A particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $l.$ The
other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates
in a circle in gravity free space. Then the stretch in the spring is:
Effective capacitance of parallel combination of two capacitors $C_{1}$ and $C_{2}$ is $10$ $\mu$ $F.$ When these capacitors are
individually connected to a voltage source of $1V,$ the energy stored in the capacitor $C_{2}$ is $4$ times that of $C_{1}.$ If
these capacitors are connected in series, their effective capacitance will be:
a.
$4.2$ $\mu$ $F$
b.
$3.2$ $\mu$ $F$
c.
$1.6$ $\mu$ $F$
Correct Answer
d.
$8.4$ $\mu$ $F$
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Q3mcq
When photon of energy $4.0eV$ strikes the surface of a metal $A,$ the ejected photoelectrons have maximum
kinetic energy $T_{A}eV$ and de-Broglie wavelength $\lambda _{A}.$ The maximum kinetic energy of photoelectrons liberated
from another metal $B$ by photon of energy $4.50eV$ is $T_{B} = (T_{A}-1.5)eV.$ If the de-Broglie wavelength of
these photoelectrons $\lambda _{B} = 2\lambda _{A},$ then the work function of metal $B$ is:
a.
$4eV$
Correct Answer
b.
$2eV$
c.
$1.5eV$
d.
$3eV$
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Q4mcq
The plot that depicts the behavior of the mean free time $Ο$ (time between two successive collisions) for the
molecules of an ideal gas, as a function of temperature $(T),$ qualitatively, is: (Graphs are schematic and not
drawn to scale)
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Q5mcq
The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass $4\,kg$ . (The
coordinates of the same are shown in the figure) are:
a.
$(1.25\,m, 1.50\,m)$
b.
$(0.75\,m, 1.75\,m)$
Correct Answer
c.
$(0.75\,m, 0.75\,m)$
d.
$(1\,m, 1.75\,m)$
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Q6mcq
Consider two solid spheres of radii $R_{1} = 1\,m$ , $R_{2} = 2\,m$ and masses $M_{1}$ and $M_{2},$ respectively. The
gravitational field due to sphere $(1)$ and $(2)$ are shown. The value of $\frac{M}{M_{2}}^{1}$ is:
a.
$\frac{2}{3}$
b.
$\frac{1}{6}$
Correct Answer
c.
$\frac{1}{2}$
d.
$\frac{1}{3}$
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Q7mcq
$|$
$|$
$|$
At time $t= 0$ magnetic field of $1000\,Gauss$ is passing perpendicularly through the area defined by the closed
loop shown in the figure. If the magnetic field reduces linearly to $500\,Gauss,$ in the next $5s,$ then induced
$EMF$ in the loop is:
a.
$56$ $\mu$ $V$
Correct Answer
b.
$28$ $\mu$ $V$
c.
$48$ $\mu$ $V$
d.
$36$ $\mu$ $V$
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Q8nat
A body $A$ of mass $m= 0.1\,kg$ has an initial velocity of $3Λi\,m\,s^{-1}$ . It collides elastically with another body $B$ of
the same mass which has an initial velocity of $5Λj\,m\,s^{-1}$ . After the collision, $A$ moves with a velocity
$\vec{v}= 4(Λi +Λj)\,m\,s^{-1}$ . The energy of $B$ after the collision is written as $\frac{x}{10}\,J$ . The value of $x$ is
✓ Accepted Answer:1
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Q9mcq
Boolean relation at the output stage- $Y$ for the following circuit is:
a.
$- -$
$A + B$
b.
$A+B$
c.
$A\cdot B$
d.
$- -$
$A \cdot B$
Correct Answer
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Q10mcq
The dimension of stopping potential $V_{0}$ in photoelectric effect in units of Planckβs constant β $h$ β, speed of light β
$c$ β and Gravitational constant β $G$ β and ampere $A$ is:
A thermodynamic cycle $xyzx$ is shown on a $V$ - $T$ diagram.
The $P$ - $V$ diagram that best describes this cycle is: (Diagrams are schematic and not to scale)
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Consider a uniform rod of mass $M = 4m$ and length $l$ pivoted about its centre. A mass $m$ moving with velocity
$v$ making angle $\theta = \frac{\pi}{4}$ to the rodβs long axis collides with one end of the rod and sticks to it. The angular speed
of the rod-mass system just after the collision is:
a.
$\frac{3}{7\sqrt{2}} \frac{v}{l}$
b.
$\frac{3}{7} \frac{v}{l}$
c.
