A pendulum with the time period of $1\,s$ is losing energy due to damping. At a certain time, its energy is $45\,J$ . If
after completing $15$ oscillations its energy has become $15\,J$ , then its damping constant (in $s^{-1}$ ) will be
a.
$\frac{1}{2}$
b.
$\frac{1}{15} ln 3$
c.
$\frac{1}{30}ln 3$
Correct Answer
d.
$2$
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Q2mcq
A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal
rod of length $L(L\gg r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see
figure). If one of the beads is now given a speed $v$ , the average force experienced by each support after a long
time is (assume all collisions are elastic):
a.
$\frac{mv^{2}}{L-nr}$
b.
$\frac{mv^{2}}{L-2nr}$
Correct Answer
c.
$\frac{mv^{2}}{2(L-nr)}$
d.
$Zero$
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Q3mcq
From the top of a $64$ metres high tower, a stone is thrown upwards vertically with the velocity of $48\,m/s.$ The
greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration
$g= 32\,m/s^{2}$ , is:
a.
$112$
b.
$88$
c.
$128$
d.
$100$
Correct Answer
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Q4mcq
A wire carrying current $I$ is tied between points $P$ and $Q$ and is in the shape of a circular arc of radius $R$ due to
a uniform magnetic field $B$ (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of
the wire. If the wire subtends an angle $2\theta _{o}$ at the center of the circle (of which it forms an arch) then the
tension in the wire is:
a.
$IBR$
Correct Answer
b.
$\frac{IBR}{sin\theta _{0}}$
c.
$\frac{IBR}{2sin\theta _{0}}$
d.
$\frac{IBR\theta _{0}}{sin\theta _{0}}$
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Q5mcq
A particle is moving in a circle of radius $r$ under the action of a force $F =\alpha r^{2}$ which is directed towards centre
of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy
$= 0$ for $r= 0$ ):
a.
$\frac{5}{6} \alpha r^{3}$
Correct Answer
b.
$\alpha r^{3}$
c.
$\frac{1}{2} \alpha r^{3}$
d.
$\frac{4}{3} \alpha r^{3}$
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Q6mcq
A cylindrical block of wood (density = $650\, kg \,m^{-3}$ ), of base area $30\, cm^{2}$ and height $54\, cm$ , floats in a liquid
of density $900\, kg \,m^{-3}$ . The block is depressed slightly and then released. The time period of the resulting
oscillations of the block would be equal to that of a simple pendulum of length (nearly) :
a.
$52\, cm$
b.
$26\, cm$
c.
$39\, cm$
Correct Answer
d.
$65\, cm$
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Q7mcq
In a Young's double slit experiment with light of wavelength $\lambda$ $,$ the separation of slits is $d$ and distance of
screen is $D$ such that $D\gg d\gg \lambda$ . If the Fringe width is $\beta$ , the distance from point of maximum intensity to
the point where intensity falls to half of the maximum intensity on either side is:
a.
$\frac{\beta}{4}$
Correct Answer
b.
$\frac{\beta}{3}$
c.
$\frac{\beta}{6}$
d.
$\frac{\beta}{2}$
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Q8mcq
An electric field $\vec{E} =(25\,ˆi + 30\,ˆj)\,N\,C^{-1}$ exists in a region of space. If the potential at the origin is taken to
be zero then the potential at $x= 2\,m$ , $y= 2\,m$ is:
a.
$-110\,J\,C^{-1}$
Correct Answer
b.
$-140\,J\,C^{-1}$
c.
$-130\,J\,C^{-1}$
d.
$-120\,J\,C^{-1}$
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Q9mcq
A particle of mass $2\, kg$ is on a smooth horizontal table and moves in a circular path of radius $0. 6\,m$ . The height
of the table from the ground is $0. 8\,m$ . If the angular speed of the particle is $12\, rad \,s^{-1}$ , the magnitude of its
angular momentum about a point on the ground right under the center of the circle is:
a.
$14 .4 \, kg \,m^{2}\,s^{-1}$
Correct Answer
b.
$11.52\, kg \,m^{2}\,s^{-1}$
c.
$20.16\, kg \,m^{2}\,s^{-1}$
d.
$8.64\, kg \,m^{2}\,s^{-1}$
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Q10mcq
A source of sound emits sound waves at frequency $f_{0}$ . It is moving towards an observer with fixed speed
$v_{s}\,(v_{s} < v)$ , where $v$ is the speed of sound in air). If the observer were to move towards the source with speed
$v_{0}$ , one of the following two graphs (A and B) will give the correct variation of the frequency $f$ heard by the
observer as $v_{0}$ is changed.
