Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2012

done JCECE Engineering Solved Paper-2012

  • question_answer1) A monkey of \[25\,\,kg\] is holding a vertical rope. The rope does not break if a body of mass \[30\,\,kg\] is suspended from it, but the rope breaks if the mass of body suspended with the rope exceeds\[30\,\,kg\]. What will be the maximum acceleration with which the monkey can climb up along the rope?

    A) \[2.0\,\,m{{s}^{-2}}\]

    B) \[2.5\,\,m{{s}^{-2}}\]

    C) \[3.0\,\,m{{s}^{2}}\]

    D) \[4.0\,\,m{{s}^{-2}}\]

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  • question_answer2) A mass of \[10\,\,g\] moving horizontally with a velocity of \[100\,\,cm{{s}^{-1}}\] strikes a pendulum bob of same mass. The two masses after collision stick together. What will be the maximum height reached by the system now? (Take\[g=10\,\,m{{s}^{-2}})\]

    A) \[zero\]

    B) \[1.25\,\,cm\]

    C) \[2.5\,\,cm\]

    D) \[5\,\,cm\]

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  • question_answer3) The three physical quantities \[x,\,\,\,y\] and \[z\] have units \[g\,\,c{{m}^{2}},\,\,g\,\,{{s}^{-1}}\] and \[cm{{s}^{-2}}\] respectively. The relation between \[x,\,\,\,y\] and \[z\] is

    A) \[x=y{{z}^{2}}\]

    B) \[x={{y}^{2}}z\]

    C) \[{{y}^{2}}=xz\]

    D) \[z={{x}^{2}}y\]

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  • question_answer4) If a vector \[\mathbf{A}\] having a magnitude of \[8\] is added to a vector \[\mathbf{B}\] which lies along\[x-axis\], then the resultant of two vectors lies along \[y-axis\] and has magnitude twice that of\[B\]. The magnitude of \[\mathbf{B}\] is

    A) \[\frac{6}{\sqrt{5}}\]

    B) \[\frac{12}{\sqrt{5}}\]

    C) \[\frac{16}{\sqrt{5}}\]

    D) \[\frac{8}{\sqrt{5}}\]

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  • question_answer5) If the length of potentiometer wire is increased, then the length of the previously obtained balance point will

    A) increase

    B) decrease

    C) remains unchanged

    D) becomes two times

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  • question_answer6) If a steel wire of length I and magnetic moment \[M\] is bent into a semi-circular arc, then the new magnetic moment is

    A) \[M\times l\]

    B) \[\frac{M}{l}\]

    C) \[\frac{2M}{\pi }\]

    D) \[M\]

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  • question_answer7) The amplitude and the periodic time of \[\text{a}\] \[SHM\] are \[5\,\,cm\] and \[6\,\,s\] respectively. At a distance of \[2.5\,\,cm\] away from the mean position, the phase will be

    A) \[\frac{\pi }{3}\]

    B) \[\frac{\pi }{4}\]

    C) \[\frac{\pi }{6}\]

    D) \[\frac{5\pi }{12}\]

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  • question_answer8) If all of a sudden the radius of the earth decreases, then which one of the following statements will be true?

    A) The angular momentum of the earth will become greater than that of the sun.

    B) The periodic time of the earth will increase.

    C) The energy and angular momentum will remain constant.

    D) The angular velocity of the earth will increase

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  • question_answer9) If the external torque acting on a system is zero \[(i.e.,\,\,\tau =0)\], then

    A) \[J=0\]

    B) \[F=0\]

    C) \[\omega =0\]

    D) \[\alpha =0\]

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  • question_answer10) Two point charges \[-q\] and \[+q/2\] are situated at the origin and the point \[(a,\,\,0,\,\,0)\] respectively. The point along the\[x-axis\], where the electric field vanishes is

    A) \[x=\sqrt{2}a\]

    B) \[x=\frac{a}{\sqrt{2}}\]

    C) \[x=\frac{\sqrt{2}a}{\sqrt{2}-1}\]

    D) \[x=\frac{\sqrt{2a}}{\sqrt{2}+1}\]

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  • question_answer11) When the kinetic energy of an electron is increased, the wavelength of the associated wave will

    A) decrease

    B) increase

    C) remains unchanged

    D) None of these

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  • question_answer12) A current \[i\] ampere flows along the inner conductor of a coaxial cable and returns along the outer conductor of the cable, then the magnetic induction at any point outside the conductor at a distance \[r\] metre from the axis is

    A) \[\infty \]

    B) \[Zero\]

    C) \[\frac{{{\mu }_{0}}}{4\pi }\frac{2i}{r}\]

    D) \[\frac{{{\mu }_{0}}}{4\pi }\frac{2\pi i}{r}\]

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  • question_answer13) Two parallel long wires carry currents \[{{i}_{1}}\] and \[{{i}_{2}}\] with\[{{i}_{1}}>{{i}_{2}}\]. When the currents are in the same direction, the magnetic field midway between the wires is\[10\,\,\mu T\]. When the direction of \[{{i}_{2}}\] is reversed, it becomes\[40\,\,\mu T\]. Then, ratio of \[{{i}_{1}}/{{i}_{2}}\]is

    A) \[3:4\]

    B) \[5:3\]

    C) \[7:11\]

    D) \[11:7\]

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  • question_answer14) The two coherent sources of equal intensity produce maximum intensity of \[100\] units at a point. If the intensity of one of the sources is reduced by \[36%\] \[\text{by}\] reducing its width then the intensity of light at the same point will be

    A) \[67\]

    B) \[81\]

    C) \[89\]

    D) \[90\]

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  • question_answer15) A convex mirror of focal length \[f\] forms an image which is \[\frac{1}{n}\] times the object. The distance of the object from the mirror is

    A) \[\left( \frac{n-1}{n} \right)f\]

    B) \[\left( \frac{n+1}{n} \right)f\]

    C) \[(n+1)f\]

    D) \[(n-1)f\]

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  • question_answer16) Consider a hydrogen like atom whose energy in nth excited state is given by\[{{E}_{n}}=\frac{13.6\,\,{{Z}^{2}}}{{{n}^{2}}}\], when this excited atom makes a transition from excited state to ground state, most energetic photons have energy \[{{E}_{\max }}=52.224\,\,eV\] and least energetic photons have energy\[{{E}_{\min }}=1.224\,\,eV\]. The atomic number of atom is

    A) \[2\]

    B) \[4\]

    C) \[5\]

    D) None of these

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  • question_answer17) A diode is connected to \[220\,\,V(rms)AC\] in series with a capacitor as shown in figure. The voltage across the capacitor is

    A) \[220\,\,V\]

    B) \[110\,\,V\]

    C) \[311.1\,\,V\]

