# Solved papers for J & K CET Engineering J and K - CET Engineering Solved Paper-2008

### done J and K - CET Engineering Solved Paper-2008

• question_answer1) A solid cylinder is rolling down on an inclined plane of angle $\theta ,$ The coefficient of static friction between the plane and cylinder is ${{\mu }_{s}}$. Then condition for the cylinder not to slip is

A) $\tan \,\,\theta \ge \,3{{\mu }_{s}}$

B) $\tan \,\,\theta >3{{\mu }_{s}}$

C) $\tan \,\,\theta \le 3{{\mu }_{s}}$

D) $\tan \,\,\theta <3{{\mu }_{s}}$

• question_answer2) The moment of inertia of a circular ring of mass $1\text{ }kg$about an axis passing through its centre and perpendicular to its plane is $4\text{ }kg-{{m}^{2}}$. The diameter of the ring is

A) $2\,\,m$

B) $4\,\,m$

C) $5\,\,m$

D) $6\,\,m$

• question_answer3) If g is the acceleration due to gravity on the surface of earth, its value at a height equal to double the radius of earth is

A) $g$

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

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

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

• question_answer4) On bombardment of ${{U}^{235}}$ by slow neutrons, $200\text{ }MeV$ energy is released. If the power output of atomic reactor is $1.6\text{ }MW,$ then the rate of fission will be

A) $5\times {{10}^{16}}/s$

B) $10\times {{10}^{16}}/s$

C) $15\times {{10}^{16}}/s$

D) $20\times {{10}^{-16}}/s$

• question_answer5) A stress of $3.18\times {{10}^{8}}\,N-{{m}^{-2}}$ is applied to a steel rod of length 1 m along its length. Its Young's modulus is $2\times {{10}^{11}}\text{ }N-{{m}^{-2}}$. Then, the elongation produced in the rod (in mm) is

A) $3.18$

B) $6.36$

C) $5.18$

D) $1.59$

• question_answer6) A liquid is allowed into a tube of truncated cone shape. Identify the correct statement from the following.

A) The speed is high at the wider end and low at the narrow end

B) The speed is low at the wider end and high at the narrow end

C) The speed is same at both ends in a stream line flow

D) The liquid flows with uniform velocity in the tube

• question_answer7) A sphere of radius R is gently dropped into liquid of viscosity $\eta$ in a vertical uniform tube. It attains a terminal velocity v. Another sphere of radius 2R when dropped into the same liquid, will attain its terminal velocity

A) $v$

B) $2v$

C) $4v$

D) $9v$

• question_answer8) The excess pressure in a bubble of radius R of a gas in a liquid of surface tension S is

A) $\frac{2\,S}{R}$

B) $\frac{2\,R}{S}$

C) $\frac{2\,S}{{{R}^{2}}}$

D) $\frac{2{{R}^{2}}}{S}$

• question_answer9) The average kinetic energy of a gas molecule is

A) proportional to pressure of gas

B) inversely proportional to volume of gas

C) inversely proportional to absolute temperature of gas

D) directly proportional to absolute temperature of gas

• question_answer10) Ideal gas undergoes an adiabatic change in its state from $({{p}_{1}},{{V}_{1}},{{T}_{1}})$ to $({{p}_{2}},{{V}_{2}},{{T}_{2}})$. The work done (W) in the process is ($\mu =$ number of molecules, ${{C}_{P}}$ and ${{C}_{V}}$ are molar specific heats of gas)

A) $W=\mu {{C}_{P}}({{T}_{1}}-{{T}_{2}})$

B) $W=\mu {{C}_{V}}({{T}_{1}}-{{T}_{2}})$

C) $W=\mu {{C}_{P}}({{T}_{1}}+{{T}_{2}})$

D) $W=\mu {{C}_{V}}({{T}_{1}}+{{T}_{2}})$

• question_answer11) For an ideal gas

A) ${{C}_{P}}$ is less than ${{C}_{V}}$

B) ${{C}_{P}}$ is equal to ${{C}_{V}}$

C) ${{C}_{P}}$ is greater than ${{C}_{V}}$

D) ${{C}_{P}}={{C}_{V}}=0$

• question_answer12) For a gas molecule with 6 degrees of freedom the law of equipartition of energy gives the following relation between the molecular specific heat $({{C}_{V}})$ and gas constant (R)

A) ${{C}_{V}}=\frac{R}{2}$

B) ${{C}_{V}}=R$

C) ${{C}_{V}}=2R$

D) ${{C}_{V}}=3R$

• question_answer13) Wien's displacement law for emission of radiation can be written as

A) ${{\lambda }_{\max }}$max is proportional to absolute temperature (T)

B) ${{\lambda }_{\max }}$ is proportional to square of absolute temperature $({{T}^{2}})$

C) ${{\lambda }_{\max }}$ is inversely proportional to absolute temperature (T)

D) ${{\lambda }_{\max }}$ is inversely proportional to square of absolute temperature $({{T}^{2}})$ (${{\lambda }_{\max }}$ = wavelength whose energy density is greatest)

• question_answer14) The frequency of the fundamental note in a wire stretched under tension T is /. If the tension is increased to 25 T, then the frequency of the fundamental note will be

A) $25\,f$

B) $5\,f$

C) $10\,f$

D) $f$

• question_answer15) The frequency of fundamental note in an organ pipe is $240\text{ }Hz.$ On blowing air, frequencies $720\text{ }Hz$and $1200\text{ }Hz$are heard. This indicates that organ pipe is

A) a pipe closed at one end

B) a pipe open at both ends

C) closed at both ends

D) having holes like flute

• question_answer16) If ${{L}_{1}}$and ${{L}_{2}}$ are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is

A) $2({{L}_{2}}+{{L}_{1}})$

B) $2({{L}_{2}}-{{L}_{1}})$

C) $2\left( {{L}_{2}}-\frac{{{L}_{1}}}{2} \right)$

D) $2\left( {{L}_{2}}+\frac{{{L}_{1}}}{2} \right)$

• question_answer17) Beats are produced by frequencies ${{f}_{1}}$ and ${{f}_{2}}({{f}_{1}}>{{f}_{2}})$. The duration of time between two successive maxima or minima is equal to

A) $\frac{1}{{{f}_{1}}+{{f}_{2}}}$

B) $\frac{2}{{{f}_{1}}-{{f}_{2}}}$

C) $\frac{2}{{{f}_{1}}+{{f}_{2}}}$

D) $\frac{1}{{{f}_{1}}-{{f}_{2}}}$

• question_answer18) If a body is executing simple harmonic motion, then

A) at extreme positions, the total energy is zero

B) at equilibrium position, the total energy is in the form of potential energy

C) at equilibrium position, the total energy is in the form of kinetic energy

D) at extreme position, the total energy is infinite

• question_answer19) An electric dipole has a pair of equal and opposite point charges q and $-q$ separated by a distance 2x. The axis of the dipole is defined as

A) direction from positive, charge to negative charge

B) direction from negative charge to positive charge

C) perpendicular to the line joining the two charges drawn at the centre and pointing upward direction

D) perpendicular to the line joining the two charges drawn at the centre and pointing downward direction

• question_answer20) The dipole moment of a dipole in an uniform external field $\vec{E}$ is $\vec{P}$. Then, the torque $(\tau )$ acting on the dipole is

A) $\vec{\tau }=\vec{P}\times \vec{E}$

B) $\vec{\tau }=\vec{P}.\vec{E}$

C) $\vec{\tau }=2(\vec{P}+\vec{E})$

D) $\vec{\tau }=(\vec{P}+\vec{E})$

• question_answer21) The electric flux through a closed surface area S enclosing charge Q is $\phi$. If the surface area is doubled, then the flux is

A) $2\,\phi$

B) $\phi /2$

C) $\phi /4$

D) $\phi$

• question_answer22) Consider a thin spherical shell of radius R consisting of uniform surface charge density $\sigma$ The electric field at a point of distance x from its centre and outside the shell is

A) inversely proportional to $\sigma$

B) directly proportional to ${{x}^{2}}$

C) directly proportional to $\sigma$

D) inversely proportional to ${{x}^{2}}$

• question_answer23) The work done in bringing at a unit positive charge from infinity distance to a point at distance X from a positive charge Q is W. Then the potential $\phi$ at that point is

A) $\frac{WQ}{X}$

B) $W$

C) $\frac{W}{Q}$

D) $WQ$

• question_answer24) The capacitance C of a capacitor is

A) independent of the charge and potential of the capacitor

B) dependent on the charge and independent of potential

C) independent of the geometrical configuration of the capacitor

D) independent of the dielectric medium between the two conducting surfaces of the capacitor

• question_answer25) Four capacitors are connected in a circuit as shown in the following figure. Calculate the effective capacitance between the points A and B.

