An electric charge $10^{-3}\mu C$ is placed at the origin $(0, 0)$ of $X- Y$ co-ordinate system. Two points $A$ and $B$ are
situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be
a.
$9\,volt$
b.
zero
Correct Answer
c.
$2\,volt$
d.
$4.5\,volt$
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Q2mcq
Charges are placed on the vertices of a square as shown. Let $E$ be the electric field and $V$ the potential at the
centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then
Which of the following transitions in hydrogen atoms emit photons of highest frequency?
a.
$n= 2$ to $n= 6$
b.
$n= 6$ to $n= 2$
c.
$n= 2$ to $n= 1$
Correct Answer
d.
$n= 1$ to $n= 2$
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Q4mcq
Two springs, of force constants $k_{1}$ and $k_{2}$ , are connected to a mass $m$ as shown. The frequency of oscillation of
the mass is $f$ . If both $k_{1}$ and $k_{2}$ are made four times their original values, the frequency of oscillation becomes
a.
$f/2$
b.
$f/4$
c.
$4f$
d.
$2f$
Correct Answer
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Q5mcq
Two lenses of power $-15\,D$ and $+5\,D$ are in contact with each other. The focal length of the combination is
a.
$-20\,cm$
b.
$-10\,cm$
Correct Answer
c.
$+20\,cm$
d.
$+10\,cm$
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Q6mcq
If $M_{o}$ is the mass of an oxygen isotope $_{8}O^{17}, M_{p}$ and $M_{N}$ are the masses of a proton and a neutron
respectively, the nuclear binding energy of the isotope is
a.
$(M_{o}-8M_{p})C^{2}$
b.
$(M_{o}-8M_{p}-9M_{N})C^{2}$
Correct Answer
c.
$M_{o}C^{2}$
d.
$(M_{o}-17M_{N})C^{2}$
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Q7mcq
An ideal coil of $10H$ is connected in series with a resistance of $5\Omega$ and a battery of $5\,V$ . $2$ second after the
connection is made the current flowing in amperes in the circuit is
a.
$(1 -e)$
b.
$e$
c.
$e^{-1}$
d.
$(1 -e^{-1})$
Correct Answer
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Q8mcq
The displacement of an object attached to a spring and executing simple harmonic motion is given by
$x= 2 \times 10^{-2} cos\pi t$ metres. The time at which the maximum speed first occurs is
a.
$0.5\,s$
Correct Answer
b.
$0.75\,s$
c.
$0.125\,s$
d.
$0.25\,s$
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Q9mcq
A body weighing $13\,kg$ is suspended by two strings $5\,m$ and $12\,m$ long, their other ends being fastened to the
extremities of a rod $13\,m$ long. If the rod be so held that the body hangs immediately below the middle point.
The tensions in the strings are
a.
$12\,kg$ and $13\,kg$
b.
$5\,kg$ and $5\,kg$
c.
$5\,kg$ and $12\,kg$
Correct Answer
d.
$5\,kg$ and $13\,kg$
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Q10mcq
A charged particle moves through a magnetic field perpendicular to its direction. Then
a.
the momentum changes but the kinetic energy is
constant
Correct Answer
b.
both momentum and kinetic energy of the
particle are not constant
c.
both, momentum and kinetic energy of the
particle are constant
d.
kinetic energy changes but the momentum is
constant
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In an a.c. circuit the voltage applied is $E = E_{0}sin\omega t$ . The resulting current in the circuit is
$I = I_{0}sin(\omega t - \frac{\pi}{2})$ . The power consumption in the circuit is given by
a.
$P = \frac{E_{0}I_{0}}{\sqrt{2}}$
b.
$P =$ zero
c.
$P = \frac{E_{0}I_{0}}{2}$
d.
$P\sqrt{2}E_{0}I_{0}$
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A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is
charged to a potential $\,V\,volts$ . The dielectric slab is slowly removed from between the plates and then
reinserted. The net work done by the system in this process is
a.
$1/2(\,K -1)CV^{2}$
b.
$CV^{2}(\,K -1)/K$
c.
$(K -1)CV^{2}$
d.
zero
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A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of
the discs coincide. The centre of mass of the new disc is $\alpha /R$ from the centre of the bigger disc. The value of $\alpha$
is
a.
$1/3$
b.
$1/2$
c.
$1/6$
d.
$1/4$
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A point mass oscillates along the $x$ -axis according to the law $x = x_{0}cos(\omega t - \pi /4)$ . If the acceleration of the
particle is written as $a = A cos(\omega t +\delta )$
a.
