Solved papers for JCECE Engineering JCECE Engineering Solved Paper-2012

JCECE Engineering Solved Paper-2012 Total Questions - 150

1) 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)

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

View Answer
2) 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)

\[5\,\,cm\]

View Answer
3) 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)

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

View Answer
4) 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)

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

View Answer
5) 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

View Answer
6) 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)

\[M\]

View Answer
7) 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)

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

View Answer
8) 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

View Answer
9) 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)

\[\alpha =0\]

View Answer
10) 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)

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

View Answer
11) 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

View Answer
12) 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)

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

View Answer
13) 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)

\[11:7\]

View Answer
14) 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)

\[90\]

View Answer
15) 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)

\[(n-1)f\]

View Answer
16) 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

View Answer
17) 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)

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

View Answer
18) 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)

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

View Answer
19) 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)

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

View Answer
20) 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)

\[50\,\,J\]

View Answer
21) 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)

\[20N,\,\,30N\]

View Answer
22) 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

View Answer
23) 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

View Answer
24) 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

View Answer
25) 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\[B\]

View Answer
26) 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)

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

View Answer
27) 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)

\[\ge T\]

View Answer
28) In the circuit shown, potential difference between \[x\] and \[y\] will be

A)

\[Zero\]

B)

\[120\,\,V\]

C)

\[60\,\,V\]

D)

\[20\,\,V\]

View Answer
29) 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)

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

View Answer
30) 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.

View Answer
31) 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)

\[84\,\,cm\]

View Answer
32) 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)

\[75{}^\circ \]

View Answer
33) 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)

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

View Answer
34) 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

View Answer
35) 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)

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

View Answer
36) 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

View Answer
37) 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)

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

View Answer
38) 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)

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

View Answer
39) 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)

\[10\Omega \]

View Answer
40) 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)

\[\sqrt{gL}\]

View Answer
41) 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

View Answer
42)  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)

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

View Answer
43) 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

View Answer
44) 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)

\[1.0\]

View Answer
45) A water drop in air reflects the light rays as

A)

B)

C)

D)

View Answer
46) 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)

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

View Answer
47) An ideal thermometer should have

A)

small heat capacity

B)

large heat capacity

C)

medium heat capacity

D)

variable heat capacity

View Answer
48) For the circuit shown in figure, the impedance of the circuit will be

A)

\[50\Omega \]

B)

\[60\Omega \]

C)

\[90\Omega \]

D)

\[120\Omega \]

View Answer
49) 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

View Answer
50) 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)

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

View Answer
51) 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

View Answer
52) 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

View Answer
53) 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)

\[0.2\,\,M\]

View Answer
54) 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)

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

View Answer
55) 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)

\[Z>X>Y\]

View Answer
56) 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)

\[18.4\]

View Answer
57) 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)

\[400\,\,\min \]

View Answer
58) 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

View Answer
59) What is the name of a phenomenon in which both adsorption and absorption takes places?

A)

Chemisorption

B)

Physisorption

C)

Desorption

D)

  Sorption

View Answer
60) 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

View Answer
61) The most important ore of tin is

A)

cassiterite

B)

cryolite

C)

cerussite

D)

  None of these

View Answer
62) 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

View Answer
63) 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)

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

View Answer
64) 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)

\[III,\,\,IV\]

View Answer
65) Ammonia will not form complex with

A)

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

B)

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

C)

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

D)

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

View Answer
66) 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)

\[3\]

View Answer
67) \[C{{e}^{4+}}\] 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

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

A)

Geometrical

B)

Optical

C)

Linkage

D)

lonisation

View Answer
69) 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

View Answer
70) Alcoholic \[KOH\] is used for

A)

dehydration

B)

dehydrogenation

C)

dehydrohalogenation

D)

dehalogenation

View Answer
71) 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)

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

View Answer
72) 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

View Answer
73) 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

View Answer
74) The formula of chloral is

A)

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

B)

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

C)

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

D)

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

View Answer
75) 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

View Answer
76) Calcium formate on dry heating yields

A)

acetone

B)

formaldehyde

C)

acetic acid

D)

acetaldehyde

View Answer
77) 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
78) 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
79) 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

View Answer
80) 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
81) 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)

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

View Answer
82) 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
83) 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
84) 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
85) 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

View Answer
86) 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

View Answer
87) 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
88) 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
89) 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)

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

View Answer
90) \[{{H}_{2}}S\] 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
91) 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
92) 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
93) 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
94) \[10\,\,g\] 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
95) 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
96) When glucose reacts with bromine water, the main product is

A)

acetic acid

B)

saccharic acid

C)

glyceraldehyde

D)

gluconic acid

View Answer
97) Protein present in hair is

A)

albumin

B)

globulin

C)

keratin

D)

chromoprotein

View Answer
98) 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
99) 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
100) 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
101) 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
102) 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
103) 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
104) 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
105) 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
106) 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
107) 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
108) 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
109) 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

View Answer
110) 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
111) \[f(x)=1+[\cos x]x,\]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
112) 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
113) 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
114) 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
115) 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

View Answer
116) \[\int{\frac{1}{{{x}^{6}}+{{x}^{4}}}dx}\]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
117) 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
118) 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
119) 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
120) 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
121) 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
122) 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
123) 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
124) 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
125) 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
126) 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
127) 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
128) lf\[\sqrt{x}+\sqrt{y}=10\], find\[\frac{dx}{dy}\]at\[y=4\].

A)

\[4\]

B)

\[-3\]

C)

\[-4\]

D)

\[3\]

View Answer
129) 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
130) 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
131) 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
132) 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
133) 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
134) 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

View Answer
135) 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

View Answer
136) 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

View Answer
137) Find the number of solutions of the equation\[\sin 2x+\cos 4x=2\].

A)

\[0\]

B)

\[1\]

C)

\[2\]

D)

infinite

View Answer
138) 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
139) 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
140) 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
141) 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
142) 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
143) 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
144) 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
145) 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
146) 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
147) 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
148) 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
149) \[\frac{{{d}^{20}}y}{d{{x}^{20}}}(2\cos x\cos 3x)\]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)

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

View Answer
150) 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)

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

View Answer