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

B) $\frac{24}{5}\mu F$

C) $9\,\mu F$

D) $5\,\mu F$

A) zero resistivity

B) high resistivity

C) low resistivity

D) infinite resistivity

• question_answer27) The electric potential inside a conducting sphere

A) increases from centre to surface

B) decreases from centre to surface

C) remains constant from centre to surface

D) is zero at every point inside

• question_answer28) Electron of mass m and charge e in external field ? experiences acceleration

A) $\frac{e}{mE},$ in the opposite direction to the field

B) $\frac{eE}{m},$ in the direction of the field

C) $\frac{em}{E},$ m the direction of the field

D) $\frac{eE}{m},$ in the opposite direction of the field,

• question_answer29) Kirchhoff?s second law for the analysis of circuit is based on

A) conservation of charge

B) conservation of energy

C) conservation of both charge and energy

D) conservation of momentum of electron

• question_answer30) In circuit shown below, the resistances are given in ohm and the battery is assumed ideal with emf equal to$3\text{ }V$. The voltage across the resistance ${{R}_{4}}$ is

A) $0.4V$

B) $0.6V$

C) $1.2\text{ }V$

D) $1.5V$

• question_answer31) The direction of induced magnetic field $d\,\,\vec{B}$ due to current element i d $\vec{L},$ at a point of distance r from it, when a current i passes through a long conductor is in the direction

A) of position vector $\vec{r}$ of the point

B) of current element $d\,\vec{L}$

C) perpendicular to both $d\,\vec{L}$ and $\vec{r}$

D) perpendicular to $\vec{L}$ only

• question_answer32) The magnetic force on a charged particle moving in the field does not work, because

A) kinetic energy of the charged particle does not change

B) the charge of the particle remains same

C) the magnetic force is parallel to velocity of the particle

D) the magnetic force is parallel to magnetic field

• question_answer33) To convert a moving coil galvanometer (MCG) into a voltmeter

A) a high resistance R is connected in parallel with MCG

B) a low resistance r is connected in parallel with MCG

C) a low resistance r is connected in series With MCG

D) a high resistance R is connected in series with MCG

• question_answer34) Identify the correct statement from the following.

A) Cyclotron frequency is dependent on speed of the charged particle

B) Kinetic energy of charged particle in cyclotron does not dependent on its mass

C) Cyclotron frequency does not depend on speed of charged particle

D) Kinetic energy of charged particle in cyclotron is independent of its charge

• question_answer35) Consider two straight parallel conductors A and B separated by a distance x and carrying individual currents ${{i}_{A}}$ and ${{i}_{B}}$ respectively. If the two conductors attract each other, it indicates that

A) the two currents are parallel in direction

B) the two currents are anti-parallel in direction

C) the magnetic lines of induction are parallel

D) the magnetic lines of induction are parallel to length of conductors

• question_answer36) The magnetic susceptibility of paramagnetic materials is

A) positive, but very high

B) negative, but small

C) negative but very high

D) positive, but small

• question_answer37) According to Lenz's law of electromagnetic induction

A) the induced emf is not in the direction opposing the change in magnetic flux

B) the relative motion between the coil and magnet produces change in magnetic flux

C) only the magnet should be moved towards coil

D) only the coil should be moved towards magnet

• question_answer38) According to phenomenon of mutual inductance

A) the mutual inductance does not dependent on geometry of the two coils involved

B) the mutual inductance depends on the intrinsic magnetic property, like relative permeability of the material

C) the mutual inductance is independent of the magnetic property of the material

D) ratio of magnetic flux produced by the coil 1 at-the place of the coil 2 and the current in the coil 2 will be different from that of the ratio defined by interchanging the coils

• question_answer39) The natural frequency $({{\omega }_{0}})$ of oscillations in L-C circuit is given by

A) $\frac{1}{2\pi }\frac{1}{\sqrt{LC}}$

B) $\frac{1}{2\pi }\,\sqrt{LC}$

C) $\frac{1}{\,\sqrt{LC}}$

D) $\sqrt{LC}$

• question_answer40) In L-C-R series circuit the resonance condition in terms of capacitive reactance $({{X}_{C}})$ and inductive reactance $({{X}_{L}})$ is

A) ${{X}_{C}}+{{X}_{L}}=0$

B) ${{X}_{C}}=0$

C) ${{X}_{L}}=0$

D) ${{X}_{C}}-{{X}_{L}}=0$

• question_answer41) In step-up transformer, relation between number of turns in primary $({{N}_{P}})$ and number of turns in secondary $({{N}_{S}})$ coils is

A) ${{N}_{s}}$ is greater than ${{N}_{p}}$

B) ${{N}_{p}}$ is greater than ${{N}_{s}}$

C) ${{N}_{s}}$ is equal to ${{N}_{p}}$

D) ${{N}_{p}}=2{{N}_{s}}$

• question_answer42) Two light sources are said to be of coherent nature

A) when they have same frequency and a varying phase difference

B) when they have same frequency and a constant phase difference

C) when they have constant phase difference and different frequencies

D) when they have varying phase difference and different frequencies

• question_answer43) In Young's double slit interference pattern the fringe width

A) can be changed only by changing the wavelength of incident light

B) can be changed only by changing the separation between the two slits

C) can be changed either by changing the wavelength or by changing the separation between two sources

D) is a universal constant and hence cannot be changed

• question_answer44) Colours in thin films are due to

A) diffraction phenomenon

B) scattering phenomenon

C) interference phenomenon

D) polarization phenomenon

• question_answer45) Brewster?s angle in terms of refractive index (n) of the medium

A) ${{\tan }^{-1}}\,\sqrt{n}$

B) ${{\sin }^{-1}}\,n$

C) ${{\sin }^{-1}}\,\sqrt{n}$

D) ${{\tan }^{-1}}\,n$

• question_answer46) The angle of incidence of light is equal to Brewster?s angle, then

 A. reflected ray is perpendicular to refracted ray B. refracted ray is parallel to reflected ray C. reflected light is polarized having its electric vector in the plane of incidence D. refracted light is polarized

A) [A] and [D] are true

B) [A] and [B] are true

C) [A] and [C] are true

D) [B] and [C] are true

• question_answer47) The working of optical fibres is based on

A) dispersion of light

B) total internal reflection

C) polarization of light

D) interference of light

• question_answer48) First Bohr radius of an atom with $Z=82$is R. Radius of its third orbit is

A) $9\,\,R$

B) $6\,\,R$

C) $3\,R$

D) $R$

• question_answer49) The de-Broglie wavelength associated with a particle moving with momentum (p) and mass (m) is

A) $\frac{h}{p}$

B) $\frac{h}{mp}$

C) $\frac{h}{{{p}^{2}}}$

D) $\frac{{{h}^{2}}}{{{p}^{2}}}$

• question_answer50) The angular momentum (L) of an electron moving in a stable orbit around nucleus is

