A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by
$\vec{E}= 2\hat{i}+ 3\hat{j}; \vec{B}= 4\hat{j}+ 6\hat{k}$
The charged particle is shifted from the origin to the point $P(x= 1;y= 1)$ along a straight path. The
magnitude of the total work done is :
a.
$(0.35)q$
b.
$5q$
Correct Answer
c.
(2.5) $q$
d.
$(0.15)q$
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Q2mcq
The region between $y= 0$ and $y= d$ contains a magnetic field $\vec{B}= B\hat{z}$ . A particle of mass $m$ and charge $q$
enters the region with a velocity $\vec{v}=v\hat{i}.$ if $d = \frac{mv}{2qB} ,$ the acceleration of the charged particle at the point of its
emergence at the other side is :
In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the
relation $VT = K,$ where $K$ is a constant. In this process the temperature of the gas is increased by $\Delta T$ . The
amount of heat absorbed by gas is (R is gas constant):
a.
$\frac{1}{2}R\Delta T$
Correct Answer
b.
$\frac{1}{2}KR\Delta T$
c.
$\frac{3}{2}R\Delta T$
d.
$\frac{2\,K}{3}\Delta T$
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Q4mcq
When $100\,g$ of a liquid $A$ at $100^{\circ }C$ is added to $50\,g$ of a liquid $B$ at temperature $75^{\circ }C$ , the temperature of the
mixture becomes $90^{\circ }C$ . The temperature of the mixture, if $100\,g$ of liquid $A$ at $100^{\circ }C$ is added to $50\,g$ of
liquid $B$ at $50^{\circ }C$ , will be:
a.
$85^{\circ }C$
b.
$60^{\circ }C$
c.
$80^{\circ }C$
Correct Answer
d.
$70^{\circ }C$
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Q5mcq
A metal ball of mass $0.1\,kg$ is heated upto $500^{\circ }C$ and dropped into a vessel of heat capacity $800JK^{-1}$ and
containing $0.5\,kg$ water. The initial temperature of water and vessel is $30^{\circ }C$ . What is the approximate
percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are,
respectively, $4200Jkg^{-1}\,K^{-1}$ and $400Jkg^{-1}\,K^{-1}$ ]
a.
$15%$
b.
$30%$
c.
$25%$
d.
$20%$
Correct Answer
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Q6mcq
A paramagnetic substance in the form of a cube with sides $1\,cm$ has a magnetic dipole moment of
$20 \times 10^{-6}\,J/T$ when a magnetic intensity of $60 \times 10^{3}\,A/m$ is applied. Its magnetic susceptibility is:
a.
$3.3 \times 10^{-2}$
b.
$4.3 \times 10^{-2}$
c.
$2.3 \times 10^{-2}$
d.
$3.3 \times 10^{-4}$
Correct Answer
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Q7mcq
A thermometer graduated according to a linear scale reads a value $x_{0}$ when in contact with boiling water, and
$x_{0}/3$ when in contact with ice. What is the temperature of an object in $^{\circ }C$ , if this thermometer in the contact
with the object reads $x_{0}/2?$
a.
25
Correct Answer
b.
60
c.
40
d.
35
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Q8mcq
In the circuit shown, the potential difference between $A$ and $B$ is
a.
$1\,V$
b.
$2\,V$
Correct Answer
c.
$3V$
d.
$6\,V$
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Q9mcq
The magnitude of torque on a particle of mass $1\,kg$ is 2.5 Nm about the origin. If the force acting on it is $1\,N,$
and the distance of the particle from the origin is $5\,m,$ the angle between the force and the position vector is (in
radians):
a.
$\frac{\pi}{6}$
Correct Answer
b.
$\frac{\pi}{3}$
c.
$\frac{\pi}{8}$
d.
$\frac{\pi}{4}$
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Q10mcq
A simple pendulum of length $1\,m$ is oscillating with an angular frequency $10rad/s$ . The support of the
pendulum starts oscillating up and down with a small angular frequency of $1rad/s$ and an amplitude of $10^{-2}\,m$
. The relative change in the angular frequency of the pendulum is best given by :
a.