    D) \[\frac{220}{\sqrt{2}}V\]

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  • question_answer18) A wave travelling along positive \[x-axis\] is given by\[y=A\sin (\omega t-kx)\]. If it is reflected from a rigid boundary such that \[80%\] amplitude is reflected, then equation of reflected wave is

    A) \[y=A\sin (\omega t+0.8\,\,kx)\]

    B) \[y=-0.8\,\,A\sin (\omega t+kx)\]

    C) \[y=A\sin (\omega t+kx)\]

    D) \[y=0.8\,\,A\sin (\omega t+kx)\]

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  • question_answer19) An engine approaches a hill with a constant speed. When it is at a distance of\[0.9\,\,km\], it blows a whistle, whose echo is heard by the driver after\[5\,\,s\]. If speed of sound in air is \[330\,\,m/s\], the speed of engine is

    A) \[10\,\,m/s\]

    B) \[20\,\,m/s\]

    C) \[30\,\,m/s\]

    D) \[40\,\,m/s\]

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  • question_answer20) The graph between the resistive force \[F\] acting on a body and the distance covered by the body is shown in the figure. The mass of the body is \[25\,\,kg\] and initial velocity is\[2\,\,m/s\]. When the distance covered by the body is \[4\,\,m,\] its kinetic energy would be

    A) \[10\,\,J\]

    B) \[20\,\,J\]

    C) \[40\,\,J\]

    D) \[50\,\,J\]

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  • question_answer21) A body of weight \[50\,\,N\] placed on a horizontal surface is just moved by a force of\[28.2\,\,N\]. The frictional force and normal reaction are

    A) \[2N,\,\,3N\]

    B) \[5N,\,\,6N\]

    C) \[10N,\,\,15N\]

    D) \[20N,\,\,30N\]

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  • question_answer22) On a railway curve, the outside rail is laid higher than the inside one so that resultant force exerted on the wheels of the rail car by the tops of the rails will

    A) equilibrate the centripetal force

    B) be vertical

    C) be decreased

    D) have a horizontal inward component

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  • question_answer23) The mass of the moon is \[\frac{1}{81}\] of the earth but the gravitational pull is \[\frac{1}{6}\] of the earth. It is due to the fact that

    A) the radius of earth is \[\frac{1}{6}\] of the moon

    B) the radius of moon is \[\frac{9}{\sqrt{6}}\] of the earth

    C) moon is the satellite of the earth

    D) None of the above

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  • question_answer24) Inertia is that property of a body by virtue of which the body is

    A) unable to change by itself the state of uniform motion

    B) unable to change by itself the state of rest and of uniform linear motion

    C) unable to change by itself the state of rest

    D) unable to change by itself the direction of motion

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  • question_answer25) The radius of two metallic spheres \[A\] and \[B\] are \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively\[({{r}_{1}}>{{r}_{2}})\]. They are connected by a thin wire and the system is given a certain charge. The charge will be greater

    A) equal on both

    B) zero on both

    C) on the surface of sphere\[A\]

    D) on the surface of sphere\[B\]

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  • question_answer26) The temperature gradient in a rod of \[0.5\,\,m\] long is\[{{80}^{o}}C/m\]. If the temperature of hotter end of the rod is\[{{30}^{o}}C\], then the temperature of the cooler end is

    A) \[{{0}^{o}}C\]

    B) \[-{{10}^{o}}C\]

    C) \[{{10}^{o}}C\]

    D) \[{{40}^{o}}C\]

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  • question_answer27) Time period of a block suspended from the upper plate of a parallel plate capacitor by a spring of stiffness \[K\] is \[T\], when block is uncharged. If a charge \[q\] is given to the block then, die new time period of oscillation will be

    A) \[T\]

    B) \[>T\]

    C) \[<T\]

    D) \[\ge T\]

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  • question_answer28) In the circuit shown, potential difference between \[x\] and \[y\] will be

    A) \[Zero\]

    B) \[120\,\,V\]

    C) \[60\,\,V\]

    D) \[20\,\,V\]

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  • question_answer29) A wire of length \[1\,\,m\] is moving at a speed of \[2\,\,m{{s}^{-1}}\]perpendicular to its length in a homogeneous magnetic field of\[0.5\,\,T\]. If the ends of the wire are joined to a circuit of resistance\[6\Omega \], then the rate at which work is being done to keep the wire moving at constant speed is

    A) \[1\,\,W\]

    B) \[\frac{1}{3}\,\,W\]

    C) \[\frac{1}{6}\,\,W\]

    D) \[\frac{1}{12}\,\,W\]

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  • question_answer30) The transformation' ratio in the step-up transformer is

    A) 1

    B) greater than one

    C) less than one

    D) the ratio greater or less than one depends on the other factors.

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  • question_answer31) The focal length of the objective of a terrestrial telescope is \[80\,\,cm\] and it is adjusted for parallel rays, then its power is\[20\]. If the focal length of erecting lens is \[20\,\,cm\], then full length of the telescope will be

    A) \[164\,\,cm\]

    B) \[124\,\,cm\]

    C) \[100\,\,cm\]

    D) \[84\,\,cm\]

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  • question_answer32) Un polarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam

    A) \[15{}^\circ \]

    B) \[35{}^\circ \]

    C) \[55{}^\circ \]

    D) \[75{}^\circ \]

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  • question_answer33) The ratio of two specific heats of gas \[{{C}_{p}}/{{C}_{V}}\] for argon is \[1.6\] and for hydrogen is\[1.4\]. If adiabatic elasticity of argon at pressure \[p\] is \[E,\] then at what pressure the adiabatic elasticity of hydrogen will also be equal to\[E\]?

    A) \[p\]

    B) \[1.4p\]

    C) \[\frac{7}{8}p\]

    D) \[\frac{8}{7}p\]

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  • question_answer34) The stress-strain curves for three wires of different materials are shown in figure, where \[P,\,\,\,Q\] and \[R\] are the elastic limits of the wires. The figure shows that

    A) elasticity of wire \[P\] is maximum

    B) elasticity of wire \[Q\] is maximum

    C) elasticity of wire \[R\] is maximum

    D) None of the above is true

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  • question_answer35) A body of density \[{{d}_{1}}\] is counterpoised by \[Mg\]of weights of density \[{{d}_{2}}\] in air of density\[d\]. Then, the true mass of the body is

    A) \[M\]

    B) \[\frac{M(1-d/{{d}_{2}})}{(1-d/{{d}_{1}})}\]

    C) \[M\left( 1-\frac{d}{{{d}_{2}}} \right)\]

    D) \[M\left( 1-\frac{d}{{{d}_{1}}} \right)\]

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  • question_answer36) According to kinetic theory of gases, total energy of a gas is equal to

    A) potential energy

    B) kinetic energy

    C) both [a] and [b]

    D) None of the above

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  • question_answer37) A dip needle lies, initially in the magnetic meridian when it shows an angle of dip \[\theta \] at a place. The dip circle is rotated through an angle \[x\] in the horizontal plane and then it shows an angle of dip\[\theta '\]. Then,\[\frac{\tan \theta '}{\tan \theta }\]will be

    A) \[\cos x\]

    B) \[\frac{1}{\cos x}\]

    C) \[\frac{1}{\sin x}\]

    D) \[\frac{1}{\tan x}\]

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  • question_answer38) The \[rms\] current in a\[AC\] circuit is\[2A\]. If the watt less current be\[\sqrt{3}A\], what is the power factor of the circuit?