$\frac{3\sqrt{2}}{7} \frac{v}{l}$
d.
$\frac{4}{7} \frac{v}{l}$
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A leak proof cylinder of length $1\,m,$ made of a metal which has very low coefficient of expansion is floating
vertically in water at $0^{o}C$ such that its height above the water surface is $20\,cm.$ When the temperature of water
is increased to $4^{o}C,$ the height of the cylinder above the water surface becomes $21\,cm.$ The density of water at
$T = 4^{o}C,$ relative to the density at $T = 0^{o}C$ is close to:
a.
$1.26$
b.
$1.04$
c.
$1.01$
d.
$1.03$
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The graph which depicts the results of Rutherford gold foil experiment with $\alpha$ -particles is:
$\theta :$ Scattering angle
$Y :$ Number of scattered $\alpha$ -particles detected
(Plots are schematic and not to scale)
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A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP.
Assuming the speed of sound in air at STP is $300\,m/s,$ the frequency difference between the fundamental and
second harmonic of this pipe is __________ Hz.
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A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the
curved surface is $30\,cm$ and the refractive index of the lens material is $1.5,$ then the focal length of the lens (in
cm) is ___________.
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Four resistances of $15\,\Omega , \,12\,\Omega , \,4\,\Omega$ and $10\,\Omega$ respectively in cyclic order to form Wheatstoneβs network. The
resistance that is to be connected in parallel with the resistance of $10\,\Omega$ to balance the network is
______________ $\Omega .$
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In finding the electric field using Gauss law the formula $\vec{E} = \frac{q_{enc}}{$\epsilon$_{0}|A|}$ is applicable. In the formula $\epsilon$ $_{0}$ is
permittivity of free space, $A$ is the area of Gaussian surface and $q_{enc}$ is charge enclosed by the Gaussian
surface. This equation can be used in which of the following situation?
a.
Only when the Gaussian surface is an
equipotential surface
b.
Only when the Gaussian surface is an
equipotential surface and $\vec{E}$ is constant on the
surface.
c.
Only when $\vec{E} =$ constant on the surface.
d.
For any choice of Gaussian surface.
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Three charged particles $A ,\, B$ and $C$ with charges $-4q, 2q$ and $-2q$ are present on the circumference of a
circle of radius $d.$ The charged particles $A, C$ and centre $O$ of the circle formed an equilateral triangle as shown
in the figure. The electric field at the point $O$ is
a.
$\frac{\sqrt{3}q}{\pi \epsilon _{0}d^{2}}$
b.
$\frac{2\sqrt{3}q}{\pi \epsilon _{0}d^{2}}$
c.
$\frac{\sqrt{3}q}{4\pi \epsilon _{0}d^{2}}$
d.
$\frac{3\sqrt{3}q}{4\pi \epsilon _{0}d^{2}}$
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The critical angle of a medium for a specific wavelength, if the medium has relative permittivity $3$ and relative
permeability $\frac{4}{3}$ for this wavelength, will be:
a.
$15^{o}$
b.
$30^{o}$
c.
$45^{o}$
d.
$60^{o}$
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Consider a solid sphere of radius $R$ and mass density $\rho (r) =\rho _{0}(1 - \frac{r^{2}}{R^{2}}), 0 <r\leq R.$ The minimum density of
a liquid in which it will float is:
a.
$\frac{\rho _{0}}{3}$
b.
$\frac{\rho _{0}}{5}$
c.
$\frac{2\rho _{0}}{5}$
d.
$\frac{2\rho _{0}}{3}$
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A particle is moving along the $x$ -axis with its coordinate with time $t$ given by $x(t) = 10 + 8t-3t^{2}.$ Another
particle is moving along the $y$ -axis with its coordinate as a function of time given by $y(t) = 5 -8t^{3}.$ At
$t= 1\,s,$ the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{v}.$ Then
$v(in\,m\,s^{-1})$ is ___________.
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The length of a potentiometer wire is $1200\,cm$ and it carries a current of $60\,mA$ For a cell of $emf\,5\,V$ and
internal resistance of $20\,\Omega$ the null point on it is found to be at $1000\,cm$ The resistance of whole wire is:
a.
$80\Omega$
b.
$120\Omega$
c.
$60\Omega$
d.
$100\Omega$
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Proton with kinetic energy of $1\,MeV$ moves from south to north. It gets an acceleration of $10^{12}\,m/s^{2}$ by an
applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is $1.6 \times 10^{-27}kg$ )
a.
$0.71mT$
b.
$7.1mT$
c.
$0.071mT$
d.