$10^{-3}rad/s$
Correct Answer
b.
$1rad/s$
c.
$10^{-1}rad/s$
d.
$10^{-5}rad/s$
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A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_{1}$ . If the length of the
pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its
maximum kinetic energy is $K_{2}$
a.
$K_{2} = 2K_{1}$
b.
$K_{2} = \frac{K_{1}}{2}$
c.
$K_{2} = \frac{K_{1}}{4}$
d.
$K_{2} =K$
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A particle moves from the point $(2.0\hat{i}+ 4.0\hat{j})m,$ at $t = 0$ , with an initial velocity $(5.0\hat{i}+ 4.0\hat{j})ms .$ It is acted
upon by a constant force which produces a constant acceleration $(4.0\hat{i}+ 4.0\hat{j})ms^{-2}.$ What is the distance of the
particle from the origin at time $2\,s?$
a.
$15\,m$
b.
$20\sqrt{2}\,m$
c.
$5\,m$
d.
$10\sqrt{2}\,m$
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An electric field of $1000\,V/m$ is applied to an electric dipole at angle of $45^{\circ }$ . The value of electric dipole
moment is $10^{-29}C \cdot m.$ What is the potential energy of the electric dipole?
a.
$-20 \times 10^{-18}\,J$
b.
$-7 \times 10^{-27}\,J$
c.
$-10 \times 10^{-29}\,J$
d.
$-9 \times 10^{-20}\,J$
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In a double-slit experiment, green light $(5303\,A)$ falls on a double slit having a separation of $19.44\mu m$ and a
width of $4.05\mu m$ . The number of bright fringes between the first and the second diffraction minima is
a.
10
b.
5
c.
4
d.
9
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The mass and the diameter of a planet are three times the respective values for the Earth. The period of
oscillation of a simple pendulum on the Earth is $2\,s$ . The period of oscillation of the same pendulum on the
planet would be:
a.
$\frac{\sqrt{3}}{2}\,s$
b.
$\frac{2}{\sqrt{3}}\,s$
c.
$\frac{3}{2}s$
d.
$2\sqrt{3}$ s
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Seven capacitors, each of capacitance $2\mu F,$ are to be connected in a configuration to obtain an effective
capacitance of $( \frac{6}{13})\mu F.$ Which of the combinations, shown in figures below, will achieve the desired value?
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a string is wound around a hollow cylinder of mass $5\,kg$ and radius $0.5\,m$ . If the string is now pulled with a
horizontal force of $40\,N$ , and the cylinder is rolling without slipping on a horizontal surface (see figure), then
the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)
a.
$20rad/s^{2}$
b.
$16rad/s^{2}$
c.
$12rad/s^{2}$
d.
$10rad/s^{2}$
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Two rods $A$ and $B$ of identical dimensions are at temperature $30^{\circ }C$ . If $A$ is heated upto $180^{\circ }C$ and $B$ upto $T^{\circ }C,$
then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4 : 3,$ then
the value of $T$ is
a.
$230^{\circ }C$
b.
$270^{\circ }C$
c.
$200^{\circ }C$
d.
$250^{\circ }C$
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In a photoelectric experiment, the wavelength of the light incident on a metal is changed from $300nm$ to
$400nm$ . The decrease in the stopping potential is close to : $(\frac{hc}{e} = 1240nm -V)$
a.
$0.5\,V$
b.
$1.5\,V$
c.
$1.0\,V$
d.
$2.0\,V$
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A galvanometer having a resistance of $20\Omega$ and 30 division on both sides has figure of merit 0.005 ampere/
division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt,
is:
a.
$100\Omega$
b.
$120\Omega$
c.
$80\Omega$
d.
$125\Omega$
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A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum
deviation. If the refractive index of the material of the prism is $\sqrt{3}$ , then the angle of incidence is :
a.
$90^{\circ }$
b.
$30^{\circ }$
c.
$60^{\circ }$
d.
$45^{\circ }$
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A circular disc $D_{1}$ of mass $M$ and radius $R$ has two identical $discsD_{2}$ and $D_{3}$ of the same mass $M$ and radius
R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO',
passing through the centre of $D_{1}$ , as shown in the figure, will be
a.