A) half integral multiple of $\frac{h}{2\pi }$

B) integral multiple of h

C) integral multiple of $\frac{h}{2\pi }$

D) half integral multiple of h

• question_answer51) According to Moseley's law of X-rays the frequency (v) of a particular characteristic X-ray and the atomic number (Z) of the element depend on each other as

A)  $\sqrt{v}=k{{Z}^{2}}$

B)  $\sqrt{v}=\frac{h}{{{Z}^{2}}}$

C)  $v=kZ$

D)  $\sqrt{v}=kZ$

• question_answer52) If $\lambda$ is decay constant and N the number of radioactive nuclei of an element, then the decay rate (R) of that element is

A) $\lambda {{N}^{2}}$

B) $\lambda N$

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

D) ${{\lambda }^{2}}N$

• question_answer53) The ratio of half-life times of two elements A and B is $\frac{{{T}_{A}}}{{{T}_{B}}}$ The ratio of respective decay constants $\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}$ is

A) $\frac{{{T}_{B}}}{{{T}_{A}}}$

B) $\frac{{{T}_{A}}}{{{T}_{B}}}$

C) $\frac{{{T}_{A}}+{{T}_{B}}}{{{T}_{A}}}$

D) $\frac{{{T}_{A}}-{{T}_{B}}}{{{T}_{A}}}$

• question_answer54) For a nuclear to be in critical condition, the value of neutron multiplication factor (k) must be

A) $k>1$

B) $k<1$

C) $k=1$

D) $k=0$

• question_answer55) If ${{n}_{E}}$ and ${{n}_{H}}$ represent the number of free electrons and holes respectively in a semiconducting material, then for n-type semiconducting material

A) ${{n}_{E}}<<{{n}_{H}}$

B) ${{n}_{E}}>>{{n}_{H}}$

C) ${{n}_{E}}={{n}_{H}}$

D) ${{n}_{E}}={{n}_{H}}=0$

• question_answer56) An intrinsic semiconductor at $0\text{ }K$temperature behaves like

A) conductor

B) p-type semiconductor

C) n-typesemiconductor

D) insulator

• question_answer57) When a p-n junction diode is connected in forward bias its barrier potential

A) decreases and less current flows in the circuit

B) decreases and more current flows in the circuit

C) increases and more current flows in the circuit

D) decreases and no current flows in the circuit

• question_answer58) The main cause of zener breakdown is

A) the base semiconductor being germanium

B) production of electron-hole pairs due to thermal excitation

C) low doping

D) high doping

• question_answer59) The depletion layer in a silicon diode is $1\,\mu m$ wide and its knee potential is $0.6\text{ }V,$ then the electric field in the depletion layer will be

A) $0.6\text{ }V/m$

B) $6\times {{10}^{4}}\,V/m$

C) $6\times {{10}^{5}}\,V/m$

D) zero

• question_answer60) Identify the true statement for OR gate

A) Output Y will be 1 when input A or B or both are 1

B) Output Y will be 0 when the either of the inputs A or B is 1

C) Output Y will be 1 only when both the inputs A and Bare 1

D) Output Y will be 1 only when either of the inputs A and B are 1

• question_answer61) Dimensional formula for force is

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

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

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

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

• question_answer62) X is a vector with magnitude A, then the unit vector a in the direction of vector A is

A) $A\,\vec{A}$

B) $\vec{A}.\,\vec{A}$

C) $\vec{A}\times \,\vec{A}$

D) $\frac{|\vec{A}|}{A}$

• question_answer63) A body is under the action of two mutually perpendicular forces of $3\text{ }N$and$4\text{ }N$. The resultant force acting on the body is

A) $7\,N$

B) $1\,N$

C) $5\,N$

D) zero

• question_answer64) If the scalar and vector products of two vectors X and S are equal in magnitude, then the angle between the two vectors is

A) ${{45}^{o}}$

B) ${{90}^{o}}$

C) ${{180}^{o}}$

D) ${{360}^{o}}$

• question_answer65) A body is moving along a straight line path with constant velocity. At an instant of time the distance travelled by it is 5 and its displacement is D, then

A) $D<s$

B) $D>s$

C) $D=s$

D) $D\le s$

• question_answer66) A body is projected at an angle $\theta$ with respect to horizontal direction with velocity u. The maximum range of the body is

A) $R=\frac{{{u}^{2}}\,\sin \,\,2\theta }{g}$

B) $R=\frac{{{u}^{2}}\,{{\sin }^{2}}\theta }{2g}$

C) $R=\frac{{{u}^{2}}}{g}$

D) $R={{u}^{2}}\,\,\sin \,\,\theta$

• question_answer67) A body moving along a circular path of radius R with velocity v, has centripetal acceleration a. If its velocity is made equal to 2v, then its centripetal acceleration is

A) $4\,a$

B) $2\,a$

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

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

• question_answer68) A cyclist is travelling with velocity v on a banked curved road of radius R. The angle $\theta$ through which the cyclist leans inwards is given by

A) $\tan \,\theta =\frac{Rg}{{{v}^{2}}}$

B) $\tan \,\theta ={{v}^{2}}\,Rg$

C) $\tan \,\theta =\frac{{{v}^{2}}\,g}{R}$

D) $\tan \,\theta =\frac{{{v}^{2}}}{Rg}$

• question_answer69) A body starts from rest and moves with uniform acceleration. Which of the following graphs represent its motion?

A)

B)

C)

D)

• question_answer70) A gun fires N bullets per second, each of mass m with velocity v. The force exerted by the bullets on the gun is

A) $vNm$

B) $\frac{mv}{N}$

C) $mv{{N}^{2}}$

D) $\frac{m{{v}^{2}}}{N}$

• question_answer71) The rate of mass of the gas emitted from rear of a rocket is initially$0.1\text{ }kg/s$. If the speed of the gas relative to the rocket is $50\text{ }m/s$and mass of the rocket is$2\text{ }kg$, then the acceleration of the rocket (in$m/{{s}^{2}}$) is

A) $5$

B) $5.2$

C) $2.5$

D) $25$

• question_answer72) The area under the displacement-force curve gives

A) distance travelled

B) total force

C) momentum

D) work done

• question_answer73) Identify the correct statement for the rotational motion of a rigid body.

A) Individual particles of the body do not undergo accelerated motion

B) The centre of mass of the body remains unchanged

C) The centre of mass of the body moves uniformly in a circular path

D) Individual particles and centre of mass the body undergo an accelerated motion

• question_answer74) The moment of inertia about an axis of a body which is rotating with angular velocity 1 rad/s is numerically equal to

A) one-fourth of its rotational kinetic energy

B) half of the rotational kinetic energy

C) rotational kinetic energy

D) twice the rotational kinetic energy

• question_answer75) The moment of inertia of a circular disc of radius$2\text{ }m$and mass $2\text{ }kg,$ about an axis passing through its centre of mass is$2\text{ }kg-{{m}^{2}}$. Its moment of inertia about an axis parallel to this axis and passing through its edge (in$kg-{{m}^{2}}$) is

A) $10$

B) $8$

C) $6$

D) $4$

• question_answer76) The phenomenon observed when a beam of light is passed through a colloidal solution, is

A) cataphoresis

B) delectrophoresis

C) coagulation

D) Tyndall effect

• question_answer77) In case of condensation of polymers

A) high molecular weight polymers are formed all at once

B) lower molecular weight polymers are formed all at once

C) molecular weight of polymer rises throughout the reaction

D) have no Specific relation to their molecular weight

• question_answer78) The element with the lowest ionization potential is

A) Na

B) K

C) Rb

D) Cs

• question_answer79) Differentiating electron in inner transition elements enters the ......... orbital.

A) s

B) p

C) d

D) $f$

• question_answer80) Which one of the following is a non-polar molecule?