$71mT$
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The volume $(in\,mL)$ of $0.125\,M\,AgNO_{3}$ required to quantitatively precipitate chloride ions in $0.3g$ of
$[Co(NH_{3})_{6}]Cl_{3}$ is __________.
$^{M}[Co(NH_{3})_{6}]Cl_{3} = 267.46g/mol$
$^{M}AgNO_{3} = 169.87g/mol$
Report the nearest integer as the answer.
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Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to
achieve $10ppm$ of iron in $100kg$ of wheat is ____________.
Atomic weight: $Fe = 55.85; S = 32.00; O = 16.00$
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What would be the electrode potential for the given half-cell reaction at $pH = 5? _________.$
$2H_{2}O \rightarrow O\rightarrow_{2}+ 4H + 4e^{\oplus }^{-}; E^{0}_{red} = 1.23V$
$(R = 8.314Jmol^{-1}K^{-1}; Temp = 298K; oxygen\,under\,s tan dard\,. atm. pressureof1bar)$
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For the Balmer series, in the spectrum of $H$ atom, $^{-}v = R_{H}{\frac{1}{n^{2}_{1}} - \frac{1}{n^{2}_{2}}},$ the correct statements among $(I)$ to
$(IV)$ are,
$(I)$ As wavelength decreases, the lines in the series converge.
$(II)$ The integer $n_{1}$ is equal to $2$ /
$(III)$ The lines of the longest wavelength correspond to $n_{2} = 3$ .
$(IV)$ The ionization energy of hydrogen can be calculated from the wave number of these lines.
a.
$(I), (III), (IV)$
b.
$(I), (II), (III)$
c.
$(I), (II), (IV)$
d.
$(II), (III), (IV)$
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A graph of vapour pressure and temperature for three different liquids $X, Y$ and $Z$ is shown below:
The following inferences are made:
$(A)X$ has higher intermolecular interactions compared to $Y.$
$(B)X$ has lower intermolecular interactions compared to $Y.$
$(C)Z$ has lower intermolecular interactions compared to $Y.$
The correct inferences is/are:
a.
$(A)$ and $(C)$
b.
$(A)$
c.
$(B)$
d.
$(C)$
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A flask contains a mixture of isohexane and $3$ -methylpentane. One of the liquids boils at $63^{o}C$ while the other
boils at $60^{o}C.$ What is the best way to separate the two liquids and which one will be distilled out first?
a.
fractional distillation, isohexane
b.
simple distillation, $3$ -methylpentane
c.
simple distillation, isohexane
d.
fractional distillation, $3$ -methylpentane
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The rate of a certain biochemical reaction at physiological temperature $(T)$ occurs $10^{6}$ times faster with
enzyme than without. The change in the activation energy upon adding enzyme is:
a.
$-6(2.303)RT$
b.
$-6RT$
c.
$+6(2.303)RT$
d.
$+6RT$
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The number of bonds between sulphur and oxygen atoms in $S_{2}O^{2-}_{8}$ and the number of bonds between sulphur
and sulphur atoms in rhombic sulphur, respectively are:
a.
$4$ and $6$
b.
$8$ and $8$
c.
$8$ and $6$
d.
$4$ and $8$
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Let the normal at a point $P$ on the curve $y^{2} -3x^{2} +y+ 10 = 0$ intersect the $y$ -axis at $(0, \frac{3}{2}).$ If $m$ is the
slope of the tangent at $P$ to the curve, then $|m|$ is equal to ___________.
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The number of all $3 \times 3$ matrices $A,$ with entries from the set ${-1, 0, 1}$ such that the sum of the diagonal
elements of $AA^{T}$ is $3,$ is ___________.
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Let $f(x) =(sin(tan^{-1} x)+ sin(cot^{-1} x))^{2} -1$ , $|x| > 1$ . If $\frac{dy}{dx} = \frac{1}{2} \frac{d}{dx}(sin^{-1}(f(x)))$ and $y(\sqrt{3})= \frac{\pi}{6},$ then
$y(-\sqrt{3})$ is equal to:
a.
$\frac{2\pi}{3}$
b.
$- \frac{\pi}{6}$
c.
$\frac{5\pi}{6}$
d.
$\frac{\pi}{3}$
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The locus of a point which divides the line segment joining the point $(0, -1)$ and a point on the parabola
$x^{2} = 4y$ internally in the ratio $1 : 2$ is:
a.
$9x^{2} -12y= 8$
b.
$9x^{2} -3y= 2$
c.
$x^{2} -3y= 2$
d.
