesses a non-zero unique solution

C) does not have a common non-zero solution

D) has infinitely many solutions

• question_answer169) If $\omega$ is a cube root of unity, then a root of the equation $\left| \begin{matrix} x+1 & \omega & {{\omega }^{2}} \\ \omega & x+{{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & x+\omega \\ \end{matrix} \right|=0$ is

A) $x=0$

B) $x=1$

C) $x=\omega$

D) $x={{\omega }^{2}}$

• question_answer170) If A is a square matrix, then AA' is a (A' is the transpose of the matrix A)

A) unit matrix

B) null matrix

C) symmetric matrix

D) skew-symmetric matrix

• question_answer171) If A is a $3\times 3$ non-singular matrix, then $\det \,\,({{A}^{-1}}\,adj\,A)$ is equal to

A) $det\text{ }A$

B) $1$

C) ${{(det\text{ }A)}^{2}}$

D) ${{(det\text{ }A)}^{-1}}$

• question_answer172) In case of a linear programming problem, feasible region is always

A) a convex set

B) a concave set

C) a bounded convex set

D) a bounded concave set

• question_answer173) Which of the following is an odd function?

A) $|x|+1$

B) $\sin x+\cos x$

C) ${{x}^{2}}\,\,\sec x+x\,{{\tan }^{2}}x$

D) ${{x}^{2}}\cot x+4{{x}^{4}}\,\text{cosec x+}{{\text{x}}^{5}}$

• question_answer174) The incentre of the triangle with vertices $(1,\sqrt{3}),\,(0,0)$and $(2,0)$is

A) $(1,\,\sqrt{3}/2)$

B) $(2/3,\,\,\,1\,\sqrt{3})$

C) $(2/3,\,\,\sqrt{3}/2)$

D) $(1,\,\,1/\sqrt{3})$

• question_answer175) If r is Karl Pearson's coefficient of correlation between two sets of variates, then

A) $r<1$

B) $r>1$

C) $r<-1$

D) $|r|\,\le \,1$

• question_answer176) Three dice are thrown simultaneously, then probability of throwing a total greater than 4 is

A) $1/54$

B) $53/54$

C) $5/108$

D) None of these

• question_answer177) An approximate evaluation of $\int_{a}^{b}{f(x)\,\,dx}$ using trapezoidal rule requires the division of $[a,b]$ into

A) an even number of sub-intervals

B) an odd number of sub-intervals

C) any number of sub-intervals

D) None of the above

• question_answer178) In a triangle ABC, $C={{90}^{o}}$. If r is the in radius and R is the circum radius of the triangle, then $2\,(r+R)$is equal to

A) $a+c$

B) $a+b+c$

C) $b+c$

D) $a+b$

• question_answer179) The relation ${{\tan }^{-1}}\left( \frac{1+x}{1-x} \right)=\frac{\pi }{4}+{{\tan }^{-1}}x$ holds true for all

A) $x\,\in R$

B) $x\,\in (-\infty ,\,1)$

C) $x\,\in (-1,\,\,\infty )$

D) $x\,\in (-\,\infty ,-1)$

• question_answer180) $\int_{0}^{\pi /2}{\frac{1}{1+{{\tan }^{3}}x}}dx$is equal to

A) $\pi /2$

B) $\pi /4$

C) $\pi$

D) None of these

• question_answer181) A letter is taken out at random from the word 'ASSISTANT and another is taken-out from the word 'STATISTICS'. The chance that the two selected letters are identical, is

A) $19/45$

B) $19/90$

C) $89/90$

D) $1/90$

• question_answer182) The probability that the 6th day of a randomly chosen month of a year is a Sunday, is

A) $1/12$

B) $1/17$

C) $1/84$

D) None of these

• question_answer183) $\underset{x\to \infty }{\mathop{\lim }}\,\left( \sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x} \right)$ is equal to