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

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

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

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

• question_answer81) The nature of the bond in diamond is

A) ionic

B) covalent

C) metallic

D) coordinate covalent

• question_answer82) According to VSEPR theory the repulsion between different pair (lone or bond) of electrons obey the order

A) $lp-bp-lp-lp>bp-bp$

B) $lp-bp>bp-bp>lp-lp$

C) $lp-lp>lp-bp>lp-bp$

D) $bp-bp>lp-lp>lp-bp$

• question_answer83) From the molecular orbital theory, one can show that the bond order in ${{F}_{2}}$molecule as

A) 2

B) 1

C) 3

D) 4

• question_answer84) Which of the following metal oxides is most basic?

A) $ZnO$

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

C) $A{{s}_{2}}{{O}_{3}}$

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

• question_answer85) In the laboratory ${{\text{H}}_{\text{2}}}\text{S}$gas is prepared by using black lumps and dil.${{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}\text{.}$ The black lumps are

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

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

C) $FeS$

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

• question_answer86) The order of electron affinity of halogens is

A) $F>Cl>Br>I$

B) $Cl>F>Br>I$

C) $Cl>F>I>Br$

D) $Br>Cl>F>I$

• question_answer87) When chlorine reacts with dil. $\text{NaOH}$under cold conditions, the oxidation state of chlorine changes from zero to

A) - 1 and + 5

B) + 1 and + 4

C) + 5 and +3

D) - 1 and + 1

• question_answer88) The highest oxidation state exhibited by transition metals is

A) + 7

B) + 8

C) + 6

D) + 5

• question_answer89) Which one of the following statements is not true with regard to transition elements?

A) They readily form complex compounds

B) They show variable oxidation states

C) All their ions are colourless

D) Their ions contain partially filled d-electrons

• question_answer90) The catalyst used in the manufacture of ammonia is

A) ${{V}_{2}}{{O}_{5}}$

B) $Pt$

C) $Fe$

D) $Ni{{(CO)}_{4}}$

• question_answer91) The most stable oxidation state of lanthanides is

A) + 2

B) + 4

C) 0

D) + 3

• question_answer92) The number of ions formed when hexamine copper (II) sulphate is dissolved in water is

A) 1

B) 2

C) 4

D) 6

• question_answer93) The number of unpaired electrons in the square planar ${{[Pt{{(CN)}_{4}}]}^{2-}}$ion is

A) 2

B) 1

C) 0

D) 3

• question_answer94) In metal carbonyl (organometallic) complexes, the M-C bond is

A) ionic

B) covalent with ionic character

C) covalent

D) coordinate covalent

• question_answer95) The complexes$[PrC{{l}_{2}}{{(N{{H}_{3}})}_{4}}]B{{r}_{2}}$ and $[PtB{{r}_{2}}{{(N{{H}_{3}})}_{4}}]C{{l}_{2}}$are examples for isomerism

A) geometrical

B) optical

C) ionisation

• question_answer96) The metallurgical process in which a metal is obtained in a fused state is called

A) smelting

B) roasting

C) calcination

D) froth floatation

• question_answer97) Metallic silver may be obtained from $\text{AgCl}$by

A) heating it in the current of ${{\text{H}}_{\text{2}}}$

B) fusing it with sand

C) treating with carbon monoxide

D) fusing it with $\text{N}{{\text{a}}_{\text{2}}}\text{C}{{\text{O}}_{\text{3}}}$

• question_answer98) Which one of the following metals is extracted by a carbon reduction process?

A) Copper

B) Iron

C) Aluminium

D) Magnesium

• question_answer99) IUPAC name of $C{{H}_{3}}-\underset{Cl}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{2}}-CHO$is $Cl$

A) 3-chlorobutanol

B) 3-chlorobutanaldehyde

C) 3-chlorobutanal

D) 2-chlorobutanol

• question_answer100) Di-chloroacetic acid is a stronger acid than acetic acid. This is due to occurrence of

A) mesomeric effect

B) hyperconjugation

C) inductive effect

D) steric effect

• question_answer101) Dehydration of alcohol is an example of which type of reaction?

A) Substitution

B) Elimination

D) Rearrangement

• question_answer102) Number of monochloro derivatives obtained when neo-pentane is chlorinated, is

A) one

B) two

C) three

D) four

• question_answer103) Which of the following alkenes gives only acetaldehyde on ozonolysis?

A) Ethene

B) Propene

C) 1-butene

D) 2-butene

• question_answer104) 1-butyne on hydration gives

A) butan-1, 2-diol

B) butan-1-ol

C) butan-2-ol

D) butan-2-one

• question_answer105) Least stable conformer of cyclohexane is

A) chair

B) boat

C) twist boat

D) planar hexagon

• question_answer106) Which one of the following monoenes does not exhibit geometric isomerism?

A) ${{C}_{4}}{{H}_{8}}$

B) ${{C}_{3}}{{H}_{6}}$

C) ${{C}_{5}}{{H}_{10}}$

D) ${{C}_{8}}{{H}_{16}}$

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

B)

C)

D)

• question_answer108) Conversion of chlorobenzene to phenol involves

A) electrophilic substitution

B) nucleophilic substitution

A) an ester

B) an anhydride

C) acetal

D) hemiacetal

• question_answer110) Which one of the following does not give iodoform?

A)

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

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

D) $C{{H}_{3}}-\underset{OH}{\mathop{\underset{|}{\mathop{C}}\,}}\,H-C{{H}_{3}}$

• question_answer111) The products obtained when anisole is heated in a sealed tube with HI are

A)

B)

C)

D) $C{{H}_{3}}OH+C{{H}_{3}}I$

• question_answer112) Which of the following diacid readily gives anhydride on heating?

A) Fumaric

B) Maleic acid

C) Malic acid

D) Terephthalic acid

• question_answer113) Hydroxamic acid test is employed to detect

A) ketones

B) aldehydes

C) esters

D) amides

• question_answer114) Picric acid is a stronger acid than acetic acid and benzoic acid. It contains

A) $-\text{S}{{\text{O}}_{\text{3}}}\text{H}$group

B) two$-COOH$ groups

C) phenolic group

D) three $-COOH$groups

• question_answer115) Benzamide can be converted into benzonitrile with

A) ${{H}_{3}}{{O}^{+}}$

B) $O{{H}^{-}}/{{H}_{2}}O$

C) KCN

D) ${{P}_{2}}{{O}_{5}}$

• question_answer116) The most basic compound in the following is

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

B) $~C{{H}_{3}}N{{H}_{2}}$

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

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

• question_answer117) The compound with foul odour among the following is-

A)

B)

C)

D)

• question_answer118) Nitration of nitrobenzene at $125{}^\circ C$ with mixed acids gives

A) meto-dinitrobenzene

B) ortho-dinitrobenzene

C) para-dinitrobenzene

D) 1, 3, 5-trinitro benzene

• question_answer119) The $\alpha -$amino acid which does not give purple colour in the ninhydrin test is

A) proline

B) glycine

C) lysine

D) aspartic acid

• question_answer120) The anomeric carbon in $\text{D}\,\text{(+)}$glucose is

A) $C-1$carbon

B) $C-2$carbon

C) $C-5$carbon

D) $C-6$ carbon

• question_answer121) The stoichiometry of the following reaction is ${{K}_{2}}{{S}_{2}}{{O}_{8}}(aq)+2KI(aq)\to 2{{K}_{2}}S{{O}_{4}}(aq)+{{I}_{2}}(aq)$

A) 2:2

B) 1:1

C) 1:2

D) 2:1

• question_answer122) Of two oxides of iron, the first contained 22% and the second contained 30% of oxygen by weight. The ratio of weights of iron in the two oxides that combine with the same weight of oxygen, is

A) 3:2

B) 2:1

C) 1:2

D) 1:1

• question_answer123) The scientist who proposed the atomic model based on the quantization of energy for the first time is

A) Max Planck

B) Niels Bohr

C) de-Broglie

D) Heisenberg

• question_answer124) Which one of the following is the set of correct quantum numbers of an electron in 3d orbital?