The variation of $f$ with $v_{0}$ is given correctly by:
a.
Graph A with slope $= \frac{f_{0}}{(v-v_{s})}$
Correct Answer
b.
Graph A with slope $= \frac{f_{0}}{(v+v_{s})}$
c.
Graph B with slope $= \frac{f_{0}}{(v-v_{s})}$
d.
Graph B with slope $= \frac{f_{0}}{(v+v_{s})}$
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A beaker contains a fluid of density $\rho \frac{kg}{m^{3}}$ , specific heat $S\frac{J}{kg^{o}C}$ and viscosity $\eta$ . The beaker is filled up to height
h. To estimate the rate of heat transfer per unit area $(\frac{Q\dot}{A})$ by convection when beaker is put on a hot plate, a
student proposes that it should depend on $\eta$ , $(\frac{S\Delta \theta}{h})$ and $(\frac{1}{\rho g})$ when $\Delta \theta$ ( $in^{o}C$ ) is the difference in the
temperature between the bottom and top of the fluid. In that situation the correct option for $(\frac{Q\dot}{A} )$ is:
Two long straight parallel wires, carrying (adjustable) currents $I_{1}$ and $I_{2}$ , are kept at a distance $d$ apart. If the
force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the
wires attract each other, the graph showing the dependence of $F$ , on the product $I_{1}I_{2}$ , would be:
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A wire of length $L= 20\,cm$ is bent into a semi-circular arc and the two equal halves of the arc are uniformly
charged with charges $+Q$ and $-Q$ as shown in the figure. The magnitude of the charge on each half is
$|Q| = 10^{3}\epsilon _{0}$ , where $\epsilon _{0}$ is the permittivity of free the space. The net electric field at the centre $O$ is
a.
$(25 \times 10^{3})ˆi\,N\,C^{-1}$
b.
$(50 \times 10^{3})ˆi\,N\,C^{-1}$
c.
$(25 \times 10^{3})ˆj\,N\,C^{-1}$
d.
$(50 \times 10^{3})ˆj\,N\,C^{-1}$
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A vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radians $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$ . In that case $\vec{B}- \vec{A}$ is :
a.
$\vec{A} [1 - \frac{(\Delta \theta )^{2}}{2} ]$
b.
$0$
c.
$\vec{A} \Delta \theta$
d.
$\vec{B} \Delta \theta - \vec{A}$
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For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor $C'$
, when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The
capacitor $C'$ , must have been connected in:
a.
Parallel with C and has a magnitude $\frac{1-\omega ^{2}LC}{\omega ^{2}L}$
b.
Series with C and has a magnitude $\frac{1-\omega ^{2}LC}{\omega ^{2}L}$
c.
Series with C and has a magnitude $\frac{C}{(\omega ^{2}LC-1)}$
d.
Parallel with C and has a magnitude $\frac{C}{(\omega ^{2}LC-1)}$
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Let $N_{\beta }$ be the number of $\beta$ particle emitted by $1\, gram$ of $Na^{24}$ radioactive nuclei having a half life of $15\,h$ . In
$7. 5\,h$ , the number $N_{\beta }$ is close to $[N_{A} = 6 .023 \times 10^{23}\, mole^{-1}]$
a.
$1.75 \times 10^{22}$
b.
$6.2 \times 10^{21}$
c.
$7.5 \times 10^{21}$
d.
$1.25 \times 10^{22}$
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A uniform thin rod AB of length $L$ has linear mass density $\mu (x) =a+ \frac{bx}{L}$ , where $x$ is measured from A. If the
CM of the rod lies at a distance of $(\frac{7}{12}L)$ from A, then $a$ and $b$ are related as:
a.
$2a=b$
b.
$a= 2b$
c.
$a=b$
d.
$3a= 2b$
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If electronic charge $e$ , electron mass $m$ , speed of light in vacuum $c$ and Planck's constant $h$ are taken as
fundamental quantities, the permeability of vacuum $\mu _{0}$ can be expressed in units of:
a.
$(\frac{mc^{2}}{he^{2}})$
b.
$(\frac{h}{me^{2}})$
c.
$(\frac{hc}{me^{2}})$
d.
$(\frac{h}{ce^{2}})$
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For plane electromagnetic waves propagating in the $+z$ -direction, which one of the following combinations
gives the correct possible direction for $\vec{E}$ and $\vec{B}$ field respectively?
a.
$(ˆi + 2ˆj)$ and $(2ˆi -j)$
b.