    A) \[\frac{1}{2}\]

    B) \[\frac{1}{3}\]

    C) \[\frac{1}{\sqrt{3}}\]

    D) \[\frac{1}{\sqrt{2}}\]

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  • question_answer39) An electric bulb rated as \[500\,\,W-100\,\,V\] is used in a circuit having \[200\,\,V\] supply. The resistance \[R\] that must be put in series with the bulb, so that the bulb draws \[500\,\,W\] is

    A) \[100\Omega \]

    B) \[50\Omega \]

    C) \[20\Omega \]

    D) \[10\Omega \]

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  • question_answer40) A string of length L and mass M hangs freely from a fixed point. Then, the velocity of transverse waves along the string at a distance\[x\] from the free end is

    A) \[gx\]

    B) \[\sqrt{gx}\]

    C) \[gL\]

    D) \[\sqrt{gL}\]

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  • question_answer41) Two equal masses each of 2 kg are suspended from a spring balance as shown in figure. The reading of the spring balance will be

    A) Zero

    B) 2 kg

    C) 4 kg

    D) between zero and 2 kg

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  • question_answer42) A body of mass \[2\,\,kg\] slides down a curved track which is quadrant of a circle of radius \[1\,\,m\] as shown in figure. All the surfaces are frictionless. If the body starts from. rest, its speed at the bottom of the track is

    A) \[2\,\,m{{s}^{-1}}\]

    B) \[0.5\,\,m{{s}^{-1}}\]

    C) \[19.6\,\,m{{s}^{-1}}\]

    D) \[4.43\,\,m{{s}^{-1}}\]

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  • question_answer43) For me circuit shown in figure,

    A) resistance\[R=46\Omega \]

    B) current through \[20\Omega \] resistance is\[0.1\,\,A\]

    C) potential difference across the middle resistance is\[2V\]

    D) All of the above are true

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  • question_answer44) If \[10000\,\,V\] is applied across an X-ray tube, what will be the ratio of de-Broglie wavelength of the incident electrons to the shortest wavelength X-ray produced? \[\left( \frac{e}{m}\,\,for\,\,electron=1.8\times {{10}^{11}}C\,\,k{{g}^{-1}} \right)\]

    A) \[0.1\]

    B) \[0.2\]

    C) \[0.3\]

    D) \[1.0\]

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  • question_answer45) A water drop in air reflects the light rays as

    A)

    B)

    C)

    D)

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  • question_answer46) Two capillary tubes of same radius \[r\] but of lengths \[{{l}_{1}}\] and \[{{l}_{2}}\] are fitted in parallel to the bottom of a vessel. The pressure head is\[p\]. What should be the length of a single tube that can replace the two tubes so that the rate of flow is same as before?

    A) \[{{l}_{1}}+{{l}_{2}}\]

    B) \[\frac{{{l}_{1}}{{l}_{2}}}{{{l}_{1}}+{{l}_{2}}}\]

    C) \[\frac{1}{{{l}_{1}}+{{l}_{2}}}\]

    D) \[\frac{1}{{{l}_{1}}}+\frac{1}{{{l}_{2}}}\]

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  • question_answer47) An ideal thermometer should have

    A) small heat capacity

    B) large heat capacity

    C) medium heat capacity

    D) variable heat capacity

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  • question_answer48) For the circuit shown in figure, the impedance of the circuit will be

    A) \[50\Omega \]

    B) \[60\Omega \]

    C) \[90\Omega \]

    D) \[120\Omega \]

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  • question_answer49) An optical fibre communication system works on a wavelength of\[1.3\mu m\]. The number of subscribers it can feed if a channel requires \[20\,\,kHz\] are

    A) \[1\times {{10}^{5}}\]

    B) \[2.3\times {{10}^{10}}\]

    C) \[1.15\times {{10}^{10}}\]

    D) None of these

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  • question_answer50) A system of logic gates is shown in the figure. From the study of truth table it can be found that to produce a high output \[(1)\] at\[R\], we must have

    A) \[X=0,\,\,Y=1\]

    B) \[X=1,\,\,Y=1\]

    C) \[X=1,\,\,Y=0\]

    D) \[X=0,\,\,Y=0\]

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  • question_answer51) The reagent commonly used to determine hardness of water titrimetric ally is

    A) oxalic acid

    B) disodium salt of\[EDTA\]

    C) sodium citrate

    D) sodium thiosulphate

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  • question_answer52) In a solid lattice, the cation has left a lattice site and is located at an interstitial position. The lattice defect is

    A) interstitial defect

    B) vacancy defect

    C) Frenkel defect

    D) Schottky defect

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  • question_answer53) The molarity of a solution obtained by mixing \[800\,\,mL\] of \[0.5\,\,M\,\,HCl\] with \[200\,\,mL\] of \[1\,\,M\,\,HCl\] will be

    A) \[0.8\,\,M\]

    B) \[0.6\,\,M\]

    C) \[0.4\,\,M\]

    D) \[0.2\,\,M\]

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  • question_answer54) A solution of sucrose (molar mass\[~=342gmo{{l}^{-1}})\] has been prepared by dissolving \[68.5\,\,g\] of sucrose in \[1000\,\,g\] of water. The freezing point of solution obtained will be (\[{{K}_{f}}\]for water\[=1.86\,\,K\,\,kg\,\,mo{{l}^{-1}})\]

    A) \[-{{0.570}^{o}}C\]

    B) \[-{{0.372}^{o}}C\]

    C) \[-{{0.520}^{o}}C\]

    D) \[+{{0.372}^{o}}C\]

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  • question_answer55) The standard electrode potential of three metals \[X,\,\,\,Y\] and \[Z\] are \[-1.2\,\,V,\,\,+0.5\,\,V\] and \[-\,\,3.0\,\,V\] respectively. The reducing power of these metals will be

    A) \[X>Y>Z\]

    B) \[Y>Z>X\]

    C) \[Y>X>Z\]

    D) \[Z>X>Y\]

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  • question_answer56) The resistance of \[1\,\,N\] solution of acetic acid is\[250\,\Omega \], when measured in a cell having a cell constant of\[1.15\,\,c{{m}^{-1}}\]. The equivalent conductance (in\[{{\Omega }^{-1}}c{{m}^{2}}equi{{v}^{-1}})\] of \[1\,\,N\] acetic acid is

    A) \[2.3\]

    B) \[4.6\]

    C) \[9.2\]

    D) \[18.4\]

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  • question_answer57) The thermal decomposition of a molecule shows first order kinetics. The molecule decomposes \[50%\] in\[120\,\,\min \]. How much time it will take to decompose\[90%\]?