A) $1/2$

B) $0$

C) $1$

D) None of these

• question_answer184) $\underset{x\to \infty }{\mathop{\lim }}\,{{\left( \frac{{{x}^{2}}+5x+3}{{{x}^{2}}+x+2} \right)}^{x}}$ is equal to

A) $e$

B) ${{e}^{2}}$

C) ${{e}^{3}}$

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

• question_answer185) If ${{b}^{2}}-4ac=0$and $a>0,$then domain of the function $f(x)=\log \{(a{{x}^{2}}+bx+c)\,\,(x+1)\}$ is

A) $R-\left( -\frac{b}{2a} \right)$

B) $R-(-\infty ,\,\,-1)$

C) $(-1,\infty )-\left\{ -\frac{b}{2a} \right\}$

D) $R-\left( \left\{ -\frac{b}{2a} \right\}\cap (-\infty ,-1) \right)$

• question_answer186) $\int{\frac{1}{{{({{x}^{4}}+1)}^{5/4}}}}$ is equal to

A) $-\frac{4}{{{({{x}^{4}}+1)}^{1/4}}}+c$

B) $\frac{1}{{{({{x}^{4}}+1)}^{1/4}}}+c$

C) $\frac{x}{{{({{x}^{4}}+1)}^{1/4}}}+c$

D) None of the above

• question_answer187) Let $f(x)=\left\{ \begin{matrix} |x|,\,\,for\,\,0<|x|\le 2 \\ 1,\,\,\,\,\,for\,\,\,\,x=0 \\ \end{matrix} \right.$, then at $x=0,$ $f$ has

A) a local maximum

B) a local minimum

C) no local extremum

D) no local maximum

• question_answer188) There are n different books and m copies of each in a college library. The number of ways in which a student can make a selection of one or more books is

A) ${{(m+1)}^{n}}$

B) $\frac{(mn)!}{{{(m!)}^{n}}}$

C) $^{mn}{{C}_{n}}{{\times }^{n}}{{C}_{1}}$

D) ${{(m+n)}^{n}}-1$

• question_answer189) Five digited numbers with distinct digits arc formed by using the digits,$5,4,3,2,1,0$. The number of those numbers which are multiples of 3, is

A) $720$

B) $240$

C) $216$

D) $120$

• question_answer190) If $A+B+C=\pi ,$then the value of $\left| \begin{matrix} \sin \,(A+B+C) & \sin B & \cos \,C \\ -\sin \,B & 0 & \tan \,A \\ \cos \,(A+B) & -\tan \,A & 0a \\ \end{matrix} \right|$ is

A) 0

B) 1

C) 2 sin B tan A cos C

D) None of the above

• question_answer191) If A and B are two matrices such that both $A+B$and AB are defined, then

A) A and B are of same order

B) A is of order $m\times m$and B is of order $n\times n$

C) both A and B are of same order $n\times n$

D) A is of order m x n and B is of order $n\times m$

• question_answer192) The number of dissimilar terms in expansion of ${{(a+b)}^{n}}$ is $n+1,$ therefore number of dissimilar terms of the expansion ${{(a+b+c)}^{12}}$ is

A) $13$

B) $39$

C) $78$

D) $91$

• question_answer193) If $|x|<1,$ then $1+n\left( \frac{2x}{1+x} \right)+\frac{n\,\,(n+1)}{2!}$${{\left( \frac{2x}{1+x} \right)}^{2}}+.......$ is equal to

A) ${{\left( \frac{2x}{1+x} \right)}^{n}}$

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

C) ${{\left( \frac{1-x}{1+x} \right)}^{n}}$

D) ${{\left( \frac{1+x}{1-x} \right)}^{n}}$

• question_answer194) Eccentricity of the curve ${{x}^{2}}-{{y}^{2}}={{a}^{2}}$is equal to

A) $2$

B) $\sqrt{2}$

C) $4$

D) None of these

• question_answer195) If forces of $12,\text{ }5$ and $13$ unit weight balance at a point, two of them are inclined at

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

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

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

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

• question_answer196) If the resultant of two forces P and Q acting on a particle is at right angle to Q, then the angle between the forces is