A) $~n=3,l=0,m=0,s=-\text{ }1/2$

B) $~n=2,l=3,m=0,s=+1/2$

C) $~n=3,l=1,m=0,s=-1/2$

D) $~n=3,l=2,m=1,s=+\,1/2$

• question_answer125) Electron density in the YZ plane of $3{{d}_{{{x}^{2}}-{{y}^{2}}}}$ orbital is

A) zero

B) 0.50

C) 0.75

D) 0.90

• question_answer126) The half-life period of a radioactive isotope is 4.8 min. Starting with 1 mg of the isotope, how much of it would remain after 10 min?

A) 0.5 mg

B) 0.726 mg

C) 0.126 mg

D) 0.236 mg

• question_answer127) The number of beta particles emitted in the radioactive decay series from $^{238}{{U}_{92}}$to $^{206}P{{b}_{82}}$is

A) 10

B) 8

C) 6

D) 2

• question_answer128) What happens to the yield on application of high pressure in the Habefs synthesis of ammonia?

A) Increases

B) Decreases

C) Unaffected

D) Reaction stops

• question_answer129) In the reaction${{H}_{2}}(g)+C{{l}_{2}}(g)\rightleftharpoons 2HCl(g)$

A) ${{K}_{p}}\ne {{K}_{c}}$

B) ${{K}_{p}}={{K}_{c}}$

C) ${{K}_{p}}>{{K}_{c}}$

D) ${{K}_{p}}<{{K}_{c}}$

• question_answer130) pH of an aqueous solution containing ${{10}^{-8}}mol/L$of $HCl$is

A) 8

B) 10

C) 6.96

D) 12

• question_answer131) An aqueous solution contains $N{{i}^{2+}},C{{o}^{2+}}$and$P{{b}^{2+}}$ions at equal concentrations. The solubility product of $\text{NiS, PbS}$and $\text{CoS}$in water at $\text{25}{{\,}^{\text{o}}}\text{C}$are $\text{1}\text{.4}\times \text{1}{{\text{0}}^{-24}},$and$3\times {{10}^{-26}},$respectively. Indicate which of these ions will be precipitated first and last when sulphide concentration is progressively increased from zero?

A) NiS and PbS

B) NiS and CoS

C) CoS and NiS

D) PbS and NiS

• question_answer132) A reaction involving A, B and C as reactants is found to obey the rate law, rate $=k{{[A]}^{x}}{{[B]}^{y}}{{[C]}^{z}}.$When the concentrations of A, B and C are doubled separately, the rate is also found to increase two, zero and four times respectively. The overall order of the reaction is

A) 1

B) 2

C) 3

D) 4

• question_answer133) The units of the rate of a second order reaction are

A) $\text{tim}{{\text{e}}^{-1}}$

B) $\text{mol}\,{{\text{L}}^{-1}}\,\text{tim}{{\text{e}}^{-1}}$

C) $\text{L}\,\text{mol}{{\,}^{-1}}\,\text{tim}{{\text{e}}^{-1}}$

D) ${{\text{L}}^{2}}\,\text{mol}{{\,}^{-2}}\,\text{tim}{{\text{e}}^{-1}}$

• question_answer134) Activation energy of a reaction

A) is independent of temperature

B) increases with temperature

C) gets doubled for every 10 degree rise in temperature

D) decreases with temperature

• question_answer135) Which one of the following concentration units is independent of temperature?

A) Normality

B) Molarity

C) Molality

D) ppm

• question_answer136) Maximum lowering of vapour pressure is observed in the case of

A) 0.1 M glucose

B) $0.1\text{ }M\text{ }BaC{{l}_{2}}$

C) $\text{ }\!\!~\!\!\text{ 0}\text{.1 M MgS}{{\text{O}}_{\text{4}}}$

D) $\text{ }\!\!~\!\!\text{ 0}\text{.1 NaCl}$

• question_answer137) A solution containing 4 g of polyvinyl chloride polymer in one litre of dioxane was found to have an osmotic pressure of $\text{4}\text{.1}\times {{10}^{-4}}\text{atm}$at $\text{27}{{\,}^{\text{o}}}\text{C}\text{.}$ The approximate molecular weight of the polymer is

A) 1500

B) 10,000

C) $\text{2}\text{.4}\times \text{1}{{\text{0}}^{5}}$

D) $\text{2}\times \text{1}{{\text{0}}^{12}}$

• question_answer138) Abnormal colligative properties are observed only when the dissolved non-volatile solute in a given dilute solution

A) is a non-electrolyte

B) offers an intense colour

C) associates or dissociates

D) offers no colour

• question_answer139) We believe in the laws of thermodynamics because they are

A) theoretical

B) derived based on mathematical analysis

C) empirical and nobody disproved

D) mere statements

• question_answer140) The latent heat of fusion of ice at $0{{\,}^{o}}C$is$\text{80}\,\text{cal/g}\text{.}$Entropy change $\text{(}\Delta S\text{)}$ accompanying the melting of 1 g of ice at $0{{\,}^{o}}C$would be (units:$cal/g/K$)

A) 273

B) 8.0

C) 0.0

D) 0.293

• question_answer141) $\Delta H$ for the reaction, $C(graphite)+2{{H}_{2}}(g)\xrightarrow{{}}C{{H}_{4}}(g)$at $298\,K$and 1  atm is$~-\text{ }17900\text{ cal}\text{.}$ The $\Delta E$for  the above conversion would be

A) $-\text{ }17900\text{ cal}$

B) $\text{ }\!\!~\!\!\text{ 17900 cal}$

C) $\text{17308 cal}$

D) $~-\text{ }17308\text{ cal}$

• question_answer142) Which one of the following is spontaneous at all temperatures?

A) ${{H}_{2}}(g)\xrightarrow{{}}2{{H}_{\text{atom}}}$ $\Delta {{H}^{o}}=436\,kJ,\Delta {{S}^{o}}=90.7\,\text{eu}$

B) $\frac{1}{2}{{N}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow{{}}NO(g);$ $\Delta {{H}^{o}}=90.3\,kJ,\Delta {{S}^{o}}=3.0\,\text{eu}$

C) $2N{{O}_{2}}(g)\xrightarrow{{}}{{N}_{2}}{{O}_{4}}(g)$ $\Delta {{H}^{o}}=-56.0\,kJ\,\Delta {{S}^{o}}=-17.7\text{eu}$

D) ${{H}_{2}}{{O}_{2}}(g)\xrightarrow{{}}{{H}_{2}}O(l)+\frac{1}{2}{{O}_{2}}(g)$ $\Delta {{H}^{o}}=-98.3\,kJ\Delta {{S}^{o}}=80.0\,\text{eu}$

• question_answer143) During a redox titration involving a solution containing $\text{F}{{\text{e}}^{\text{2+}}}$ions against$\text{MnO}_{4}^{-}$in the presence of excess of ${{\text{H}}^{\text{+}}}$ions, the number of electrons that gets transferred is.