$MR^{2}$
b.
$3MR^{2}$
c.
$\frac{4}{5}MR^{2}$
d.
$\frac{2}{3}MR^{2}$
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A particle of mass $m$ is moving in a straight line with momentum p. Starting at time $t= 0,$ a force $F =k$ t acts
in the same direction on the moving particle during time interval T so that its momentum changes from $p$ to $3p$ .
Here $k$ is a constant. The value of $T$ is
a.
$2\sqrt{\frac{k}{p}}$
b.
$2\sqrt{\frac{p}{k}}$
c.
$\sqrt{\frac{2k}{p}}$
d.
$\sqrt{\frac{2p}{k}}$
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In the experimental set up of metre bridge shown in the figure, the null point is obtaine data distance of $40\,cm$
from A. If a $10\Omega$ resistor is connected in series with $R_{1},$ the null point shifts by $10\,cm$ . The resistance that
should be connected in parallel with $(R_{1}+ 10)\Omega$ such that the null point shifts back to its initial position is
a.
$20\Omega$
b.
$40\Omega$
c.
$60\Omega$
d.
$30\Omega$
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A $27\,mW$ laser beam has a cross-sectional area of $10\,mm^{2}$ . The magnitude of the maximum electric field in
this electromagnetic wave is given by: [Given permittivity of space $\epsilon _{0} = 9 \times 10^{-12}SI$ units, Speed of light
$c = 3 \times 10^{8}\,m/s]$
a.
$2kV/m$
b.
$0.7kV/m$
c.
$1kV/m$
d.
$1.4kV/m$
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The circuit shown below contains two ideal diodes, each with a forward resistance of $50\Omega$ . If the battery
voltage is $6\,V,$ the current through the $100\Omega$ resistance (in Amperes) is:
a.
0.036
b.
0.02
c.
0.027
d.
0.03
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A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear
dimension of each side of the frame is increased by a factor of $3,$ keeping the number of turns of the coil per
unit length of the frame the same, then the self inductance of the coil:
a.
decreases by a factor of 9
b.
increases by a factor of 27
c.
increases by a factor of 3
d.
decreases by a factor of $9\sqrt{3}$
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In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted
radiation is $L$ . If an electron jumps from $N$ -shell to the $L$ -shell, the wavelength of emitted radiation will be:
a.
$\frac{27}{20} \lambda$
b.
$\frac{16}{25}\lambda$
c.
$\frac{25}{16} \lambda$
d.
$\frac{20}{27}\lambda$
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$25\,mL$ of the given $HCl$ solution requires $30\,mL$ of $0.1M$ sodium carbonate solution. What is the volume of
this $HCl$ solution required to titrate $30\,mL$ of $0.2M$ aqueous $NaOH$ solution?
a.
$25\,mL$
b.
$75\,mL$
c.
$50\,mL$
d.
$12.5\,mL$
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The standard reaction Gibbs energy for a chemical reaction at an absolute temperature $T$ is given by
$\Delta G^{\circ } = A -BT$ where A and $B$ are non-zero constants. Which of the following is true about this reaction?
a.
Exothermic if $B< 0$
b.
Endothermic if $A > 0$
c.
Endothermic if $A < 0$ and $B > 0$
d.
Exothermic if $A > 0$ and $B < 0$
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The reaction $2X \rightarrow B\rightarrow$ is a zeroth order reaction. If the initial concentration of $X$ is $0.2M$ , the half-life is $6\,h$ .
When the initial concentration of $X$ is $0.5M$ , the time required to reach its final concentration of $0.2M$ will be
a.
$9.0\,h$
b.
$12.0\,h$
c.
$18.0\,h$
d.
$7.2\,h$
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The reaction $MgO(s) + C(s) \rightarrow Mg(s) + CO(g),\rightarrow$ for which $\Delta H^{\circ } = +491.1\,kJ\,mol^{-1}$ and
$\Delta S^{\circ } = 198.0JK^{-1}\,mol^{-1}$ is not feasible at $298\,K$ . Temperature above which reaction will be feasible is
a.