A) ${{\cos }^{-1}}\left( \frac{P}{Q} \right)$

B) $\pi -{{\cos }^{-1}}\left( \frac{Q}{P} \right)$

C) $\pi -{{\cos }^{-1}}\left( \frac{P}{Q} \right)$

D) None of these

• question_answer197) To open a lock, a key is taken out from a collection of n keys at random. If the lock is not opened with this key, it is put back into the collection and another key is tried. The process is repeated again and again. If it is given that with only one key in the collection, the lock can be opened, then the probability that the lock will open in n trials, is

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

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

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

D) None of these

• question_answer198) The function $f(x)=x+\frac{1}{x}$ has

A) a local maxima at $x=1$and a local minima at $x=-1$

B) a local minima at $x=1$ and a local maxima at $x=-1$

C) absolute maxima at $x=1$ and absolute minima at $x=-1$

D) Absolute minima at $x=1$ and absolute maxima at $x=-1$

• question_answer199) If the sides of a triangle are $13,7,8,$ then the greatest angle of the triangle is

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

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

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

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

• question_answer200) $\underset{h\to \frac{x}{4}}{\mathop{\lim }}\,\frac{\tan \,x-1}{x-\frac{\pi }{4}}$is equal to

A) $1$

B) $1/2$

C) $2$

D) $0$

• question_answer201) $\underset{h\to 0}{\mathop{lim}}\,\frac{\sin \,\sqrt{x+h}-\sin \,\sqrt{x}}{h}$ is equal to

A) $\cos \,\,\sqrt{x}$

B) $1/(2\,\sin \sqrt{x})$

C) $(\cos \sqrt{x})/2\sqrt{x}$

D) $\sin \sqrt{x}$

• question_answer202) If $f(x)={{x}^{2}}+4x+1,$ then

A) $f(x)=f(-x),$ for all x

B) $f(x)\ne 1,$ for $x=0$

C) $f''(x)>0,$ for all x

D) $f(x)>1,$ for $x\le 1$

• question_answer203) If a, b, c are different real numbers and $a\,\,\hat{i}+b\,\,\hat{j}+c\,\,\hat{k},$$b\,\,\hat{i}+c\,\,\hat{j}+a\,\,\hat{k}$ and $c\,\,\hat{i}+a\,\,\hat{j}+b\,\,\hat{k}$are position vectors of three non-collinear points, then

A) centroid of $\Delta ABC$ is s$\frac{a+b+c}{3}\,(\hat{i}+\hat{j}+\hat{k})$

B) $(\hat{i}+\hat{j}+\hat{k})$ is not really inclined to three vectors

C) triangle ABC is a scalene triangle

D) perpendicular from the origin to the plane of the triangle does not meet it at the centroid

• question_answer204) Given four lines with equations $x+2y-3=0,$ $2x+3y-4=0,$ $3x+4y-5=0,$ $4x+5y-6=0.$ These lines are

A) concurrent

C) the sides of a parallelogram

D) the sides of a square

• question_answer205) The equations of lines through the point $(1,\,1)$ and making angles of ${{45}^{o}}$with the line $x+y=0$are

A) $x-1=0,\,\,x-y=0$

B) $x-1=0,\,\,y-1=0$

C) $x-y=0,\,\,y-1=0$

D) $x+y-2=0,\,\,\,y-1=0$

• question_answer206) If a function F is such that $f(0)=2,\,\,F(1)=3,$ $F(n+2)=2F(n)-F(n+1)$for $n\ne 0,$ then $F(5)$ is equal to