A) 6

B) 5

C) 4

D) 2

• question_answer144) The oxidation state of sulphur in sodium tetrathionate $\text{(N}{{\text{a}}_{2}}{{\text{S}}_{4}}{{\text{O}}_{6}}\text{)}$is

A) 2

B) 0

C) 2.5

D) 3.5

• question_answer145) Galvanic cell is a device in which

A) chemical energy is converted into electrical energy

B) electrical energy is converted into chemical energy

C) chemical energy is seen in the form of heat

D) thermal energy from an outside source is used to drive the cell reaction

• question_answer146) The relationship between Gibbs' free energy change$(\Delta G)$and emf$(E)$of a reversible electrochemical cell is given by

A) $\Delta G=nFE$

B) $\Delta G=nF/E$

C) $\Delta G=-nFE$

D) $\Delta G=E/nF$

• question_answer147) The units of van der Waals' constants a, b respectively, are

A) $\text{L}\,\,\text{at}{{\text{m}}^{\text{2}}}\,\text{mo}{{\text{l}}^{-1}}$and $\text{mo}{{\text{l}}^{-1}}$

B) $\text{L}\,\,\text{atm}\,\text{mo}{{\text{l}}^{2}}$and $\text{mol L}$

C) ${{\text{L}}^{2}}\,\,\text{atm}\,\text{mo}{{\text{l}}^{-2}}$and $\text{mo}{{\text{l}}^{-1}}\text{ L}$

D) ${{\text{L}}^{-2}}\,\,\text{at}{{\text{m}}^{-1}}\,\text{mo}{{\text{l}}^{-1}}$and $\text{L}\,\text{mo}{{\text{l}}^{-2}}$

• question_answer148) Identify the pair of gases that have equal rates of diffusion

A) CO, NO

B) Np.CO

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

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

• question_answer149) For AX ionic crystal to exist in bcc structure, the ratio of radii $\left( \frac{{{r}_{cation}}}{{{r}_{anion}}} \right)$ should be

A) between 0.41 and 0.73

B) greater than 0.73

C) less than 0.41

D) equal to 1.0

• question_answer150) Identify the correct statement for the adsorption of a real gas on charcoal at 1 atm and $\text{15}{{\,}^{\text{o}}}\text{C}\text{.}$

A) gases which are small in molecular size are adsorbed more

B) decrease in pressure increases the extent of adsorption

C) gases which are easily liquefiable are adsorbed more in quantity

D) gas which has a behaviour similar to an inert gas is adsorbed more

• question_answer151) The probability that number selected at random from the number 1, 2, 3, 4, 5, 6, 7, 8, ..., 100 is a prime, is

A) $0.4$

B) $0.25$

C) $0.45$

D) $0.43$

• question_answer152) $\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{m}}-1}{{{x}^{n}}-1}$is equal to

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

B) $\frac{m}{n}$

C) $\frac{2m}{n}$

D) $\frac{2n}{m}$

• question_answer153) $\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{{{e}^{5x}}-{{e}^{4x}}}{x}$is equal to

A) $1$

B) $2$

C) $4$

D) $5$

• question_answer154) If the function s$f:R\to R$ given by $f(x)=\left\{ \begin{matrix} x+a, & if & x\le 1 \\ 3-{{x}^{2}}, & if & x>1 \\ \end{matrix} \right.$ is continuous at $x=1,$ then a is equal to

A) $4$

B) $3$

C) $2$

D) $1$

• question_answer155) If n[A] denotes the number of elements in the Set A and if $n(A)=4,\,n(B)=5,$ and $(A\cap B)=3,$then $n[(A\times B)\cap (B\times A)]$ is equal to

A) $8$

B) $9$

C) $10$

D) $11$

• question_answer156) The function $f:R\to R$ given by $f(x)={{x}^{3}}-1$ is

A) a one-one function

B) an onto function

C) a bijection

D) neither one-one nor onto

• question_answer157) If $\omega$ is a non-real cube root of unity, then $1+\omega +{{\omega }^{2}}+....+{{\omega }^{101}}$ is equal to

A) $1$

B) $\omega$

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

D) $0$

• question_answer158) The square roots of $-7-24\sqrt{-1}$ are

A) $\pm (4+3\sqrt{-1})$

B) $\pm (3+4\sqrt{-1})$

C) $\pm (3-4\sqrt{-1})$

D) $\pm (4-3\sqrt{-1})$

• question_answer159) A value of k for which the quadratic equation ${{x}^{2}}-2x(1+3k)+7(2k+3)=0$has equal roots, is

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer160) If $\alpha ,\beta$ are the roots of the equation ${{x}^{2}}+ax+b=0,$ then $\frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}$is equal to

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

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

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

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

• question_answer161) If $|a|<1,$ then $1+2a+3{{a}^{2}}+4{{a}^{3}}+.....$ is equal to

A) $\frac{1}{1-a}$

B) $\frac{1}{1+a}$

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

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

• question_answer162) If pth term of an arithmetic progression is q and the qth term is p, then 10th term is

A) $p-q+10$

B) $p+q+11$

C) $p+q-9$

D) $p+q-10$

• question_answer163) If ${{C}_{0}},{{C}_{1}},{{C}_{2}},.....{{C}_{n}}$ denotes the binomial coefficients in the expansion of ${{(1+x)}^{n}},$then ${{C}_{0}}+\frac{{{C}_{1}}}{2}+\frac{{{C}_{2}}}{3}+....+\frac{{{C}_{n}}}{n+1}$ is equal to

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

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

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

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

• question_answer164) The coefficient of ${{x}^{r}}$ in the expansion of ${{(1-x)}^{-2}}$is

A) $r$

B) $r+1$

C) $r+3$

D) $r-1$

• question_answer165) The number of permutations of 4 letters that can be made out of the letters of the word EXAMINATION is

A) $2454$

B) $2452$

C) $2450$

D) $1806$

• question_answer166) $\frac{1}{3!}+\frac{2}{5!}+\frac{3}{7!}+...$ is equal to

A) $\frac{{{e}^{-1}}}{2}$

B) $e$

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

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

• question_answer167) $\frac{x-y}{x}+\frac{1}{2}{{\left( \frac{x-y}{x} \right)}^{2}}+\frac{1}{3}{{\left( \frac{x-y}{x} \right)}^{3}}+....$ is equal to

A) ${{\log }_{e}}\,(x-y)$

B) ${{\log }_{e}}\,(x+y)$

C) ${{\log }_{e}}\,\left( \frac{x}{y} \right)$

D) ${{\log }_{e}}\,\,xy$

• question_answer168) The standard deviation of the first n natural numbers is

A) $\frac{\sqrt{{{n}^{2}}+1}}{12}$

B) $\frac{{{n}^{2}}-1}{12}$

C) $\sqrt{\frac{{{n}^{2}}-1}{12}}$

D) $\frac{{{n}^{2}}+1}{12}$

• question_answer169) A point P moves so that the sum of its distances from $(-ae,\,0)$and $(ae,\,0)$ is$2a$. Then the locus of P is

A) $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$

B) $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1-{{e}^{2}})}=1$

C) $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1$

D) $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}(1+{{e}^{2}})}=1$

• question_answer170) The length of the perpendicular from the origin to the line $\frac{x\,\,\sin \alpha }{b}-\frac{y\,\cos \,\alpha }{a}-1=0$ is

A) $\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha -{{b}^{2}}\,{{\sin }^{2}}\alpha }}$

B) $\frac{|ab|}{\sqrt{{{a}^{2}}\,{{\cos }^{2}}\alpha +{{b}^{2}}\,{{\sin }^{2}}\alpha }}$

C) $\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha -{{b}^{2}}\,{{\cos }^{2}}\alpha }}$

D) $\frac{|ab|}{\sqrt{{{a}^{2}}\,si{{n}^{2}}\alpha +{{b}^{2}}\,{{\cos }^{2}}\alpha }}$

• question_answer171) The distance between the parallel lines $y=x+a,\,\,y=x+b$is

A) $\frac{|b-a|}{\sqrt{2}}$

B) $|a-b|$

C) $|a+b|$

D) $\frac{|a+b|}{\sqrt{2}}$

• question_answer172) The line passing through the point of intersection of $x+y=2,\,x-y=0$ and is parallel to $x+2y=5$is

A) $x+2y=1$

B) $x+2y=2$

C) $x+2y=4$

D) $x+2y=3$

• question_answer173) If the line $y=7x-25$meets the circle ${{x}^{2}}+{{y}^{2}}=25$in the points A, B then the distance between A and B is