$4x^{2} -3y= 2$
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For $a> 0,$ let the curves $C_{1} :y^{2} =ax$ and $C_{2} :x^{2} =ay$ intersect at origin $O$ and a point $P.$ Let the line
$x=b(0 <b<a)$ intersect the chord $OP$ and the $x$ -axis at points $Q$ and $R,$ respectively. If the line $x=b$
bisects the area bounded by the curves, $C_{1}$ and $C_{2},$ and the area of $\Delta OQR= \frac{1}{2} ,$ then β $a$ β satisfies the
equation:
a.
$x^{6} -6x^{3} + 4 = 0$
b.
$x^{6} -12x^{3} + 4 = 0$
c.
$x^{6} + 6x^{3} -4 = 0$
d.
$x^{6} -12x^{3} -4 = 0$
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Let the line $y=mx$ and the ellipse $2x^{2} +y^{2} = 1$ intersect at a point $P$ in the first quadrant. If the normal to
this ellipse at $P$ meets the co-ordinate axes at $(- \frac{1}{3\sqrt{2}}, 0)$ and $(0,\beta )$ , then $\beta$ is equal to
a.
$\frac{2\sqrt{2}}{3}$
b.
$\frac{2}{\sqrt{3}}$
c.
$\frac{2}{3}$
d.
$\frac{\sqrt{2}}{3}$
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An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then, the number of ways in which $4$
marbles can be drawn so that at the most three of them are red is ___________.
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Let $y=y(x)$ be a solution of the differential equation, $\sqrt{1 -x^{2}} \frac{dy}{dx} +\sqrt{1 -y^{2}} = 0, |x| < 1.$ If $y(\frac{1}{2})= \frac{\sqrt{3}}{2},$
then $y(\frac{-1}{\sqrt{2}})$ is equal to
a.
$\frac{\sqrt{3}}{2}$
b.
$- \frac{1}{\sqrt{2}}$
c.
$\frac{1}{\sqrt{2}}$
d.
$- \frac{\sqrt{3}}{2}$
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The mean and the standard deviation (s.d.) of $10$ observations are $20$ and $2$ respectively. Each of these $10$
observations is multiplied by $p$ and then reduced by $q,$ where $p\neq 0$ and $q\neq 0.$ If the new mean and new s.d.
become half of their original values, then $q$ is equal to
a.
$-5$
b.
$10$
c.
$-20$
d.
$-10$
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If $c$ is a point at which Rolleβs theorem holds for the function, $f(x) = log_{e}(\frac{x^{2}+\alpha}{7x})$ in the interval $[3, 4],$ where
$\alpha \in R,$ then $f''(c)$ is equal to
a.
$-\frac{1}{12}$
b.
$\frac{1}{12}$
c.
$-\frac{1}{24}$
d.
$\frac{\sqrt{3}}{7}$
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If $\int \frac{cosxdx}{362} =f(x)(1 + sin^{6}x)\frac{1}{\lambda} +c$ , where $c$ is a constant of integration, then $\lambda f(\frac{\pi}{3})$ is equal to
$sin x(1+sin x)^{3}$
a.
$-\frac{9}{8}$
b.
$2$
c.
$\frac{9}{8}$
d.
$-2$
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Let the volume of a parallelepiped whose coterminous edges are given by $\vec{u}= Λi+ Λj+\lambda Λk, \vec{v}= Λi+ Λj+ 3Λk$ and
$\vec{w}= 2Λi+ Λj+ Λk$ be $1$ cu. unit. If $\theta$ be the angle between the edges $\vec{u}$ and $\vec{w},$ then the value of $cos\theta$ can be
a.
$\frac{7}{6\sqrt{6}}$
b.
$\frac{7}{6\sqrt{3}}$
c.
$\frac{5}{7}$
d.
$\frac{5}{3\sqrt{3}}$
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Let two points be $A(1, -1)$ and $B(0, 2).$ If a point $P(x', \,y')$ be such that the area of $\Delta PAB= 5$ sq. units and
it lies on the line $3x+y-4\lambda = 0,$ then a value of $\lambda$ is
a.
$4$
b.
$3$
c.
$1$
d.
$-3$
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For which of the following ordered pairs $(\mu ,\delta ),$ the system of linear equations
$x+ 2y+ 3z= 1$
$3x+ 4y+ 5z=\mu$
$4x+ 4y+ 4z=\delta$
is inconsistent?
a.
$(4, 3)$
b.
$(4, 6)$
c.
$(1, 0)$
d.
$(3, 4)$
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