The resistance of a wire is $R$ . It is bent at the middle by $180^{\circ }$ and both the ends are twisted together to make a
shorter wire. The resistance of the new wire is
a.
$2R$
b.
$R/2$
c.
$R/4$
Correct Answer
d.
$R/8$
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Q2mcq
This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement 1: It is not possible to make a sphere of capacity 1 farad
using a conducting material. Statement 2: It is possible for earth as its radius is $6.4 \times 10^{6}\,m$ .
a.
Statement 1 is true, Statement 2 is true,
Statement 2 is the correct explanation of
Statement 1.
b.
Statement 1 is false, Statement 2 is true.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation of
Statement 1.
d.
Statement 1 is true, Statement 2 is false.
Correct Answer
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Q3mcq
A telescope of aperture $3 \times 10^{-2}\,m$ diameter is focused on a window at $80\,m$ distance fitted with a wire mesh
of spacing $2 \times 10^{-3}\,m$ . Given: $\lambda = 5.5 \times 10^{-7}\,m$ , which of the following is true for observing the mesh
through the telescope?
a.
Yes, it is possible with the same aperture size.
Correct Answer
b.
Possible also with an aperture half the present
diameter.
c.
No, it is not possible.
d.
Given data is not sufficient.
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Q4mcq
Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires $A$ and $B$ respectively in
opposite directions. Wire $A$ is infinitely long and the length of the wire $B$ is $2\,m$ . The force acting on the
conductor $B$ , which is situated at $10\,cm$ distance from $A$ will be
a.
$8 \times 10^{-5}\,N$
Correct Answer
b.
$5 \times 10^{-5}\,N$
c.
$8\pi \times 10^{-7}\,N$
d.
$4\pi \times 10^{-7}\,N$
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Q5mcq
Photoelectrons are ejected from a metal when light of frequency $v$ falls on it. Pick out the wrong statement
from the following.
(1) No electrons are emitted if $v$ is less than $W/h$ , (2) The ejection of the photoelectrons is
where $W$ is the work function of the metal instantaneous.
(3) The maximum energy of the photoelectrons is hu.(4) The maximum energy of the photoelectrons is
independent of the intensity of the light.
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Q6mcq
The counting rate observed from a radioactive source at $t= 0$ was 1600 counts $s^{-1}$ , and $t= 8\,s$ , it was 100
counts $s^{-1}$ . The counting rate observed as counts $s^{-1}$ at $t= 6\,s$ will be
a.
250
b.
400
c.
300
d.
200
Correct Answer
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Q7mcq
A thick-walled hollow sphere has outside radius $R_{0}$ . It rolls down an incline without slipping and its speed at
the bottom is $v_{0}$ . Now the incline is waxed, so that it is practically frictionless and the sphere is observed to
slide down (without any rolling). Its speed at the bottom is observed to be $5v_{0}/4$ . The radius of gyration of the
hollow sphere about an axis through its centre is
a.
$3R_{0}/2$
b.
$3R_{0}/4$
Correct Answer
c.
$9R_{0}/16$
d.
$3R_{0}$
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Q8mcq
The terminal velocity of a small sphere of radius $a$ in a viscous liquid is proportional to
a.
$a^{2}$
Correct Answer
b.
$a^{3}$
c.
$a$
d.
$a^{-1}$
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Q9mcq
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement 1: A charged particle is moving at right angle to a static
magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static
magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field.
a.
Statement 1 is false, Statement 2 is true.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation of
Statement 1.
c.
Statement 1 is true, Statement 2 is false.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is the correct explanation of
Statement 1.
Correct Answer
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Q10mcq
A radio transmitter transmits at $830kHz$ . At a certain distance from the transmitter magnetic field has
amplitude $4.82 \times 10^{-11}\,T$ . The electric field and the wavelength are respectively
a.
$0.014\,N/C, 36\,m$
b.
$0.14\,N/C, 36\,m$
c.
$0.14\,N/C, 360\,m$
d.
$0.014\,N/C, 360\,m$
Correct Answer
No explanation saved for this question yet.
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A satellite moving with velocity $v$ in a force free space collects stationary interplanetary dust at a rate of
$\frac{dM}{dt} =\alpha v$ where $M$ is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite
is
a.
$- \frac{\alpha v^{2}}{2M}$
b.
$- \frac{\alpha v^{2}}{M}$
c.
$-\alpha v^{2}$
d.