$(-2ˆi -3ˆj)$ and $(3ˆi -2ˆj)$
c.
$(2ˆi + 3ˆj)$ and $(ˆi + 2ˆj)$
d.
$(3ˆi + 4ˆj)$ and $(4ˆi -3ˆj)$
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An experiment takes $10\, min$ to raise the temperature of water in a container from $0^{o}C$ to $100^{o}C$ and another
$55\, min$ to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific
heat of the container and taking specific heat of the water to be $1\, cal \,(g^{\circ }C)^{-1}$ , the heat of vaporization
according to this experiment will come out to be:
a.
$530\, cal \,g^{-1}$
b.
$550\, cal \,g^{-1}$
c.
$540\, cal \,g^{-1}$
d.
$560\, cal \,g^{-1}$
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A thin convex lens of focal length $f$ is put on a plane mirror as shown in the figure. When an object is kept at a
distance $a$ from the lens-mirror combination, its image is formed at a distance $\frac{a}{3}$ in front of the combination.
The value of $a$ is:
a.
$2f$
b.
$\frac{3}{2}f$
c.
$3f$
d.
$f$
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Unpolarized light of intensity $I_{0}$ is incident on surface of a block of glass at Brewster's angle. In that case,
which one of the following statements is true?
(1) transmitted light is partially polarized with (2) transmitted light is completely polarized with
intensity $\frac{I_{0}}{2}$ intensity less than $\frac{I_{0}}{2}$
(3) reflected light is partially polarized with intensity(4) reflected light is completely polarized with
$\frac{I_{0}}{2}$ intensity less than $\frac{I_{0}}{2}$
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Using equipartition of energy, the specific heat (in $J\, kg^{-1} \,K^{-1}$ ) of Aluminium at high temperature can be
estimated to be (atomic weight of Aluminium $= 27$ )
a.
$25$
b.
$1850$
c.
$410$
d.
$925$
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Which of the following most closely depicts the correct variation of the gravitation potential, $V(r)$ with
distance $r$ due to a large planet of radius $R$ and uniform mass density? (figures are not drawn to scale)
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A short bar magnet is placed in the magnetic meridian of the earth with North Pole pointing north. Neutral
points are found at a distance of $30\, cm$ from the magnet on the East-West line, drawn through the middle point
of the magnet. The magnetic moment of the magnet in $Am^{2}$ is close to:
(Given $\frac{\mu _{0}}{4\pi} = 10^{-7}$ in SI units and $B_{H} =$ Horizontal component of earth's magnetic field $= 3.6 \times 10^{-5}$ Tesla.)
a.
4.9
b.
14.6
c.
19.4
d.
9.7
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In the electric network shown, when no current flows through the $4\,\Omega$ resistor in the arm EB, the potential
difference between the points A and D will be:
a.
$5\,V$
b.
$3\,V$
c.
$4\,V$
d.
$6\,V$
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At $298\,K$ , the standard reduction potentials are $1. 51\,V$ for $MnO^{-}_{4} \,Mn^{2+}$ , $1. 36\,V$ for $Cl_{2}|Cl^{-}$ , $1. 07\,V$ for
$Br_{2}|Br^{-}$ , $0. 54\,V$ for $I_{2}|I^{-}$ . At $pH = 3$ , permanganate is expected to oxidize: $( \frac{RT}{F} = 0.059)$
a.
$Cl^{-}$ and $Br^{-}$
b.
$Br^{-}$ and $I^{-}$
c.
$I^{-}$ only
d.
$Cl^{-}\,, \,Br^{-}$ and $I^{-}$
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Molecule AB has a bond length of $1.617\,$ Åand a dipole moment of 0.38 D. The fractional charge on each
atom(absolute magnitude) is: $(e_{0} = 4.802 \times 10^{-10}\,esu)$
a.
0.5
b.
0.05
c.
0
d.
1.0
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Match the organic compounds in column - $I$ with the Lassaigne's test result in column - $II$ appropriately:
Column - $I$ Column - $II$
A. Aniline i. Red colour with $FeCl_{3}$
B. Benzene sulfonic acid ii. Violet color with sodium nitroprusside
C. Thiourea iii. Blue color with and acidic solution of $FeSO_{4}$
a.
A - ii ; B - iii ; C - i
b.
A - iii ; B - ii ; C - i
c.
A - ii ; B - i ; C - iii
d.