    A) \[300\,\,\min \]

    B) \[360\,\,\min \]

    C) \[398.8\,\,\min \]

    D) \[400\,\,\min \]

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  • question_answer58) In the respect of the equation,\[k=A{{e}^{-Ea/RT}}\] in chemical kinetics, which one of the following statement is correct?

    A) \[k\] is equilibrium constant

    B) \[A\] is adsorption factor

    C) \[{{E}_{a}}\] is activation energy

    D) \[R\] is Rydberg constant

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  • question_answer59) What is the name of a phenomenon in which both adsorption and absorption takes places?

    A) Chemisorption

    B) Physisorption

    C) Desorption

    D) Sorption

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  • question_answer60) Colloidal solutions of gold, prepared by different methods are of different colours because of

    A) variable valency of gold

    B) different concentration of gold particles

    C) impurities produced by different methods

    D) different diameters of colloidal gold particles

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  • question_answer61) The most important ore of tin is

    A) cassiterite

    B) cryolite

    C) cerussite

    D) None of these

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  • question_answer62) Which process of purifications is represented by the following scheme? \[\underset{impure}{\mathop{Ti}}\,+2{{I}_{2}}\xrightarrow{{{250}^{o}}C}Ti{{I}_{4}}\xrightarrow{{{1400}^{o}}C}\underset{Pure}{\mathop{Ti}}\,+2{{I}_{2}}\]

    A) Cupellation

    B) Zone refining

    C) van-Arkel process

    D) Poling

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  • question_answer63) If the supply of oxygen is limited, \[{{H}_{2}}S\] reacts with \[{{O}_{2}}\] to form

    A) \[{{H}_{2}}O+S{{O}_{3}}\]

    B) \[{{H}_{2}}O+S\]

    C) \[{{H}_{2}}S{{O}_{4}}+S\]

    D) \[{{H}_{2}}O+S{{O}_{2}}\]

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  • question_answer64) Which two of the following salts are used for preparing iodised salt? \[(I)KI{{O}_{3}}\,\,(II)KI\,\,(III){{I}_{2}}\,\,(IV)HI\]

    A) \[I,\,\,II\]

    B) \[I,\,\,III\]

    C) \[II,\,\,IV\]

    D) \[III,\,\,IV\]

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  • question_answer65) Ammonia will not form complex with

    A) \[A{{g}^{2+}}\]

    B) \[P{{b}^{2+}}\]

    C) \[C{{u}^{2+}}\]

    D) \[C{{d}^{2+}}\]

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  • question_answer66) The magnetic moment of a transition metal ion is\[\sqrt{15}BM\]. Therefore, the number of unpaired electrons present in it is

    A) \[4\]

    B) \[1\]

    C) \[2\]

    D) \[3\]

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  • question_answer67) \[C{{e}^{4+}}\] is stable. This is because

    A) half-filled \[d-\]orbitals

    B) all paired electrons in \[d-\]orbitals

    C) empty \[d-\]orbitals

    D) fully filled \[d-\]orbitals

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  • question_answer68) \[[Co{{(N{{H}_{3}})}_{4}}C{{l}_{2}}]N{{O}_{2}}\]and\[[Co{{(N{{H}_{3}})}_{4}}ClN{{O}_{2}}]Cl\] exhibit which type is isomerism?

    A) Geometrical

    B) Optical

    C) Linkage

    D) lonisation

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  • question_answer69) The \[\pi -\]bonded organometallic compound which has ethene as one of its component is

    A) Zeise's salt

    B) ferrocene

    C) dibenzene chromium

    D) tetraethyltin

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  • question_answer70) Alcoholic \[KOH\] is used for

    A) dehydration

    B) dehydrogenation

    C) dehydrohalogenation

    D) dehalogenation

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  • question_answer71) Freon used as refrigerant is

    A) \[C{{F}_{2}}=C{{F}_{2}}\]

    B) \[C{{H}_{2}}{{F}_{2}}\]

    C) \[CC{{l}_{2}}{{F}_{2}}\]

    D) \[C{{F}_{4}}\]

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  • question_answer72) Which of the following reacts fastly with\[Na?\]

    A) \[{{1}^{o}}\]alcohol

    B) \[{{2}^{o}}\]alcohol

    C) \[{{3}^{o}}\]alcohol

    D) The reactivity of all is equal

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  • question_answer73) Consider the following reaction\[Phenol\xrightarrow{Zn\,\,dust}X\xrightarrow[anhy\,\,AlC{{l}_{3}}]{C{{H}_{3}}Cl}Y\]\[\xrightarrow{alk\,\,KMn{{O}_{4}}}Z\] The product \[Z\] is

    A) toluene

    B) benzaldehyde

    C) benzoic acid

    D) benzene

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  • question_answer74) The formula of chloral is

    A) \[CHC{{l}_{3}}\]

    B) \[C{{H}_{2}}ClCHO\]

    C) \[CC{{l}_{3}}CHO\]

    D) \[CHC{{l}_{2}}CHO\]

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  • question_answer75) One of the following named reaction is an example of disproportionation reaction. Identify it

    A) Birch reduction

    B) Aldol condensation

    C) Reimer-Tiemann reaction

    D) Cannizaro reaction

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  • question_answer76) Calcium formate on dry heating yields

    A) acetone

    B) formaldehyde

    C) acetic acid

    D) acetaldehyde

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  • question_answer77) Which amongst the following is the most stable carbocation?

    A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{+}{\mathop{C}}}\,-H\]

    B) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{{{C}^{+}}}}}\,\]

    C) \[\overset{+}{\mathop{C}}\,{{H}_{3}}\]

    D) \[C{{H}_{3}}\overset{+}{\mathop{C}}\,{{H}_{2}}\]

    View Answer play_arrow
  • question_answer78) At\[{{25}^{o}}C\], the dissociation constant of a base,\[BOH\] is\[1.0\times {{10}^{-12}}\]. The concentration of hydroxyl ions in 0.01 M aqueous solution of the base would be

    A) \[2.0\times {{10}^{-6}}mol\,\,{{L}^{-1}}\]

    B) \[1.0\times {{10}^{-5}}mol\,\,{{L}^{-1}}\]

    C) \[1.0\times {{10}^{-6}}mol\,\,{{L}^{-1}}\]

    D) \[1.0\times {{10}^{-7}}mol\,\,{{L}^{-1}}\]

    View Answer play_arrow
  • question_answer79) Which one of the following pairs represents stereoisomerism?