A) $\sqrt{10}$

B) $10$

C) $5\sqrt{2}$

D) $5$

• question_answer174) One of the directrices of the ellipse $8{{x}^{2}}+6{{y}^{2}}-16x+12y+13=0$is

A) $3y-3=\sqrt{6}$

B) $3y+3=\sqrt{6}$

C) $y+1=\sqrt{3}$

D) $y-1=-\sqrt{3}$

• question_answer175) If OAB is an equilateral triangle inscribed in the parabola ${{y}^{2}}=4ax$ with O as the vertex, then the length of the side of the$\Delta \,\,OAB$ is

A) $8\,a\,\sqrt{3}$

B) $4\,a\,\sqrt{3}$

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

D) $a\,\sqrt{3}$

• question_answer176) If $x\,\sin \theta =y\,\cos \theta =\frac{2z\,\tan \theta }{1-{{\tan }^{2}}\theta },$ then $4{{z}^{2}}({{x}^{2}}+{{y}^{2}})$ is equal to

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

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

C) ${{({{x}^{2}}-{{y}^{2}})}^{2}}$

D) ${{({{x}^{2}}+{{y}^{2}})}^{2}}$

• question_answer177) $\tan {{25}^{o}}+\tan {{20}^{o}}+\tan {{25}^{o}}\,\tan {{20}^{o}}$ is equal to

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer178) If $\cos x=3\cos y,$ then $2\tan \frac{y-x}{2}$ is equal to

A) $\cot \left( \frac{y-x}{2} \right)$

B) $\cot \left( \frac{x+y}{4} \right)$

C) $\cot \left( \frac{y-x}{4} \right)$

D) $\cot \left( \frac{y-x}{4} \right)$

• question_answer179) In any $\Delta \,ABC$ under usual notation, $a(b\,\cos \,C-c\,\cos B)$ is equal to

A) ${{b}^{2}}-{{c}^{2}}$

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

C) $\frac{{{b}^{2}}-{{c}^{2}}}{2}$

D) $\frac{{{c}^{2}}-{{b}^{2}}}{2}$

• question_answer180) If $4\,\sin \,A=4\,\sin B=3\,\sin \,C$ in a triangle ABC, then $\cos \,\,C$ is equal to

A) $1/3$

B) $1/9$

C) $1/27$

D) $~1/18$

• question_answer181) If $\cos \,x\ne \frac{1}{2},$ then the solutions of $\cos \,x+\cos \,2x+\cos \,3x=0$are

A) $2n\pi \pm \frac{\pi }{4},n\in Z$

B) $2n\pi \pm \frac{\pi }{3},n\in Z$

C) $2n\pi \pm \frac{\pi }{6},n\in Z$

D) $2n\pi \pm \frac{\pi }{2},n\in Z$

• question_answer182) ${{\tan }^{-1}}\,\frac{x}{\sqrt{{{a}^{2}}-{{x}^{2}}}}$is equal to

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

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

C) ${{\sin }^{-1}}\frac{x}{a}$

D) ${{\cos }^{-1}}\frac{x}{a}$

• question_answer183) The solution of ${{\tan }^{-1}}\,2\theta +{{\tan }^{-1}}3\theta =\frac{\pi }{4}$ is

A) $\frac{1}{\sqrt{3}}$

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

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

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

• question_answer184) The number of solutions of $\sin x=\sin 2x$between $\frac{-\pi }{2}$ and $\frac{\pi }{2}$ is

A) $3$

B) $2$

C) $1$

D) $0$

• question_answer185) If $y=\frac{3a{{t}^{2}}}{1+{{t}^{3}}},\,x=\frac{3at}{1+{{t}^{3}}},$ then $\frac{dy}{dx}$ is equal to

A) $\frac{t(2-{{t}^{3}})}{(1-2{{t}^{3}})}$

B) $\frac{t(2+{{t}^{3}})}{(1-2{{t}^{3}})}$

C) $\frac{t(2-{{t}^{3}})}{(1+2{{t}^{3}})}$

D) $\frac{t(2+{{t}^{3}})}{(1+2{{t}^{3}})}$

• question_answer186) If $y={{\sec }^{-1}}\left( \frac{1}{\sqrt{1-{{x}^{2}}}} \right),$ then $\frac{dy}{dx}$ is equal to

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

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

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

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

• question_answer187) The point on the curve $y={{x}^{3}}$at which the tangent to the curve is parallel to the x axis, is

A) $(2,2)$

B) $(3,3)$

C) $(4,4)$

D) $(0,0)$

• question_answer188) The equation of normal to the curve ${{x}^{2}}y={{x}^{2}}-3x+6$ at the point with abscissa $x=3$is

A) $3x+27y=79$

B) $27\text{ }x-3y=79$

C) $27x+3y=79$

D) $3x-27y=79$

• question_answer189) The function $f(x)=2{{x}^{3}}+3{{x}^{2}}-12x+1$ decreases in the interval

A) $(2,3)$

B) $(1,2)$

C) $(-2,1)$

D) $(-3,-2)$

• question_answer190) The function $f(x)={{x}^{2}}{{e}^{-x}}$ increases in the interval

A) $(0,2)$

B) $(2,3)$

C) $(3,4)$

D) $(4,5)$

• question_answer191) The number of real roots of $f(x)=0,$where $f(x)=(x-1)(x-2)(x-3)(x-4)$ lying the interval $(1,3)$ is

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer192) If ${{x}^{y}}={{y}^{x}},$ then $\frac{dy}{dx}$ is equal to

A) $\frac{{{y}^{2}}-xy\,\log \,y}{{{x}^{2}}-xy\,\log \,x}$

B) $\frac{{{y}^{2}}+xy\,\log \,y}{{{x}^{2}}+xy\,\log \,x}$

C) $\frac{{{y}^{2}}-xy\,\log \,x}{{{x}^{2}}-xy\,\log \,y}$

D) $\frac{{{y}^{2}}+xy\,\log \,y}{{{x}^{2}}-xy\,\log \,x}$

• question_answer193) Rectilinear motion is performed in accordance with the formulae $s=\frac{2}{9}\sin \frac{\pi t}{2}+{{s}_{0}}.$ Then the acceleration at the end of the 1st second (in$cm/{{s}^{2}}$) is

A) $\frac{{{\pi }^{2}}}{18}$

B) $\frac{{{\pi }^{2}}}{7}$

C) $\frac{-{{\pi }^{2}}}{9}$

D) $\frac{-{{\pi }^{2}}}{18}$

• question_answer194) A value on x in the interval $(1,2)$ such that $f'(x)=0,$ where $f(x)={{x}^{3}}-3{{x}^{2}}+2x+10$ is

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

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

C) $1+\sqrt{2}$

D) $\sqrt{2}$

• question_answer195) Given that the force acting on a material point is inversely proportional to the velocity of the moving point. Then the kinetic energy of the point is a ...... function of time.