$A = x_{0},\delta = -\pi /4$
b.
$A = x_{0}\omega ^{2},\delta = -\pi /4$
c.
$A = x_{0}\omega ^{2},\delta = -\pi /4$
d.
$A = x_{0}\omega ^{2},\delta = 3\pi /4$
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The half-life period of a radio-active element $X$ is same as the mean life time of another radioactive element $Y$
. Initially they have the same number of atoms. Then
a.
$X$ will decay faster than $Y$
b.
$Y$ will decay faster than $X$
c.
$X$ and $Y$ have same decay rate initially
d.
$X$ and $Y$ decay at same rate always.
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In a Young's double slit experiment the intensity at a point where the path difference is $\frac{\lambda}{6}$ ( $\lambda$ being the
wavelength of the light used) is $I$ . If $I_{0}$ denotes the maximum intensity, $\frac{I}{I_{0}}$ is equal to
a.
$\frac{1}{\sqrt{2}}$
b.
$\frac{\sqrt{3}}{2}$
c.
$1/2$
d.
$3/4$
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A particle of mass $m$ executes simple harmonic motion with amplitude ' $a$ ' and frequency ' $v$ '. The average
kinetic energy during its motion from the position of equilibrium to the end is
a.
$\pi ^{2}ma^{2}v^{2}$
b.
$\frac{1}{4}\pi ^{2}ma^{2}v^{2}$
c.
$4\pi ^{2}ma^{2}v^{2}$
d.
$2\pi ^{2}ma^{2}v^{2}$
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The potential at a point $x$ (measured in $\mu m$ ) due to some charges situated on the $x$ -axis is given by
$V(x) = 20/(x^{2} -4)\,Volts$ . The electric field $E$ at $x = 4\,\mu m$ is given by
a.
$5/3\,Volt/\mu m$ and in the $-ve x$ direction
b.
$5/3\,Volt/\mu m$ and in the $+ve x$ direction.
c.
$10/9\,Volt/\mu m$ and in the $-ve x$ direction
d.
$10/9\,Volt/\mu m$ and in the $+ve x$ direction.
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A round uniform body of radius $R$ , mass $M$ and moment of inertia ' $I$ ', rolls down (without slipping) an inclined
plane making an angle $\theta$ with the horizontal. Then its acceleration is
a.
$\frac{g sin\theta}{1+^{I}}$
$MR2$
b.
$\frac{g sin\theta}{1+^{MR2}}$
$I$
c.
$\frac{g sin\theta}{1-^{I}}$
$MR2$
d.
$\frac{g sin\theta}{1-^{MR2}}$
$I$
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A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes
equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work
done by the battery will be
a.
$1$
b.
$2$
c.
$\frac{1}{4}$
d.
$\frac{1}{2}$
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A particle just clears a wall of height $b$ at distance $a$ and strikes the ground at a distance $c$ from the point of
projection. The angle of projection is
a.
$tan^{-1} \frac{b}{ac}$
b.
$45^{\circ }$
c.
$tan^{-1} \frac{bc}{a(c-a)}$
d.
$tan^{-1} \frac{bc}{a}$
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A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\vec{E}$ and $\vec{B}$
witha velocity $\vec{v}$ perpendicular to both $\vec{E}$ and $\vec{B}$ , and comes out without any change in magnitude or direction
of $\vec{v}$ . Then
a.
$\vec{v}= \vec{E}\times \vec{B}/B^{2}$
b.
$\vec{v}= \vec{B}\times \vec{E}/B^{2}$
c.
$\vec{v}= \vec{E}\times \vec{B}/E^{2}$
d.
$\vec{v}= \vec{B}\times \vec{E}/E^{2}$
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Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries
an electric current $I_{1}$ and $COD$ carries a current $I_{2}$ . The magnetic field on a point lying at a distance ' $d$ ' from
$O$ , in a direction perpendicular to the plane of the wires $AOB$ and $COD$ , will be given by
A block of mass ' $m$ ' is connected to another block of mass ' $M$ ' by a spring (massless) of spring constant ' $k$ '.
The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched.
Then a constant force ' $F$ ' starts acting on the block of mass ' $M$ ' to pull it. Find the force on the block of mass ' $m$ '
a.
$\frac{mF}{M}$
b.
$\frac{(M+m)F}{m}$
c.
$\frac{mF}{(m+M)}$
d.
$\frac{MF}{(m+M)}$
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A Carnot engine, having an efficiency of $\eta = 1/10$ as heat engine, is used as a refrigerator. If the work done on
the system is $10\,J$ , the amount of energy absorbed from the reservoir at lower temperature is
a.