    A) Chain isomerism and rotational isomerism,

    B) Structural isomerism and geometric isomerism

    C) Linkage isomerism and geometric isomerism

    D) Optical isomerism and geometric isomerism

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  • question_answer80) Aniline in a set of reactions yielded a product\[D\]. The structure of the product D would be

    A) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}N{{H}_{2}}\]

    B) \[{{C}_{6}}{{H}_{5}}NHC{{H}_{2}}C{{H}_{3}}\]

    C) \[{{C}_{6}}{{H}_{5}}NHOH\]

    D) \[{{C}_{6}}{{H}_{5}}C{{H}_{2}}OH\]

    View Answer play_arrow
  • question_answer81) The correct order in which the \[O-O\] bond length increases in the following is

    A) \[{{H}_{2}}{{O}_{2}}<{{O}_{2}}<{{O}_{3}}\]

    B) \[{{O}_{3}}<{{H}_{2}}{{O}_{2}}<{{O}_{2}}\]

    C) \[{{O}_{2}}<{{O}_{3}}<{{H}_{2}}{{O}_{2}}\]

    D) \[{{O}_{2}}<{{H}_{2}}{{O}_{2}}<{{O}_{3}}\]

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  • question_answer82) The mass of carbon anode consumed (giving only carbon dioxide) in the production of \[270\,\,kg\] of aluminium metal from bauxite by the Hall process is (Atomic mass\[Al=27)\]

    A) \[180\,\,kg\]

    B) \[270\,\,kg\]

    C) \[540\,\,kg\]

    D) \[90\,\,kg\]

    View Answer play_arrow
  • question_answer83) The number of moles of \[KMn{{O}_{4}}\] reduced by one mole of \[KI\] in alkaline medium is

    A) one fifth

    B) five

    C) one

    D) two

    View Answer play_arrow
  • question_answer84) Which of the following molecules has trigonal planar geometry?

    A) \[I{{F}_{3}}\]

    B) \[PC{{l}_{3}}\]

    C) \[N{{H}_{3}}\]

    D) \[B{{F}_{3}}\]

    View Answer play_arrow
  • question_answer85) Which one of the following forms micelles in aqueous solution above certain concentration?

    A) Urea

    B) Dodecyl trimethyl ammonium chloride

    C) Pyridinium chloride

    D) Glucose

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  • question_answer86) A nuclide of an alkaline earth metal undergoes radioactive decay by emission of three \[\alpha -\]particles in succession. The group of the periodic table to which the resulting daughter element would belong is

    A) group 14

    B) group 16

    C) group 4

    D) group 6

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  • question_answer87) Which of the following pairs of a chemical reaction is certain to result in a spontaneous reaction?

    A) Exothermic and decreasing disorder

    B) Endothermic and increasing disorder

    C) Exothermic and increasing disorder

    D) Endothermic and decreasing disorder

    View Answer play_arrow
  • question_answer88) The monomer of the polymer

    A)

    B) \[{{(C{{H}_{3}})}_{2}}C=C{{(C{{H}_{3}})}_{2}}\]

    C) \[C{{H}_{3}}CH=CH\cdot C{{H}_{3}}\]

    D) \[C{{H}_{3}}CH=C{{H}_{2}}\]

    View Answer play_arrow
  • question_answer89) The correct sequence of increasing covalent character is represented by

    A) \[LiCl<NaCl<BeC{{l}_{2}}\]

    B) \[BeC{{l}_{2}}<NaCl<LiCl\]

    C) \[NaCl<LiCI<BeC{{l}_{2}}\]

    D) \[BeC{{l}_{2}}<LiCl<NaCl\]

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  • question_answer90) \[{{H}_{2}}S\] gas when passed through a solution of cations containing HC1 precipitates the cations of second group of qualitative analysis but not those belonging to the fourth group. It is because

    A) presence of \[HCl\] decreases the sulphide ion concentration

    B) presence of \[HCl\] increases the sulphide ion concentration

    C) solubility product of group II sulphides is more than that of group IV sulphides

    D) sulphides of group IV cations are unstable in\[HCl\]

    View Answer play_arrow
  • question_answer91) The energy of second Bohr orbit of the hydrogen atom is \[-328\,\,kJ\,\,mo{{l}^{-1}}\]; hence the energy of fourth Bohr orbit would be

    A) \[-41\,\,kJ\,\,mo{{l}^{-1}}\]

    B) \[-1312\,\,kJ\,\,mo{{l}^{-1}}\]

    C) \[-164\,\,kJ\,\,mo{{l}^{-1}}\]

    D) \[-82\,\,kJ\,\,mo{{l}^{-1}}\]

    View Answer play_arrow
  • question_answer92) Equilibrium constants \[{{K}_{1}}\] and \[{{K}_{2}}\] for the following equilibria\[NO(g)+\frac{1}{2}{{O}_{2}}N{{O}_{2}}(g)\]and\[2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)\]are related as

    A) \[{{K}_{2}}=\frac{1}{{{K}_{1}}}\]

    B) \[{{K}_{2}}=K_{1}^{2}\]

    C) \[{{K}_{2}}=\frac{{{K}_{1}}}{2}\]

    D) \[{{K}_{2}}=\frac{1}{K_{1}^{2}}\]

    View Answer play_arrow
  • question_answer93) Names of some compounds are given. Which one is not correct in \[IUPAC\] system?