$- \frac{2\alpha v^{2}}{M}$
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In a cylindrical water tank, there are two small holes $A$ and $B$ on the wall at a depth of $h_{1}$ , from the surface of
water and at a height of $h_{2}$ from the bottom of water tank. Surface of water is at height of $h_{2}$ from the bottom
of water tank. Surface of water is at heigh $H$ from the bottom of water tank. Water coming out from both holes
strikes the ground at the same point $S$ . Find the ratio of $h_{1}$ and $h_{2}$
a.
Depends on $H$
b.
$1 : 1$
c.
$2 : 2$
d.
$1 : 2$
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The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R=_{a}$ where ' $\rho$ '
is the electrical resistivity. What is the dimensional formula for electrical conductivity ' $\sigma$ ' which is reciprocal
of resistivity?
a.
$[M^{-1}L^{-3}T^{3}A^{2}]$
b.
$[ML^{-3}T^{-3}A^{2}]$
c.
$[ML^{3}T^{-3}A^{-2}]$
d.
$[M^{-2}L^{3}T^{2}A^{-1}]$
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A ball is dropped vertically downwards from a height $h$ above the ground. It hits the ground inelastically and
bounces up vertically. Neglecting subsequent motion and air resistance, which of the following graph represents
variation between speed $(v)$ and height $(h)$ correctly?
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An air column in a pipe, which is closed at one end, will be in resonance wtih a vibrating tuning fork of
frequency $264\,Hz$ if the length of the column in $cm$ is (velocity of sound $= 330\,m/s$ )
a.
$125.00$
b.
$93.75$
c.
$62.50$
d.
$187.50$
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In Young's double slit interference experiment, the slit widths are in the ratio $1 : 25$ . Then the ratio of intensity
at the maxima and minima in the interference pattern is
a.
$3 : 2$
b.
$1 : 25$
c.
$9 : 4$
d.
$1 : 5$
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A point particle is held on the axis of a ring of mass $m$ and radius $r$ at a distance $r$ from its centre $C$ . When
released, it reaches $C$ under the gravitational attraction of the ring. Its speed at $C$ will be
a.
$\sqrt{\frac{2Gm}{r}}( -1\sqrt{2}$
b.
$\sqrt{\frac{Gm}{r}}$
c.
$\sqrt{\frac{2Gm}{r}}(1 - \frac{1}{\sqrt{2}})$
d.
$\sqrt{\frac{2Gm}{r}}$
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In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length $\ell$ is
obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance
$R$ . If $R$ is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will
be
a.
$\ell$
b.
$2\ell$
c.
$\ell /2$
d.
$\ell /4$
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A stone of mass $m$ , tied to the end of a string, is whirled around in a circle on a horizontal frictionless table. The
length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the
circle constant. Then, the tension in the string is given by $T =Ar^{n}$ , where $A$ is a constant, $r$ is the
instantaneous radius of the circle. The value of $n$ is equal to
a.
$-1$
b.
$-2$
c.
$-4$
d.
$-3$
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The force $\vec{F} =F\hat{i}$ on a particle of mass $2\,kg$ , moving along the $x$ -axis is given in the figure as a function of its
position $x$ . The particle is moving with a velocity of $5\,m/s$ along the $x$ -axis at $x= 0$ . What is the kinetic energy
of the particle at $x= 8\,m?$
a.
$34\,J$
b.
$34.5\,J$
c.
$4.5\,J$
d.
$29.4\,J$
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The disturbance $y(x,t)$ of a wave propagating in the positive $x$ -direction is given by $y= \frac{1}{1+x^{2}}$ at time $t= 0$
and by $y= \frac{1}{[1+(x-1^{2})]}$ at $t= 2\,s$ , where $x$ and $y$ are in meters. The shape of the wave disturbance does not
change during the propagation. The velocity of wave in $m/s$ is
a.
$2.0$
b.
$4.0$
c.
$0.5$
d.
$1.0$
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This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement 1: If you push on a cart being pulled by a horse so that it does
not move, the cart pushes you back with an equal and opposite force. Statement 2: The cart does not move
because the force described in statement 1 cancel each other.
a.
Statement 1 is true, Statement 2 is true, Statement
2 is the correct explanation of Statement 1.
b.
Statement 1 is false, Statement 2 is true.
c.
Statement 1 is true, Statement 2 is false.
d.
Statement 1 is true, Statement 2 is true, Statement
2 is not the correct explanation of Statement 1.
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The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the
resonance frequency of the circuit is $10kHz$ . When the container is filled with a gas, the resonance frequency
changes by $50\,Hz$ . The dielectric constant of the gas is
a.