$99\,J$
b.
$90\,J$
c.
$1\,J$
d.
$100\,J$
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One end of a thermally insulated rod is kept at a temperature $T_{1}$ and the other at $T_{2}$ . The rod is composed of
two sections of lengths $\ell _{1}$ and $\ell _{2}$ and thermal conductivities $k_{1}$ and $k_{2}$ respectively. The temperature at the
interface of the two sections is
If $g_{E}$ and $g_{m}$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if
Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio
$\frac{\,electronic charge on the moon\,}{\,electronic charge on the earth\,}$ to be
a.
$1$
b.
$0$
c.
$g_{E}/g_{m}$
d.
$g_{m}$ / $g_{E}$
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A long straight wire of radius ' $a$ ' caries a steady current $i$ . The current is uniformly distributed across its cross
section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ is
a.
$\frac{1}{4}$
b.
$4$
c.
$1$
d.
$\frac{1}{2}$
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A $2\,kg$ block slides on a horizontal floor with a speed of $4\,m/s$ . It strikes a uncompressed spring, and
compresses it till the block is motionless. The kinetic friction force is $15\,N$ and spring constant is $10, 000. N/m$ .
The spring compresses by
a.
$5.5\,cm$
b.
$2.5\,cm$
c.
$11.0\,cm$
d.
$8.5\,cm$
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When a system is taken from state $i$ to state $f$ along the path $iaf$ , it is found that $Q= 50\,cal$ and $W = 20\,cal$ .
Along the path' $ibf Q = 36\,cal$ . $W$ along the path $ibf$ is
a.
$6\,cal$
b.
$16\,cal$ .
c.
$66\,cal$ .
d.
$14\,cal$ .
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A $5.25%$ solution of a substance is isotonic with a $1.5%$ solution of urea $($ molar mass $= 60\,g\,mol^{-1}$ ) in the
same solvent. If the densities of both the solutions are assumed to be equal to $1.0\,g\,cm^{-3}$ , molar mass of the
substance will be
a.
$90.0\,g\,mol^{-1}$
b.
$115.0\,g\,mol^{-1}$
c.
$105.0\,g\,mol^{-1}$
d.
$210.0\,g\,mol^{-1}$
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The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences
represents the increasing order of the polarizinig order of the polarizing power of the cationic species,
$K^{+}, Ca^{2+}, Mg^{2+}, Be^{2+}$ ?
a.
$Mg^{2+}, Be^{2+}, K^{+}, Ca^{2+}$
b.
$Be^{2+}, K^{+}, Ca^{2+}, Mg^{2+}$
c.
$K^{+}, Ca^{2+}, Mg^{2+}, Be^{2+}$
d.
$Ca^{2+}, Mg^{2+}, Be^{2+}, K^{+}$
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Consider the reaction, $2A + B \rightarrow \rightarrow$ Products When concentration of $B$ alone was doubled, the half-life did not
change. When the concentration of $A$ alone was doubled, the rate increased by two times. The unit of rate
constant for this reaction is
a.
$L\,mol^{-1}\,s^{-1}$
b.
no unit
c.
$mol\,L^{-1}\,s^{-1}$
d.
$s^{-1}$
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Assuming that water vapour is an ideal gas, the internal energy $(\Delta U)$ when $1\,mol$ of water is vapourised at
$1\,bar$ pressure and $100^{\circ }C$ , (Given: Molar enthalpy of vapourization of water at $1\,bar$ and
$373\,K = 41\,kJ\,mol^{-1}$ and $R = 8.3\,J\,mol^{-1}\,K^{-1}$ ) will be
a.
$4.100\,kJ\,mol^{-1}$
b.
$3.7904\,kJ\,mol^{-1}$
c.
$37.904\,kJ\,mol^{-1}$
d.
$41.00\,kJ\,mol^{-1}$
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In a sautrated solution of the sparingly soluble strong electrolyte $AgIO_{3}$ (Molecular mass $= 283$ ) the
equilibrium which sets in is $AgIO_{3(s)} \rightleftharpoons Ag^{+}_{(aq)} + IO^{-}_{3(aq)}$ If the solubility product constant $K_{sp}$ of $AgIO_{3}$ at a
given temperature is $1.0 \times 10^{-8}$ , what is the mass of $AgIO_{3}$ contained in $100\,ml$ of its saturated solution?
a.
$28.3 \times 10^{-2}\,g$
b.
$2.83 \times 10^{-3}\,g$
c.
$1.0 \times 10^{-7}\,g$
d.