    A) \[C{{H}_{3}}-\underset{\begin{smallmatrix} | \\ OH \end{smallmatrix}}{\mathop{C}}\,H-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\] 3-methyl-2-butanol

    B) \[C{{H}_{3}}-C{{H}_{2}}\equiv C-CH{{(C{{H}_{3}})}_{2}}\] 4-methyl-2-pentyne

    C) \[C{{H}_{3}}-C{{H}_{2}}-\underset{\begin{smallmatrix} || \\ C{{H}_{2}} \end{smallmatrix}}{\mathop{C}}\,-\underset{\begin{smallmatrix} | \\ C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{3}}\] 2-ethyl-3-methyl-but-1-ene

    D) \[C{{H}_{3}}-C{{H}_{2}}-C{{H}_{2}}-\underset{\begin{smallmatrix} | \\ C{{H}_{2}}C{{H}_{3}} \end{smallmatrix}}{\mathop{C}}\,H-\overset{\begin{smallmatrix} C{{H}_{3}} \\ | \end{smallmatrix}}{\mathop{C}}\,H-C{{H}_{2}}C{{H}_{3}}\] 3-methyl-4-ethyle heptane

    View Answer play_arrow
  • question_answer94) \[10\,\,g\] of hydrogen and \[64\,\,g\] of oxygen were filled in a steel vessel and exploded. Amount to water produced in this reaction will be

    A) \[3\,\,mol\]

    B) \[4\,\,mol\]

    C) \[1\,\,mol\]

    D) \[2\,\,mol\]

    View Answer play_arrow
  • question_answer95) Dominance of strong repulsive forces among the molecules of the gas \[(Z=\]compressibility factor)

    A) depends on \[Z\] and indicated by\[Z=1\]

    B) depends on \[Z\] and indicated by\[Z>1\]

    C) depends on \[Z\] and indicated by\[Z<1\]

    D) is independent of\[Z\]

    View Answer play_arrow
  • question_answer96) When glucose reacts with bromine water, the main product is

    A) acetic acid

    B) saccharic acid

    C) glyceraldehyde

    D) gluconic acid

    View Answer play_arrow
  • question_answer97) Protein present in hair is

    A) albumin

    B) globulin

    C) keratin

    D) chromoprotein

    View Answer play_arrow
  • question_answer98) The hydrolysis of 2-bromo-3-methyl butane by \[{{S}_{N}}1\] mechanism gives mainly

    A) 3-methl-2-butanol

    B) 2-methyl-2-butanol

    C) 2, 2-dimethyl-l-propanol

    D) 2 methyl-1-butanol

    View Answer play_arrow
  • question_answer99) The \[pH\] value of an acid is \[5\] and its concentration is\[1\,\,M\] . What is the value of \[{{K}_{a}}\] for the acid?

    A) \[{{10}^{-7}}\]

    B) \[{{10}^{-5}}\]

    C) \[{{10}^{-10}}\]

    D) \[{{10}^{-8}}\]

    View Answer play_arrow
  • question_answer100) If \[1\] mole of an ideal gas expands isothermally at \[{{37}^{o}}C\] from \[15\,\,L\] to\[25\,\,L\], the maximum work obtained is

    A) \[12.87\,\,J\]

    B) \[6.43\,\,J\]

    C) \[8.57\,\,J\]

    D) \[2.92\,\,J\]

    View Answer play_arrow
  • question_answer101) If the lines represented by \[{{x}^{2}}-2pxy-{{y}^{2}}\] are rotated about the origin through an angle\[\theta \], one in clockwise direction and other in anti-clockwise direction. Then, die equation of bisectors of the angles between the lines in the new position is

    A) \[p{{x}^{2}}+2xy+p{{y}^{2}}=0\]

    B) \[p{{x}^{2}}-2xy+p{{y}^{2}}=0\]

    C) \[p{{x}^{2}}+2xy-p{{y}^{2}}=0\]

    D) None of these

    View Answer play_arrow
  • question_answer102) If\[z=i{{\log }_{e}}(2-\sqrt{3})\], then find the value of\[\cos z\].

    A) \[2\]

    B) \[-2\]

    C) \[2i\]

    D) \[-2i\]

    View Answer play_arrow
  • question_answer103) The sum of the roots of quadratic equation \[a{{x}^{2}}+bx+c=0(a,\,\,b,\,\,c\ne 0)\] is equal to the sum of squares of their reciprocals, then \[\frac{a}{c},\,\,\frac{b}{a}\] and \[\frac{c}{b}\]are in

    A) \[AP\]

    B) \[GP\]

    C) \[HP\]

    D) None of these

    View Answer play_arrow
  • question_answer104) Find the value of \[^{1}{{P}_{1}}+2{{\cdot }^{2}}{{P}_{2}}+3{{\cdot }^{3}}{{P}_{3}}+4{{\cdot }^{4}}{{P}_{4}}+...{{+}^{n}}{{P}_{n}}\]

    A) \[^{n+1}{{P}_{n+1}}\]

    B) \[^{n+1}{{P}_{n+1}}-1\]

    C) \[^{n+1}{{P}_{n+1}}-2\]

    D) \[^{n+1}{{P}_{n+1}}+1\]

    View Answer play_arrow
  • question_answer105) The eccentricity of an ellipse whose pair of a conjugate diameter are \[y=x\] and \[3y=-2x\] is

    A) \[\frac{2}{3}\]

    B) \[\frac{1}{3}\]

    C) \[\frac{1}{\sqrt{3}}\]

    D) None of these

    View Answer play_arrow
  • question_answer106) If the shortest distance between the lines \[\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}\] and\[\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\] is\[\lambda \sqrt{30}\]units, then the value of\[\lambda \]is

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[4\]

    View Answer play_arrow
  • question_answer107) Let \[u\] and \[v\] be two odd functions, then the function \[uov\] is

    A) an even function

    B) an odd function

    C) neither even nor odd

    D) a periodic function

    View Answer play_arrow
  • question_answer108) The period of the function \[f(x)=2\sin x+3\cos 2x\]is

    A) \[\pi \]

    B) \[2\pi \]

    C) \[\frac{\pi }{2}\]

    D) None of these

    View Answer play_arrow
  • question_answer109) If\[y=\frac{1}{{{t}^{2}}-t-6}\]and\[t=\frac{1}{x-2}\], then the values of \[x\]which make the function \[y\] discontinuous, are

    A) \[2,\,\,\frac{2}{3},\,\,\frac{7}{3}\]

    B) \[2,\,\,\frac{3}{2},\,\,\frac{7}{3}\]

    C) \[2,\,\,\frac{3}{2},\,\,\frac{3}{7}\]

    D) None of the above

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  • question_answer110) The sub tangent at any point of the curve\[{{x}^{m}}{{y}^{n}}={{a}^{m+n}}\]varies as

    A) \[{{(abscissa)}^{2}}\]

    B) \[{{(abscissa)}^{3}}\]

    C) abscissa

    D) ordinate

    View Answer play_arrow
  • question_answer111) \[f(x)=1+[\cos x]x,\]in\[0<x\le \frac{\pi }{2}\]

    A) has a minimum value

    B) has a maximum value\[2\]

    C) is continuous in\[\left[ 0,\,\,\frac{\pi }{2} \right]\]

    D) is not differentiable at\[x=\frac{\pi }{2}\]

    View Answer play_arrow
  • question_answer112) If the force represented by \[\mathbf{i}+\mathbf{j}+\mathbf{k}\] is acting through the point \[5\mathbf{i}+4\mathbf{j}-3\mathbf{k}\], then its moment about the point\[(1,\,\,2,\,\,2)\]is

    A) \[14\mathbf{i}-8\mathbf{j}+12\mathbf{k}\]

    B) \[-14\mathbf{i}-8\mathbf{j}-12\mathbf{k}\]

    C) \[7\mathbf{i}+9\mathbf{j}+2\mathbf{k}\]

    D) \[7\mathbf{i}-9\mathbf{j}+2\mathbf{k}\]

    View Answer play_arrow
  • question_answer113) If the planes\[x-cy-bz=0\], \[ex-y+az=0\] and\[bx+ay-z=0\], pass through a line, then find the value of\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2abc\].