$2040.5\,K$
b.
$1890.0\,K$
c.
$2480.3\,K$
d.
$2380.5\,K$
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Given the equilibrium constant: $K_{C}$ of the reaction: $Cu(s) + 2Ag^{+}(aq) Cu^{2+}(aq) + 2Ag(s)$ is $10 \times 10^{15}$
calculate the $E_{cell\,}^{0}$ of this reaction at $298\,K[2.303\frac{RT}{F}$ at $298\,K = 0.059\,\vec{V}]$
a.
$0.04736mV$
b.
$0.4736mV$
c.
$0.4736\,V$
d.
$0.04736\,V$
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The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is
: (Edge length is represented by 'a')
a.
0.027 a
b.
0.047 a
c.
$0.134a$
d.
0.067 a
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The de Broglie wavelength $(\lambda )$ associated with a photoelectron varies with the frequency $(v)$ of the incident
radiation as, $[v_{0}$ is threshold frequency]:
a.
$\lambda \propto \frac{1}{(v-v_{0})}$
b.
$\lambda \propto \frac{1}{1}$
$(v-v_{0}) 4$
c.
$\lambda \propto \frac{1}{3}$
$(v-v_{0}) 2$
d.
$\lambda \propto \frac{1}{1}$
$(v-v_{0}) 2$
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If the area of the triangle whose one vertex is at the vertex of the parabola, $y^{2} + 4(x- a^{2})= 0$ and the other
two vertices are the points of intersection of the parabola and $y$ -axis, is 250 sq. units, then a value of 'a' is :
a.
$5\sqrt{5}$
b.
$5(2^{1/3})$
c.
$(10)^{33}$
d.
5
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If the point $(2,\alpha ,\beta )$ lies on the plane which passes through the points (3,4,2) and (7,0,6) and is perpendicular
to the plane $2x-5y= 15,$ then $2\alpha -3\beta$ is equal to :
a.
12
b.
7
c.
5
d.
17
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Let $K$ be the set of all real values of $x$ where the function $f(x) = sin |x| -|x| + 2(x- \pi ) cos |x|$ is not
differentiable. Then the set $K$ is equal to :
a.
$\phi$ (an empty set)
b.
$(\pi }$
c.
${0}$
d.
${0,\pi }$
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A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with
replacement. If $X$ be the number of white balls drawn, then $( \frac{\,mean of\,X}{\,standard deviation of\,X})$ is equal to:
a.
4
b.
$4\sqrt{3}$
c.
$3\sqrt{2}$
d.
$\frac{4\sqrt{3}}{3}$
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Let $A$ and $B$ be two invertible matrices of order $3 \times 3$ . If $det(ABA^{T})= 8$ and det $(AB^{-1})= 8$ , then det
$(BA^{-1}\,B^{T})$ is equal to
a.
$\frac{1}{4}$
b.
1
c.
$\frac{1}{16}$
d.
16
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Two lines $\frac{x-3}{1} = \frac{y+1}{3} = \frac{z-6}{-1}$ and $\frac{x+5}{7} = \frac{y-2}{-6} = \frac{z-3}{4}$ intersect at the point $R$ . The reflection of $R$ in the $xy$ -
plane has coordinates:
a.
(2,-4,-7)
b.
(2,4,7)
c.
(2,-4,7)
d.
(-2,4,7)
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The number of functions $f$ from ${1, 2, 3, … , 20}$ onto ${1, 2, 3, … , 20}$ such that $f(k)$ is a multiple of $3,$
whenever $k$ is a multiple of 4 is:
a.
$6^{5} \times (15)!$
b.
$5! \times 6!$
c.
$(15)! \times 6!$
d.
$5^{6} \times 15$
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If in a parallelogram $ABDC$ , the coordinates of $A, B$ and $C$ are respectively (1,2),(3,4) and $(2, 5),$ then the
equation of the diagonal $AD$ is :
a.
$5x-3y+ 1 = 0$
b.
$5x+ 3y-11 = 0$
c.
$3x-5y+ 7 = 0$
d.