A - iii ; B - i ; C - ii
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A $2 V$ battery is connected across $AB$ as shown in the figure. The value of the current supplied by the battery
when in first case battery's positive terminal is connected to $A$ and in second case when positive terminal of
battery is connected to $B$ will respectively be:
a.
$0.2\,A$ and $0.1\,A$
b.
$0.1\,A$ and $0.2\,A$
c.
$0.2\,A$ and $0.4\,A$
d.
$0.4\,A$ and $0.2\,A$
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The increase of pressure on $ice\, \rightleftharpoons water$ system at constant temperature will lead to:
(1) A decrease in the entropy of the system (2) An increase in the Gibbs energy of the system
(3) A shift of the equilibrium in the forward direction(4) No effect on the equilibrium
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An element $X$ shows $+3$ , oxidation state in its compounds. Out of the four compounds given below, choose the
incorrect formula for the element $X$ .
a.
$X_{2}O_{3}$
b.
$X_{2}(SO_{4})_{3}$
c.
$XPO_{4}$
d.
$X_{2}Cl_{3}$
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In the following reaction:
$A + 2B + 3C \rightleftharpoons AB_{2}C_{3}$
$6. 0\,g$ of $A$ , $6.0 \times 10^{23}$ atoms of $B$ and $0. 036\, mol$ of $C$ reacted and formed $4. 8\,g$ of compound $AB_{2}C_{3}$ . If the
atomic mass of $A$ and $C$ are $60$ and $80\, amu$ , respectively. What is the atomic mass of $B$ in $amu$ ? (Avogadro
number $= 6 \times 10^{23}$ )
a.
$40\, amu$
b.
$60\, amu$
c.
$70\, amu$
d.
$50\, amu$
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$A + 2B \rightarrow C\rightarrow$ , the rate equation for the reaction is given as
Rate $= k [A] [B]$
If the concentration of A is kept the same but that of B is doubled what will happen to the rate itself?
a.
Doubled
b.
Halved
c.
The same
d.
Quadrupled
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For the equilibrium, $A(g) \rightleftharpoons B(g), \, \Delta H\, is \, -40\, kJ / mol$ . If the ratio of the activation energies of the
forward $(E_{f})$ and reverse $(E_{b})$ reactions is $\frac{2}{3}$ then:
When concentrated $HCl$ is added to aqueous solution of $CoCl_{2}$ , its colour changes from reddish pink to deep
blue. Which complex ion gives blue colour in reaction?
a.
$[CoCl_{6}]^{4-}$
b.
$[CoCl_{6}]^{3-}$
c.
$[Co(H_{2}O)_{6}]^{2+}$
d.
$[CoCl_{4}]^{2-}$
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Let $k$ and $K$ be the minimum and the maximum values of the function $f(x) = \frac{(1+x)^{0.6}}{1+x^{0.6}}\,in\,[0, \,1]$ , respectively,
then the ordered pair $(k, \,K)$ is equal to:
a.
$(2^{-0.4}, 1)$
b.
$(2^{-0.6}, \,1)$
c.
$(2^{-0.4}, 2^{0.6})$
d.
$(1,2^{0.6})$
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Let $f : (-1, \,1) \rightarrow \rightarrow R$ be a continuous function. If $\int _{0}^{sinx} f(t)\,dt= \frac{\sqrt{3}}{2}x,$ then $f(\frac{\sqrt{3}}{2})$ is equal to:
a.
$\frac{\sqrt{3}}{2}$
b.
$\sqrt{3}$
c.
$\frac{1}{2}$
d.
$\sqrt{\frac{3}{2}}$
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$\{ \neq 0$
$\frac{(e^{x}-1)^{2}}{_{sin}_{(}x_{k}_{)}_{log}_{(}_{1+}_{x}_{4}_{)},} x$
Let $k$ be a non - zero real number. If $f(x) =$ is a continuous function at $x= 0$
$\{$
$12 , x = 0$
, then the value of $k$ is
a.
$2$
b.
$4$
c.
$3$
d.
$1$
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Let $10$ vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $\alpha$ at a
point $O$ on this line and all the poles are on the same side of $O$ . If the height of the longest pole is $h$ and the
distance of the foot of the smallest pole from $O$ is $a$ ; then the distance between two consecutive poles, is
a.
$\frac{hsin\alpha +acos\alpha}{9\, cos\alpha}$
b.
$\frac{hcos\alpha -a\,sin$\alpha$}{9 sin\alpha}$
c.
$\frac{hsin\alpha +acos\alpha}{9 sin\alpha}$
d.