$1.0 \times 10^{-4}\,g$
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The energies of activation for forward and reverse reactions for $A_{2}+B_{2} \rightleftharpoons 2AB$ are $180\,kJ\,mol^{-1}$ and
$200\,kJ\,mol^{-1}$ respectively. The presence of catalyst lowers the activation energy of both (forward and reverse)
reactions by $100\,kJ\,mol^{-1}$ . The enthalpy change of the reaction $(A_{2}+ B_{2} \longrightarrow 2AB)$ in the presence of
catalyst will be (in $kJ\,mol^{-1}$ )
a.
$300$
b.
$120$
c.
$280$
d.
$20$
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The first and second dissociation constants of an acid $H_{2}A$ are $1.0 \times 10^{-5}$ and $5.0 \times 10^{-10}$ respectively. The
overall dissociation constant of the acid will be
a.
$5.0 \times 10^{-5}$
b.
$5.0 \times 10^{15}$
c.
$5.0 \times 10^{-15}$
d.
$0.0 \times 10^{5}$
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In conversion of lime-stone to lime, $CaCO_{3}(\,s)\longrightarrow CaO(s) + CO_{2}(\,g)$ the vales of $\Delta H^{\circ }$ and $\Delta S^{\circ }$ are
$+179.1\,kJ\,mol^{-1}$ and $160.2\,J/K$ respectively at $298\,K$ and $1\,bar$ . Assuming that $\Delta H^{\circ }$ do not change with
temperature, temperature above which conversion of limestone to lime will be spontaneous is
a.
$1008\,K$
b.
$1200$
c.
$845\,K$
d.
$1118\,K$
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The equivalent conductances of two strong electrolytes at infinite dilution in $H_{2}O$ (where ions move freely
through a solution) at $25^{\circ }C$ are given below: $\wedge ^{\circ }CH_{3}COONa = 91.0\,S\,cm^{2}$ /equiv $\wedge ^{\circ }_{HCl} = 426.2\,S\,cm^{2}$ /
equiv What additional information/quantity one needs to calculate $\wedge ^{\circ }$ of an aqueous solution of acetic acid?
a.
$\wedge ^{\circ }$ of $NaCl$
b.
$\wedge ^{\circ }$ of $CH_{3}COOK$
c.
The limiting equivalent conductance of
$H^{+} (\wedge ^{\circ }_{H^{+}})$
d.
$\wedge ^{\circ }$ of chloroacetic acid $(C/CH_{2}COOH)$
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A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of $290\,mm$ at $300\,K$ . The vapour pressure
of propyl alcohol is $200\,mm$ . If the mole fraction of ethyl alcohol is $0.6$ , its vapour pressure (in $mm$ ) at the
same temperature will be
a.
$350$
b.
$300$
c.
$700$
d.
$360$
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A radioactive element gets spilled over the floor of a room. Its half-life period is $30$ days. If the initial activity
is ten times the permissible value, after how many days will it be safe to enter the room?
a.
$1000$ days
b.
$300$ days
c.
$10$ days
d.
$100$ days
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The cell, $Zn Zn^{2+}(1M)\parallel Cu^{2+}(1M) Cu(E^{0}_{cell\,} = 1.10\,V)$ , was allowed to be completely discharged at $298\,K$ .
The relative concentration of $Zn^{2+}$ to $Cu^{2+} [\frac{[Zn^{2+}]}{[Cu^{2+}]} ]$ is
a.
antilog $(24.08)$
b.
$37.3$
c.
$10^{37.3}$
d.
$9.65 \times 10^{4}$
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The function $f :R\sim {0} \rightarrow \rightarrow R$ given by $f(x) = \frac{1}{x} - \frac{2}{e^{2}^{x}-1}$ can be made continuous at $x= 0$ by defining
$f(0)$ as
a.
$2$
b.
$-1$
c.
$0$
d.
$1$
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In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then
the common ratio of this progression equals
a.
$\frac{1}{2}(1 -)\sqrt{5}$
b.
$\frac{1}{2}\sqrt{5}$
c.
$\sqrt{5}$
d.
$\frac{1}{2}( -1)\sqrt{5}$
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The largest interval lying in $(-\frac{\pi}{2}, \frac{\pi}{2})$ for which the function $[f(x) = 4^{-x^{2}} + cos^{-1} ( \frac{x}{2} -1)+ log(cosx)]$ is
defined, is
a.
$[0,\pi ]$
b.
$(-\frac{\pi}{2}, \frac{\pi}{2})$
c.
$[-\frac{\pi}{4} , \frac{\pi}{2} )$
d.