A) $-7$

B) $-3$

C) $7$

D) $13$

• question_answer207) If $f(x)=\frac{1}{\sqrt{-x}},$ then domain of fof is

A) $(0,\,\,\infty )$

B) $(-\,\infty ,\,\,0)$

C) $\{0\}$

D) $\{\,\,\}$

• question_answer208) If x and y are odd integers, then ${{x}^{2}}+{{y}^{2}}$is

A) an odd integer

B) an even integer divisible by 4

C) an even integer not divisible by 4

D) None of the above

• question_answer209) The minimum value of $sin{{\,}^{4}}x+co{{s}^{4}}x$is

A) $1$

B) $0$

C) $1/2$

D) None of these

• question_answer210) The locus of the point of intersection of the lines $x\,cot\,\theta +y\,cosec\,\theta \text{=}2$and $x\,cosec\,\theta +y\,cot\,\theta =6$is

A) a straight line

B) circle

C) a hyperbola

D) an ellipse

• question_answer211) If $2/3,\,k,\,5/8$are in AP, find the value of k.

A) $15$

B) $21$

C) $12$

D) $31/48$

• question_answer212) If $x=\sqrt{3018+\sqrt{36+\sqrt{169}}},$ then the value of x is

A) $55$

B) $44$

C) $63$

D) $42$

• question_answer213) The number of diagonals that can be drawn by joining the vertices of an octagon, is

A) $28$

B) $48$

C) $20$

D) $15$

• question_answer214) If the fourth term in the expansion of ${{\left( ax+\frac{1}{x} \right)}^{n}}$ is $\frac{5}{2},$ then find the value of a and n.

A) $a=1/2$and $n=6$

B) $a=1/3$ and $n=5$

C) $a=2$and $n=3$

D) $a=1/4$and $n=1$

• question_answer215) If ${{e}^{x}}=y+\sqrt{1+{{y}^{2}}},$ then the value of y is

A) ${{e}^{x}}-{{e}^{-x}}$

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

C) ${{e}^{x}}+{{e}^{-x}}$

D) None of these

• question_answer216) In the group $G=\{1,3,7,9\}$under multiplication modulo 10, the inverse of 7 is

A) $7$

B) $3$

C) $9$

D) $1$

• question_answer217) If A and B are two mutually exclusive events then

A) $P(A)<P(\bar{B})$

B) $P(A)>P(\bar{B})$

C) $P(A)<P(B)$

D) None of these

• question_answer218) The equation of the directrix of the parabola ${{y}^{2}}+4y+4x+2=0$ is

A) $-1$

B) $x=1$

C) $x=-3/2$

D) $x=3/2$

• question_answer219) Let ${{T}_{n}}$ denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If ${{T}_{n+1}}-{{T}_{n}}=21,$ then n equals

A) $5$

B) $7$

C) $6$

D) $4$

• question_answer220) In a triangle ABC, $2ca\,\sin \left( \frac{A-B+C}{2} \right)$ is equal to

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

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

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

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

• question_answer221) A fair die is tossed eight times. The probability that a third six is observed on the eight throw is

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

B) $\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{8}}}$

C) $\frac{^{7}{{C}_{2}}\times {{5}^{5}}}{{{6}^{6}}}$

D) None of these

• question_answer222) The greatest distance of the point from the circle ${{x}^{2}}+{{y}^{2}}-4x-2y-20=0$is

A) $10$

B) $15$

C) $5$

D) None of these

• question_answer223) The vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle ABC. The length of the median through A is

A) $\sqrt{18}$

B) $\sqrt{72}$

C) $\sqrt{33}$

D) $\sqrt{288}$

• question_answer224) A particle acted on by constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ is displaced from the point $\hat{i}+2\hat{j}+3\hat{k}$ to the point $5\hat{i}+4\hat{j}+\hat{k}$. The total work done by the forces is

A) 20 unit

B) 30 unit

C) 40 unit

D) 50 unit

• question_answer225) If $f(x)$ is a differentiable function, then $\underset{x\to a}{\mathop{\lim }}\,$ $\frac{a\,\,f(x)-x\,f(a)}{x-a}$ is equal to

A) $a\,\,f'(a)-f(a)$

B) $a\,\,f(a)-f'(a)$

C) $a\,\,f'(a)+f(a)$

D) $\,f'(a)+a\,f(a)$