    A) \[0\]

    B) \[1\]

    C) \[-1\]

    D) \[\frac{1}{2}\]

    View Answer play_arrow
  • question_answer114) A parallelepiped is formed by planes drawn through the points \[(2,\,\,3,\,\,5)\] and \[(5,\,\,9,\,\,7)\] parallel to the coordinate planes. The length of the diagonal of the parallelepiped is

    A) \[7\]

    B) \[8\]

    C) \[4\]

    D) \[11\]

    View Answer play_arrow
  • question_answer115) Equation of the chord of the hyperbola \[25{{x}^{2}}-16{{y}^{2}}=400\] which is bisected at the point \[(6,\,\,2)\] is

    A) \[16x-75y=418\]

    B) \[75x-16y=418\]

    C) \[25x-4y=400\]

    D) None of these

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  • question_answer116) \[\int{\frac{1}{{{x}^{6}}+{{x}^{4}}}dx}\]is equal to

    A) \[-\frac{1}{3{{x}^{3}}}+\frac{1}{x}+\cos \text{e}{{\text{c}}^{-1}}x+C\]

    B) \[-\frac{1}{3{{x}^{3}}}+\frac{1}{x}+{{\cot }^{-1}}x+C\]

    C) \[-\frac{1}{3{{x}^{3}}}+\frac{1}{x}+ta{{n}^{-1}}x+C\]

    D) None of the above

    View Answer play_arrow
  • question_answer117) Find the sum of the series\[\frac{1}{2\cdot 3}+\frac{1}{4\cdot 5}+\frac{1}{6\cdot 7}+...\]

    A) \[\log \frac{e}{2}\]

    B) \[\log \frac{e}{4}\]

    C) \[\log \frac{2}{3}\]

    D) \[\log \frac{2}{4}\]

    View Answer play_arrow
  • question_answer118) The equation \[{{\tan }^{4}}x-2{{\sec }^{2}}x+{{a}^{2}}=0\] will have atleast one solution, if

    A) \[|a|\,\,\le 4\]

    B) \[|a|\,\,\le 2\]

    C) \[|a|\,\,\le \sqrt{3}\]

    D) \[|a|\,\,\le \sqrt{2}\]

    View Answer play_arrow
  • question_answer119) If\[\sin \theta +\cos \theta =\sqrt{2}\cos ({{90}^{o}}-\theta )\], then find the value of\[\cot \theta \]

    A) \[\frac{1}{2}\]

    B) \[0\]

    C) \[-1\]

    D) \[2\]

    View Answer play_arrow
  • question_answer120) If\[2-{{\cos }^{2}}\theta =3\sin \theta \cos \theta \],\[\sin \theta \ne cos\theta \], then find the value of\[\cot \theta \]

    A) \[\frac{1}{2}\]

    B) \[0\]

    C) \[-1\]

    D) \[2\]

    View Answer play_arrow
  • question_answer121) Two posts are \[x\] metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is

    A) \[x\sqrt{2}\]

    B) \[\frac{x}{\sqrt{2}}\]

    C) \[\frac{x}{2\sqrt{2}}\]

    D) \[\frac{x}{4}\]

    View Answer play_arrow
  • question_answer122) The coefficient of \[{{x}^{n}}\] in the expansion of\[{{(1-x)}^{-2}}\]is

    A) \[\frac{{{2}^{n}}}{2!}\]

    B) \[n+1\]

    C) \[n+2\]

    D) \[2n\]

    View Answer play_arrow
  • question_answer123) If \[f(x)\] is an even function, then\[\int_{0}^{x}{f(t)}\,\,dt\]

    A) odd function

    B) even function

    C) neither even nor odd

    D) None of the above

    View Answer play_arrow
  • question_answer124) Solve\[(xy-1)\frac{dy}{dx}+{{y}^{2}}=0\]

    A) \[xy+\log x=C\]

    B) \[xy+\log y=C\]

    C) \[xy-\log y=C\]

    D) \[xy-\log x=C\]

    View Answer play_arrow
  • question_answer125) Find the order and degree of the differential equation \[{{\left( \frac{{{d}^{4}}y}{d{{x}^{4}}} \right)}^{3/5}}-5\frac{{{d}^{3}}y}{d{{x}^{3}}}+6\frac{{{d}^{2}}y}{d{{x}^{2}}}-8\frac{dy}{dx}+5=0\]

    A) \[4,\,\,3\]

    B) \[3,\,\,4\]

    C) \[4,\,\,5\]

    D) \[5,\,\,4\]

    View Answer play_arrow
  • question_answer126) If the circle\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] touches by the line \[y=x\] at the point \[P\] such that \[OP=6\sqrt{2}\], where \[O\] is the origin, then the value of \[c\] is equal to

    A) \[74\]

    B) \[62\]

    C) \[64\]

    D) \[72\]

    View Answer play_arrow
  • question_answer127) The locus of the middle points of chords of the parabola \[{{y}^{2}}=8x\] drawn through the vertex is a parabola whose

    A) focus is\[(2,\,\,0)\]

    B) latusrectum\[=8\]

    C) focus is\[(0,\,\,2)\]

    D) latusrectum\[=4\]

    View Answer play_arrow
  • question_answer128) lf\[\sqrt{x}+\sqrt{y}=10\], find\[\frac{dx}{dy}\]at\[y=4\].

    A) \[4\]

    B) \[-3\]

    C) \[-4\]

    D) \[3\]

    View Answer play_arrow
  • question_answer129) Find the value of\[{{e}^{iA}}.{{e}^{iB}}.{{e}^{iC}}.{{e}^{iD}}\], where \[A,\,\,\,B,\,\,\,C\] and \[D\] are the angles of a quadrilateral.

    A) \[i\]

    B) \[-i\]

    C) \[1\]

    D) \[-1\]

    View Answer play_arrow
  • question_answer130) The equation\[z\bar{z}+z+\bar{z}+10=0\], represents

    A) a circle

    B) a parabola

    C) an ellipse

    D) a hyperbola

    View Answer play_arrow
  • question_answer131) The lengths of three unequal edges of a rectangular solid block are in\[GP\]. The volume and total surface area of the block are \[216\,\,c{{m}^{3}}\] and\[252\,\,c{{m}^{2}}\], respectively. Find the shortest edge of the block.