A) exponential

B) linear

C) second degree

D) non-linear

• question_answer196) If $f(x)={{x}^{2}}-5x,A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right],$ then $f(A)$ is equal to

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

B) $\left[ \begin{matrix} 0 & -7 \\ -7 & 0 \\ \end{matrix} \right]$

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

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

• question_answer197) If A is a square matrix. A' its transpose, then $\frac{1}{2}(A-A')$is

A) a symmetric matrix

B) a skew symmetric matrix

C) a unit matrix

D) an elementary matrix

• question_answer198) The number of solutions of the system of equations $x-y+z=2$ $2x+y-z=5$ $4x+y+z=10$ is

A) $\infty$

B) $1$

C) $2$

D) $0$

• question_answer199) The adjoin of the matrix$\left[ \begin{matrix} \cos \,\theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right]$is

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

B) $\left[ \begin{matrix} sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]$

C) $\left[ \begin{matrix} \cos \,\theta & sin\theta \\ -sin\theta & \cos \theta \\ \end{matrix} \right]$

D) $\left[ \begin{matrix} -sin\,\theta & \cos \theta \\ \cos \theta & sin\theta \\ \end{matrix} \right]$

• question_answer200) If $x\ne 0,\,\left| \begin{matrix} x+1 & 2x+1 & 3x+1 \\ 2x & 4x+3 & 6x+3 \\ 4x+4 & 6x+4 & 8x+4 \\ \end{matrix} \right|=0,$ then $x+1$ is equal to

A) $x$

B) $0$

C) $2x$

D) $3x$

• question_answer201) $\left| \begin{matrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \\ \end{matrix} \right|$ is equal to

A) $0$

B) $x$

C) $y$

D) $xyz$

• question_answer202) If P is any point with in a triangle ABC, then $\overrightarrow{PA}+\overrightarrow{CP}$ is equal to

A) $\overrightarrow{AC}+\overrightarrow{CB}$

B) $\overrightarrow{BC}+\overrightarrow{BA}$

C) $\overrightarrow{CB}+\overrightarrow{AB}$

D) $\overrightarrow{CB}+\overrightarrow{BA}$

• question_answer203) If the vector $3i-2\hat{j}-5\hat{k}$ is perpendicular to $c\hat{k}-\hat{j}+6\hat{i},$ then c is equal to

A) $3$

B) $4$

C) $5$

D) $6$

• question_answer204) The vector $\vec{a}\times (\vec{b}\times \vec{c})$ is coplanar with the vectors

A) $\vec{b},\,\vec{c}$

B) $\vec{a},\,\vec{b}$

C) $\vec{a},\,\vec{c}$

D) $\vec{a},\,\,\vec{b}\,,\vec{c}$

• question_answer205) If $\vec{a},\,\,\vec{b}\,$ are any two vectors, then $(2\vec{a}+3\vec{b})\times (5\vec{a}+7\vec{b})+\vec{a}\times \vec{b}$ is equal to

A) $\vec{0}$

B) $0$

C) $\vec{a}\times \vec{b}$

D) $\vec{b}\times \vec{a}$

• question_answer206) A unit vector perpendicular to $\hat{i}-\hat{j}+\hat{k}$and $\hat{i}+\hat{j}-\hat{k}$ is

A) $\frac{\hat{k}+\hat{i}}{\sqrt{2}}$

B) $\frac{\hat{j}+\hat{k}}{\sqrt{2}}$

C) $\frac{\hat{i}-\hat{k}}{\sqrt{3}}$

D) $\frac{\hat{j}-\hat{k}}{\sqrt{2}}$

• question_answer207) If $\vec{a}\times \vec{b}=\vec{c}\times \vec{d}$and $\vec{a}\times \vec{c}=\vec{b}\times \vec{d},$ then $\vec{a}-\vec{d}$ is parallel to

A) $\vec{b}+\vec{c}$

B) $\vec{b}-2\vec{c}$

C) $\vec{b}+2\vec{c}$

D) $\vec{b}-\vec{c}$

• question_answer208) $3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx$is equal to

A) $a-1+{{(a-1)}^{-2}}$

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

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

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

• question_answer209) $\int_{-\pi /2}^{\pi /2}{\frac{dx}{1+\cos x}}$ is equal to

A) $0$

B) $1$

C) $2$

D) $3$

• question_answer210) $\int{\sin \,\,\sqrt{x}}\,\,dx$ is equal to

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

B) $2(\sin \,\sqrt{x}-\sqrt{x}\,\cos \,\sqrt{x})+c$

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

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

• question_answer211) $\int{\frac{\sqrt{x}}{x+1}\,dx}$ is equal to

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

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

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

D) $2(\sqrt{x}-ta{{n}^{-1}}\sqrt{x})+c$

• question_answer212) The area (in square unit) bounded by the curves $y={{x}^{3}}$and $y=x$ is

A) $1/2\text{ }sq\text{ }unit$

B) $1/4\text{ }sq\text{ }unit$

C) $1/8\text{ }sq\text{ }unit$

D) $1/16\text{ }sq\text{ }unit$

• question_answer213) The area (in square unit) bounded by the curves $4y={{x}^{2}}$and $2y=6-{{x}^{2}}$is

A) $8$

B) $6$

C) $4$

D) $10$

• question_answer214) The general solution of the differential equation $\frac{dy}{dx}=\frac{(1+{{y}^{2}})}{xy(1+{{x}^{2}})}$ is

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

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

C) $(1-{{x}^{2}})(1-{{y}^{2}})=c$

D) $(1+{{x}^{2}})(1+{{y}^{2}})=c{{y}^{2}}$

• question_answer215) A particle moves along a straight line with the law of motion given by ${{s}^{2}}=a{{t}^{2}}+2bt+c$. Then the acceleration varies are

A) $1/{{s}^{3}}$

B) $1/s$

C) $~1/{{s}^{4}}$

D) $1/{{s}^{2}}$

• question_answer216) A point is moving with uniform acceleration in the eleventh and fifteenth seconds from the commencement it moves through 720 and 960 cm respectively. Its initial velocity and the acceleration with which it moves are

A) $60\text{ }m/s,\text{ }40\text{ }m/{{s}^{2}}$

B) $70\text{ }m/s,\text{ }30\text{ }m/{{s}^{2}}$

C) $90\text{ }m/s,\text{ }60\text{ }m/{{s}^{2}}$

D) None of the above

• question_answer217) A particle of mass m is projected from a fixed point 0 into the air with velocity u in a direction making an angle a with the horizontal. Then the motion of the particle describes a parabola with the latusrectum is

A) $\frac{2}{g}{{(horizontal\text{ }velocity)}^{2}}$

B) $\frac{2}{g}(vertical\text{ }velocity)$

C) $\frac{2}{{{g}^{2}}}{{(horizontal\text{ }velocity)}^{2}}$

D) $\frac{2}{{{g}^{2}}}{{(vertical\text{ }velocity)}^{2}}$

• question_answer218) The vector equation of the line passing through the points $(3,2,1)$ and $(-2,1,3)$ is

A) $\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}-\hat{j}+2\hat{k})$

B) $\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}+\hat{j}+\hat{k})$

C) $\vec{r}=-2\hat{i}+\hat{j}+3\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})$

D) $\vec{r}=-2\hat{i}+\hat{j}+\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})$

• question_answer219) The line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ meets the plane $2x+3y-z=-4$in the point

A) $(1,2,3)$

B) $(-1,-1,-1)$

C) $(2,1,3)$

D) $(1,1,1)$

• question_answer220) The shortest distance between the lines $1+x=2y=-12z$and $x=y+2=6z-6$is

A) $1$

B) $2$

C) $3$

D) $4$

• question_answer221) The foot of the perpendicular from $(2,4,-1)$to the line $x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$

A) $(-4,1,-3)$

B) $(4,-1,-3)$

C) $(-4,-1,3)$

D) $(-4,-1,-3)$

• question_answer222) The radius of the sphere ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}=x+2y+3z$is

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

B) $\sqrt{7}$

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

D) $\frac{\sqrt{7}}{2}$

• question_answer223) The distance between the planes $2x-2y+z+3=0$and $4x-4y+2z+5=0$ is

A) $3$

B) $6$

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

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

• question_answer224) If B is a Boolean algebra and $a,\,\,b\,\,\in \,B,$ then $a.(a+b)$is equal to

A) $a$

B) $b$

C) $1$

D) $a'$

• question_answer225) Let ${{E}_{1}},{{E}_{2}}$ be two mutually exclusive events of an experiment with $P(not\,{{E}_{2}})=0.6=P({{E}_{1}}\cup {{E}_{2}}).$Then $P({{E}_{1}})$ is equal to

A) $0.1$

B) $0.3$

C) $0.4$

D) $0.2$