$3x+ 5y-13 = 0$
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Let $f(x) = \frac{x}{\sqrt{a^{2}+x^{2}}} - \frac{d-x}{\sqrt{b^{2}+(d-x)^{2}}} x\in R$ wherea, b and d are non-zero real constants. Then :
$,$
a.
$f$ is an increasing function of $x$
b.
$f$ is a decreasing function of $x$
c.
$f'$ is not a continuous function of $x$
d.
$f$ is neither increasing nor decreasing function of
$x$
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The area (in sq. units) in the first quadrant bounded by the parabola, $y=x^{2} + 1$ , the tangent to it at the point
(2,5) and the coordinate axes is :
a.
$\frac{8}{3}$
b.
$\frac{37}{24}$
c.
$\frac{187}{24}$
d.
$\frac{14}{3}$
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Let $S_{n} = 1 +q+q^{2} + … . +q^{n}$ and $T_{n} = 1 +(\frac{q+1}{2} )+( \frac{q+1}{2})^{2} + … +(\frac{q+1}{2})^{n}$ where $q$ is a real number
and $q\neq 1$ . If $^{101}C_{1}+^{101}C_{2}\cdot S_{1}+ … . +^{101}C_{101}\cdot S_{100} =\alpha T_{100},$ then $\alpha$ is equal to :
a.
$2^{99}$
b.
202
c.
200
d.
$2^{100}$
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Let $\sqrt{3}\hat{i}+ \hat{j}, \hat{i}+ \sqrt{3}\hat{j}$ and $\beta \hat{i}+ (1 - \beta )\hat{j}$ respectively be the position vectors of the points $A, B$ and $C$ with
respect to the origin $O$ . If the distance of $C$ from the bisector of the acute angle between $OA$ and $OB$ is $\frac{3}{\sqrt{2}},$
then the sum of all possible values of $\beta$ is:
a.
4
b.
3
c.
2
d.
1
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Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^{2} sin\theta - x(sin\theta cos\theta + 1) + cos\theta = 0 (0 <\theta < 45^{\circ }),$ and
$\alpha <\beta .$ Then $\sum ^{\infty }_{n=0} (\alpha ^{n}+ \frac{(-1)^{n}}{\beta ^{n}} )$ is equal to :
a.
$\frac{1}{1-cos\theta} - \frac{1}{1+sin\theta}$
b.
$\frac{1}{1+cos\theta} + \frac{1}{1-sin\theta}$
c.
$\frac{1}{1-cos\theta} + \frac{1}{1+sin\theta}$
d.
$\frac{1}{1+cos\theta} - \frac{1}{1-sin\theta}$
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Let $S = {1, 2, … . . , 20}$ . A subset $B$ of $S$ is said to be "nice", if the sum of the elements of $B$ is 203 . Than the
probability that a randomly chosen subset of $S$ is "nice" is :
a.
$\frac{7}{2^{20}}$
b.
$\frac{5}{2^{20}}$
c.
$\frac{4}{2^{20}}$
d.
None of the above
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Given $\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$ for a $\Delta ABC$ with usual notation. If $\frac{cos A}{\alpha} = \frac{cos B}{\beta} = \frac{cos C}{\gamma},$ then the ordered triad
$(\alpha ,\beta ,\gamma )$ has a value
a.
(7,19,25)
b.
(3,4,5)
c.
(5,12,13)
d.
(19,7,25)
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A circle cuts a chord of length 4 a on the $x$ -axis and passes through a point on the $y$ -axis, distant $2\,b$ from the
origin. Then the locus of the centre of this circle, is:
a.
a hyperbola
b.
an ellipse
c.
a straight line
d.
a parabola
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Let the length of the latus rectum of an ellipse with its major axis along $x$ -axis and centre at the origin, be 8 .
If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the
following points lies on it?
a.
$(4, 2)\sqrt{2} \sqrt{2}$
b.
$(4, 2)\sqrt{3} \sqrt{2}$
c.
$(4, 2)\sqrt{3} \sqrt{3}$
d.
$(4, 2)\sqrt{2} \sqrt{3}$
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