    A) \[12\,\,cm\]

    B) \[6\,\,cm\]

    C) \[18\,\,cm\]

    D) \[3\,\,cm\]

    View Answer play_arrow
  • question_answer132) If\[\log (p+r)+\log (p+r-2q)=2\log (p-r)\], then \[p,\,\,\,q\] and \[r\] are in

    A) \[AP\]

    B) \[GP\]

    C) \[HP\]

    D) None of these

    View Answer play_arrow
  • question_answer133) Find the sum of the real roots of the equation\[{{x}^{2}}+5|x|+\,\,6=0\]

    A) \[5\]

    B) \[10\]

    C) \[-5\]

    D) None of these

    View Answer play_arrow
  • question_answer134) If\[A=\left[ \begin{matrix} 1 & 2 \\ 2 & 1 \\ \end{matrix} \right]\]and\[f(x)=\frac{1+x}{1-x}\], find the value of\[f(A)\].

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

    B) \[\left[ \begin{matrix} -1 & -1 \\ -1 & -1 \\ \end{matrix} \right]\]

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

    D) None of these

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  • question_answer135) A skew-symmetric matrix \[M\] satisfies the relation\[M+I=0\], where \[I\] is the unit matrix. Then, \[MM'\]is equal to

    A) \[I\]

    B) \[2I\]

    C) \[-I\]

    D) None of these

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  • question_answer136) Let \[X\] and \[Y\] be two random variables. The relationship \[E(XY)=E(X)\cdot E(Y)\] holds

    A) always

    B) if\[E(X+Y)=E(X)+E(Y)\]is true

    C) if \[X\] and \[Y\] are independent

    D) if \[X\] can be obtained from \[Y\] by a linear transformation

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  • question_answer137) Find the number of solutions of the equation\[\sin 2x+\cos 4x=2\].

    A) \[0\]

    B) \[1\]

    C) \[2\]

    D) infinite

    View Answer play_arrow
  • question_answer138) In any\[\Delta ABC\], find the least value of\[\frac{{{\sin }^{2}}A+\sin A+1}{\sin A}\].

    A) \[3\]

    B) \[\sqrt{3}\]

    C) \[1\]

    D) \[2\]

    View Answer play_arrow
  • question_answer139) Find the critical points of the function \[f(x)={{(x-2)}^{2/3}}(2x+1)\].

    A) \[-1\]and\[2\]

    B) \[1\]

    C) \[1\]and\[-\frac{1}{2}\]

    D) \[1\]and\[2\]

    View Answer play_arrow
  • question_answer140) If\[\mathbf{a}=2\mathbf{i}+2\mathbf{j}+3\mathbf{k}\],\[\mathbf{b}=-\mathbf{i}+2\mathbf{j}+\mathbf{k}\]and\[\mathbf{c}=3\mathbf{i}+\mathbf{j}\], then \[\mathbf{a}+t\mathbf{b}\] is perpendicular to \[\mathbf{c};\] if\[t\] is equal to

    A) \[2\]

    B) \[4\]

    C) \[6\]

    D) \[8\]

    View Answer play_arrow
  • question_answer141) Find the angle between the straight lines \[\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}\]and \[\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}\]

    A) \[{{45}^{o}}\]

    B) \[{{30}^{o}}\]

    C) \[{{60}^{o}}\]

    D) \[{{90}^{o}}\]

    View Answer play_arrow
  • question_answer142) The equation of the plane passing through the line of intersection of the planes \[2x-y=0\] and \[3z-y=0\] and perpendicular to the plane \[4x+5y-3z=8\] is

    A) \[2x+17y+9z=0\]

    B) \[28x-17y+9z=0\]

    C) \[2x+17y-9z=0\]

    D) None of these

    View Answer play_arrow
  • question_answer143) The function defined by the equation \[xy-\log y=1\]satisfies\[x(yy''+y{{'}^{2}})-y''+kyy'=0\]. Find the value of\[k\].

    A) \[-3\]

    B) \[3\]

    C) \[1\]

    D) \[-1\]

    View Answer play_arrow
  • question_answer144) If\[f(x)={{[1-{{(x-3)}^{4}}]}^{1/7}}\], find\[{{f}^{-1}}(x)\].

    A) \[3+{{(1-x)}^{7/4}}\]

    B) \[3+{{(1-{{x}^{4}})}^{7}}\]

    C) \[3+{{(1-{{x}^{7}})}^{1/4}}\]

    D) \[3-{{(1-{{x}^{4}})}^{1/7}}\]

    View Answer play_arrow
  • question_answer145) Find the value of\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{a}^{n}}+{{b}^{n}}}{{{a}^{n}}+{{d}^{n}}},\,\,a>b,\,\,d\].

    A) \[-1\]

    B) \[1\]

    C) \[0\]

    D) \[\frac{1}{2}\]

    View Answer play_arrow
  • question_answer146) The function \[y={{x}^{2}}+ax+b\] has a minimum at \[x=3\] and minimum value is\[5\]. Find\[a+b\].

    A) \[-6\]

    B) \[14\]

    C) \[20\]

    D) \[8\]

    View Answer play_arrow
  • question_answer147) The coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1-9x+20{{x}^{2}})}^{-1}}\]

    A) \[{{5}^{n}}-{{4}^{n}}\]

    B) \[{{5}^{n+1}}-{{4}^{n+1}}\]

    C) \[{{5}^{n-1}}-{{4}^{n-1}}\]

    D) None of these

    View Answer play_arrow
  • question_answer148) The minimum value of\[f(x)=|x-1|+|x-2|+|x-3|\] is equal to

    A) \[1\]

    B) \[2\]

    C) \[3\]

    D) \[0\]

    View Answer play_arrow
  • question_answer149) \[\frac{{{d}^{20}}y}{d{{x}^{20}}}(2\cos x\cos 3x)\]is equal to

    A) \[{{2}^{20}}(\cos 2x-{{2}^{20}}\cos 4x)\]

    B) \[{{2}^{20}}(\cos 2x+{{2}^{20}}\cos 4x)\]

    C) \[{{2}^{20}}(\sin 2x+{{2}^{20}}\sin 4x)\]

    D) \[{{2}^{20}}(\sin 2x-{{2}^{20}}\sin 4x)\]

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  • question_answer150) The logically equivalent proposition of \[p\Leftrightarrow q\] is

    A) \[(p\wedge q)\vee (p\wedge q)\]

    B) \[(p\Rightarrow q)\wedge (q\Rightarrow p)\]

    C) \[(p\wedge q)\vee (q\Rightarrow p)\]

    D) \[(p\wedge q)\Rightarrow (q\vee p)\]

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