$1.001$
b.
$2.001$
c.
$1.01$
d.
$3.01$
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An ideal monatomic gas with pressure $P$ , volume $V$ and temperature $T$ is expanded isothermally to a volume
$2V$ and a final pressure $P_{i}$ . If the same gas is expanded adiabatically to a volume $2\,V$ , the final pressure is $P_{a}$ .
The ratio $\frac{P_{a}}{P_{i}}$ is
a.
$2^{-1/3}$
b.
$2^{1/3^{6}}$
c.
$2^{2/3}$
d.
$2^{-2/3}$
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A beam of light consisting of red, green and blue colours is incident on a right-angled prism on face $AB$ . The
refractive indices of the material for the above red, green and blue colours are $1.39, 1.44$ and $1.47$ respectively.
A person looking on surface $AC$ of the prism will see
a.
no light
b.
green and blue colours
c.
red and green colours
d.
red colour only
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A transition metal $M$ forms a volatile chloride which has a vapour density of $94.8$ . If it contains $74.75%$ of
chlorine the formula of the metal chloride will be
a.
$MCl_{3}$
b.
$MCl_{2}$
c.
$MCl_{4}$
d.
$MCl_{5}$
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One mole of an ideal gas is expanded isothermally and reversibly to half of its initial pressure. $\Delta S$ for the
process in $JK^{-1}\,mol^{-1}$ is $[ln 2 = 0.693$ and $R= 8.314, \,J/(molK)]$
a.
$6.76$
b.
$5.76$
c.
$10.76$
d.
$8.03$
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The following sets of quantum numbers represent four electrons in an atom. (i) $n= 4,l= 1$ (ii) $n= 4,l= 0$
(iii) $n= 3,l= 2$ (iv) $n= 3,l= 1$ The sequence representing increasing order of energy, is
a.
(iii) < (i) < (iv) < (ii)
b.
(iv) < (ii) < (iii) < (i)
c.
(i) < (iii) < (ii) < (iv)
d.
(ii) < (iv) < (i) < (iii)
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The solubility of $PbI_{2}$ at $25^{\circ }C$ is $0.7\,g\,L^{-1}$ . The solubility product of $PbI_{2}$ at this temperature is (molar mass
of $PbI_{2} = 461.2\,g\,mol^{-1}$ )
a.
$1.40 \times 10^{-9}$
b.
$0.14 \times 10^{-9}$
c.
$140 \times 10^{-9}$
d.
$14.0 \times 10^{-9}$
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One mole of $O_{2(\,g)}$ and two moles of $SO_{2(\,g)}$ were heated in a closed vessel of one-litre capacity at $1098\,K$ . At
equilibrium $1.6$ moles of $SO_{3(\,g)}$ were found. The equilibrium constant $K_{c}$ of the reaction would be
a.
30
b.
40
c.
80
d.
60
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The freezing point of a $1.00\,m$ aqueous solution of $HF$ is found to be $-1.91^{\circ }C$ . The freezing point constant of
water, $K_{f}$ is $1.86\,K\,kg\,mol^{-1}$ . The percentage dissociation of $HF$ at this concentration is
a.
$30%$
b.
$10%$
c.
$5.2%$
d.
$2.7%$
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The chord $PQ$ of the parabola $y^{2} =x$ , where one end $P$ of the chord is at point $(4, -2)$ , is perpendicular to the
axis of the parabola. Then the slope of the normal at $Q$ is
a.
$-4$
b.
$- \frac{1}{4}$
c.
4
d.
$\frac{1}{4}$
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Statement 1: If the system of equations $x+ky+ 3z= 0, 3x+ky-2z= 0, 2x+ 3y-4z= 0$ has a nontrivial
solution, then the value of $k$ is $\frac{31}{2}$ . Statement 2: A system of three homogeneous equations in three variables
has a non trivial solution if the determinant of the coefficient matrix is zero.
a.
Statement 1 is false, Statement 2 is true.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation for
Statement 1.
c.
Statement 1 is true, Statement 2 is true,,
Statement 2 is not a correct explanation for
Statement 1.
d.
Statement 1 is true, Statement 2 is false.
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If a metallic circular plate of radius $50\,cm$ is heated so that its radius increases at the rate of $1\,mm$ per hour,
then the rate at which, the area of the plate increases (in $cm^{2}/$ hour) is
a.
$5\pi$
b.
$10\pi$
c.
$100\pi$
d.