$[0, \frac{\pi}{2})$
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Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are
$0.3$ and $0.2$ , respectively. The second plane will bomb only if the first misses the target. The probability that
the target is hit by the second plane is
a.
$0.06$
b.
$0.14$
c.
$0.2$
d.
None of these
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The normal to a curve at $P(x,y)$ meets the $x$ -axis at $G$ . If the distance of $G$ from the origin is twice the
abscissa of $P$ , then the curve is a
a.
ellipse
b.
parabola
c.
circle
d.
pair of straight lines
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Consider a family of circles which are passing through the point $(-1, 1)$ and are tangent to $x-$ axis. If $(h,k)$
are the co-ordinates of the centre of the circles, then the set of values of $k$ is given by the interval
a.
$0 < k < 1/2$
b.
$k\geq 1/2$
c.
$-1/2 \leq k\leq 1/2$
d.
$k\leq 1/2$
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The resultant of two forces $P\,N$ and $3\,N$ is a force of $7\,N$ . If the direction of $3\,N$ force were reversed, the
resultant would be $\sqrt{19}\,N$ . The value of $P$ is
a.
$5\,N$
b.
$6\,N$
c.
$3\,N$
d.
$4\,N$
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$-$
Let $-a = \hat{i}+ \hat{j}+ \hat{k}, b = \hat{i}- \hat{j}+ 2\hat{k}$ and $-c = x\hat{i}+ (x -2)\hat{j}- \hat{k}$ . If the vector $-c$ lies in the plane of $a-$ and $-b$ , then
$x$ equals
a.
$0$
b.
$1$
c.
$-4$
d.
$-2$
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Let $L$ be the line of intersection of the planes $2x+ 3y+z= 1$ and $x+ 3y+ 2z= 2$ . If $L$ makes an angles $\alpha$
with the positive $x$ -axis, then $cos\alpha$ equals
a.
$\frac{1}{\sqrt{3}}$
b.
$\frac{1}{2}$
c.
$1$
d.
$\frac{1}{\sqrt{2}}$
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If a line makes an angle of $\frac{\pi}{4}$ with the positive directions of each of $x$ -axis and $y$ -axis, then the angle that the
line makes with the positive direction of the $z-$ axis is
a.
$\frac{\pi}{6}$
b.
$\frac{\pi}{3}$
c.
$\frac{\pi}{4}$
d.
$\frac{\pi}{2}$
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A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that
$AB(=a)$ subtends an angle of $60^{\circ }$ at the foot of the tower, and the angle of elevation of the top of the tower
from $A$ or $B$ is $30^{\circ }$ . The height of the tower is
a.
$\frac{2a}{\sqrt{3}}$
b.
$2a\sqrt{3}$
c.
$\frac{a}{\sqrt{3}}$
d.
$a\sqrt{3}$
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If $(2, 3, 5)$ is one end of a diameter of the sphere $x^{2} +y^{2} +z^{2} -6x-12y-2z+ 20 = 0$ , then the
coordinates of the other end of the diameter are
a.
$(4, 9, -3)$
b.
$(4, -3, 3)$
c.
$(4, 3, 5)$
d.
$(4, 3, -3)$
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The equation of a tangent to the parabola $y^{2} = 8x$ is $y=x+ 2$ . The point on this line from which the other
tangent to the parabola is perpendicular to the given tangent is
a.
$(-1, 1)$
b.
$(0, 2)$
c.
$(2, 4)$
d.
$(-2, 0)$
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The average marks of boys in a class is $52$ and that of girls is $42$ . The average marks of boys and girls
combined is $50$ . The percentage of boys in the class is
a.
$40$
b.
$20$
c.
$80$
d.
$60$
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Let $A(h,k),B(1, 1)$ and $C(2, 1)$ be the vertices of a right angled triangle with $AC$ as its hypotenuse. If the
area of the triangle is $1$ , then the set of values which ' $k$ ' can take is given by
a.
${1, 3}$
b.
${0, 2}$
c.
${-1, 3}$
d.
${-3, -2}$
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The set $S = {1, 2, 3, … , 12)$ is to be partitioned into three sets $A,B,C$ of equal size. Thus,
$A\cup B\cup C =S,A\cap B=B\cap C =A\cap C =\phi$ . The number of ways to partition $S$ is
a.
$\frac{12!}{3!(4!)^{3}}$
b.
$\frac{12!}{3!(3!)^{4}}$
c.
$\frac{12!}{(4!)^{3}}$
d.
$\frac{12!}{(3!)^{4}}$
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