$\frac{hcos\alpha -asin\alpha}{9 cos\alpha}$
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If the incentre of an equilateral triangle is $(1, 1)$ and the equation of its one side is $3x+ 4y+ 3 = 0$ , then the
equation of the circumcircle of this triangle is:
a.
$x^{2} +y^{2} -2x-2y-2 = 0$
b.
$x^{2} +y^{2} -2x-2y+ 2 = 0$
c.
$x^{2} +y^{2} -2x-2y-7 = 0$
d.
$x^{2} +y^{2} -2x-2y-14 = 0$
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Consider the following statements:
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest
The negation of the statement, "Suman is brilliant and dishonest if and only if Suman is rich" can be
equivalently expressed as
a.
$~Q\leftrightarrow ~P \vee R$
b.
$~Q\leftrightarrow P \vee ~R$
c.
$~Q\leftrightarrow P \wedge ~R$
d.
$~Q\leftrightarrow ~P \wedge R$
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If the mean and the variance of a binomial variate $X$ are $2\,&\,1$ respectively, then the probability that $X$ takes a
value greater than or equal to one is:
a.
$\frac{1}{16}$
b.
$\frac{9}{16}$
c.
$\frac{3}{4}$
d.
$\frac{15}{16}$
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If $PQ$ be a double ordinate of the parabola, $y^{2} = -4x,$ where $P$ lies in the second quadrant. If $R$ divides $PQ$
in the ratio $2 : 1,$ then the locus of $R$ is:
a.
$3y^{2} = -2x$
b.
$9y^{2} = 4x$
c.
$9y^{2} = -4x$
d.
$3y^{2} = 2x$
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Let $f :R\rightarrow \rightarrow R$ be a function such that $f(2 - x) =f(2 +x)$ and $f(4 - x) =f(4 +x)$ , for all $x\in R$ and
$2 50$
$\int f(x)dx= 5$ . Then the value of $\int f(x)dx$ is
$0 10$
a.
$100$
b.
$125$
c.
$80$
d.
$200$
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The sum of the $3^{rd}$ and the $4^{th}$ terms of a $G. P.$ is $60$ and the product of its first three terms is $1000.$ If the first
term of this $G. P.$ is positive, then its $7^{th}$ term is:
a.
$320$
b.
$640$
c.
$2430$
d.
$7290$
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A straight line $L$ through the point $(3, \, -2)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x+y= 1.$ If $L$ also
intersects the $X$ -axis, then the equation of $L$ is:
a.
$y+ \,\sqrt{3} x+ 2 -3 = 0\sqrt{3}$
b.
$\sqrt{3}\,y- x+ 3 + 2 = 0\sqrt{3}$
c.
$\sqrt{3}\,y+x-3 + 2 = 0\sqrt{3}$
d.
$y- \sqrt{3}x+ 2 + 3 = 0\sqrt{3}$
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If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability
that the triangle is of maximum area given that it is an isosceles triangle, is:
a.
$\frac{1}{69}$
b.
$\frac{1}{26}$
c.
$\frac{1}{21}$
d.
$\frac{1}{15}$
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Let $A= {x_{1},x_{2}, … ,x_{7}}\,and\,B= {y_{1},y_{2},y_{3}}$ be two sets containing seven and three distinct elements
respectively. Then the total number of functions $f :A\rightarrow \rightarrow B$ that are onto, if there exist exactly three elements
$x$ in $A$ such that $f(x) =y_{2},$ is equal to:
a.
$12 \cdot ^{7} C_{2}$
b.
$16 \cdot ^{7} C_{3}$
c.
$14 \cdot \,^{7}C_{3}$
d.
$14 \cdot ^{7} C_{2}$
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If $cos\alpha + cos\beta = \frac{3}{2} \,and\, sin\alpha + sin\beta = \frac{1}{2}$ and $\theta$ is the arithmetic mean of $\alpha \,&\,\beta ,$ then $sin 2\theta + cos 2\theta$ is
equal to:
a.
$\frac{3}{5}$
b.
$\frac{7}{5}$
c.
$\frac{4}{5}$
d.
$\frac{8}{5}$
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If the two roots of the equation, $(a-1)\,(x^{4} +x^{2} + 1)+ (a+ 1)(x^{2} +x+ 1)^{2} = 0$ are real and distinct, then
the set of all values of $a$ is equal to
a.
$(0, \frac{1}{2} )$
b.
$(-\frac{1}{2}, 0)\, \cup (0, \frac{1}{2})$
c.
$(-\infty , -2)\, \cup (2, \,\infty )$
d.
$(-\frac{1}{2}, \,0)$
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