$50\pi$
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Statement 1: The variance of first $n$ odd natural numbers is $\frac{n^{2}-1}{3}$ Statement 2: The sum of first $n$ odd natural
number is $n^{2}$ and the sum of square of first $n$ odd natural numbers is $\frac{n(4n^{2}+1)}{3}$ .
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is true, Statement 2 is true;
Statement 2 is not a correct explanation for
Statement 1.
c.
Statement 1 is false, Statement 2 is true.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation for
Statement 1.
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If the sum of the series $1^{2} + 2 \cdot 2^{2} + 3^{2} + 2 \cdot 4^{2} + 5^{2}+$ ... $2.6^{2} + …$ upto $n$ terms, when $n$ is even, is $\frac{n(n+1)^{2}}{2}$ ,
then the sum of the series, when $n$ is odd, is
a.
$n^{2}(n+ 1)$
b.
$\frac{n^{2}(n-1)}{2}$
c.
$\frac{n^{2}(n+1)}{2}$
d.
$n^{2}(n-1)$
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Let $f : (-\infty , \infty ) \rightarrow (-\infty , \infty )\rightarrow$ be defined by $f(x) =x^{3} + 1$ Statement 1: The function fhas a local extremum
at $x= 0$ Statement 2: The function $f$ is continuous and differentiable on $(-\infty , \infty )$ and $f'(0) = 0$
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation for
Statement 1.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation for
Statement 1.
d.
Statement 1 is false, Statement 2 is true.
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The line parallel to $x$ -axis and passing through the point of intersection of lines $ax+ 2by+ 3b= 0$ and
$bx-2ay-3a= 0$ , where $(a,b) \neq (0, 0)$ is
a.
above $x$ -axis at a distance $2/3$ from it
b.
above $x$ -axis at a distance $3/2$ from it
c.
below $x$ -axis at a distance $3/2$ from it
d.
below $x$ -axis at a distance $2/3$ from it
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Statement 1: The vectors $\vec{a}, \vec{b}$ and $\vec{c}$ lie in the same plane if and only if $\vec{a}\cdot (\vec{b}\times \vec{c}) = 0$ Statement 2: The vectors
$\vec{u}$ and $\vec{v}$ are perpendicular if and only if $\vec{u}\cdot \vec{v}= 0$ where $\vec{u}\times \vec{v}$ is a vector perpendicular to the plane of $\vec{u}$ and $\vec{v}$
a.
Statement 1 is false, Statement 2 is true.
b.
Statement 1 is true, Statement 2 is true,
Statement 2 is correct explanation for Statement
1.
c.
Statement 1 is true, Statement 2 is false.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation for
Statement 1.
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Let $A$ and $B$ be non empty sets in $R$ and $f :A\rightarrow \rightarrow B$ is a bijective function. Statement 1: $f$ is an onto function.
Statement 2: There exists a function $g:B\rightarrow \rightarrow A$ such that fog $=I_{B}$ .
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is true, Statement 2 is true;
Statement 2 is a correct explanation for
Statement 1.
c.
Statement 1 is false, Statement 2 is true.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation for
Statement 1.
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There are two balls in an urn. Each ball can be either white or black. If a white ball is put into the urn and there
after a ball is drawn at random from the urn, then the probability that it is white is
a.
$\frac{1}{4}$
b.
$\frac{2}{3}$
c.
$\frac{1}{5}$
d.
$\frac{1}{3}$
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If seven women and seven men are to be seated around a circular table such that there is a man on either side
of every woman, then the number of seating arrangements is
a.
$6!7!$
b.
$(6!)^{2}$
c.
$(7!)^{2}$
d.
7 !
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Let $p$ and $q$ denote the following statements $p$ : The sun is shining $q$ : I shall play tennis in the afternoon The
negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is
a.
$q\Rightarrow \sim p$
b.
$q\wedge \sim p$
c.
$p\wedge \sim q$
d.
$\sim q\Rightarrow \sim p$
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The distance of the point $-\hat{i}+ 2\hat{j}+ 6\hat{k}$ from the straight line that passes through the point $2\hat{i}+ 3\hat{j}-4\hat{k}$ and is
parallel to the vector $6\hat{i}+ 3\hat{j}-4\hat{k}$ is
a.
9
b.
8
c.
7
d.
10
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If the A.M. between $p^{th\,}$ and $q^{th\,}$ terms of an A.P. is equal to the A.M. between $r^{th\,}$ and $s^{th\,}$ terms of the same
A.P., then $p+q$ is equal to
a.
$r+s-1$
b.
$r+s-2$
c.
$r+s+ 1$
d.
$r+s$
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