A liquid of density $\rho$ is coming out of a hose pipe of radius a with horizontal speed $v$ and hits a mesh. $50%$ of
the liquid passes through the mesh unaffected. $25%$ looses all of its momentum and $25%$ comes back with the
same speed. The resultant pressure on the mesh will be:
a.
$\frac{1}{4} \rho v^{2}$
b.
$\frac{3}{4} \rho v^{2}$
Correct Answer
c.
$\frac{1}{2} \rho v^{2}$
d.
$\rho v^{2}$
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Q2mcq
Equation of travelling wave on a stretched string of linear density $5\,g/m$ is $y = 0.03 sin(450t -9x)$ where
distance and time are measured in SI units. The tension in the string is:
a.
$10\,N$
b.
$7.5\,N$
c.
$12.5\,N$
Correct Answer
d.
$5\,N$
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Q3mcq
In a Wheatstone bridge (see fig.), Resistances $P$ and $Q$ are approximatelyequal. When $R= 400\Omega$ , the bridge is
balanced. On interchanging $P$ and $Q$ , the value of $R,$ for balance, is $405\Omega$ . The value of $Y$ is close to
a.
$401.5ohm$
b.
$404.5ohm$
c.
$403.5ohm$
d.
$402.5ohm$
Correct Answer
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Q4mcq
The given graph shows variation (with distancer from centre) of:
a.
Electric field of a uniformly charged sphere
b.
Potential of a uniformly charged spherical shell
Correct Answer
c.
Potential of a uniformly charged sphere
d.
Electric field of a uniformly charged spherical
shell
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Q5mcq
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between
temperature and volume for this process is $TV^{x} =$ constant, then $x$ is:
a.
$\frac{3}{5}$
b.
$\frac{2}{5}$
Correct Answer
c.
$\frac{2}{3}$
d.
$\frac{5}{3}$
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Q6mcq
The resistance of the meter bridge AB in given figure is $4\Omega$ . With a cell of emf $\epsilon = 0.5\,V$ and rheostat
resistance $R_{h} = 2\Omega$ the null point is obtained at some point J. When the cell is replaced by another one of emf
$\epsilon =\epsilon _{2}$ the same null point $J$ is found for $R_{h} = 6\Omega$ . The $emf\epsilon _{2}$ is:
a.
$0.4\,V$
b.
$0.3\,V$
Correct Answer
c.
$0.6\,V$
d.
$0.5\,V$
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Q7mcq
An amplitude modulated signal is given by $V(t) = 10[1 + 0.3 cos(2.2 \times 10^{4}t)]sin(5.5 \times 10^{5}t).$ Here $t$ is in
seconds. The sideband frequencies (in $kHz$ ) are, [Given $\pi = 22/7$ ]
a.
1785 and 1715
b.
$178.5$ and $171.5$
c.
$89.25$ and $85.75$
Correct Answer
d.
$892.5$ and $857.5$
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Q8mcq
If the deBroglie wavelength of an electron is equal to $10^{-}$ times the wavelength of a photon of frequency
$6 \times 10^{14} Hz$ , then the speed of electron is equal to : (Speed of light $= 3 \times 10^{8}\,m/s)$ Planck's constant
$= 6.63 \times 10^{-34}\,J. s$ Mass of electron $= 9.1 \times 10^{-31}\,kg)$
a.
$1.1 \times 10^{6}\,m/s$
b.
$1.7 \times 10^{6}\,m/s$
c.
$1.8 \times 10^{6}\,m/s$
d.
$1.45 \times 10^{6}\,m/s$
Correct Answer
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Q9mcq
Ice at $-20^{\circ }C$ is added to $50\,g$ of water at $40^{\circ }C$ , When the temperature of the mixture reaches $0^{\circ }C,$ it is found
that 20 $g$ of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water
$= 4.2\,J/g/^{\circ }C$ Specific heat of Ice $= 2.1\,J/g/^{\circ }C$ Heat of fusion of water at $0^{\circ }C = 334\,J/g)$
a.
$50\,g$
b.
$100\,g$
c.
$60\,g$
d.
$40\,g$
Correct Answer
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Q10mcq
In an experiment, electrons are accelerated, from rest, by applying a voltage of $500\,V$ . Calculate the radius of
the path if a magnetic field $100mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19}C$ Mass of the
electron $= 9.1 \times 10^{-31}\,kg]$
a.
$7.5 \times 10^{-3}\,m$
b.
$7.5 \times 10^{-2}\,m$
c.
$7.5\,m$
d.
$7.5 \times 10^{-4}\,m$
Correct Answer
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A body of mass $1\,kg$ falls freely from a height of $100\,m$ , on a platform of mass $3\,kg$ which is mounted on a
spring having spring constant $k = 1.25 \times 10^{6}\,N/m$ . The bodysticks to the platform and the spring's maximum
compression is found to be $x$ . Given that $g= 10\,ms^{-2},$ the value of $x$ will be close to :
a.
$40\,cm$
b.
$4\,cm$
c.
$80\,cm$
d.
$8\,cm$
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A body is projected at $t= 0$ with a velocity $10\,ms^{-1}$ at an angle of $60^{\circ }$ with the horizontal. The radius of
curvature of its trajectory at $t= 1$ s is $R$ . Neglecting air resistance and taking acceleration due to gravity
$g = 10\,ms^{-2}$ , the value of $R$ is:
a.
$10.3\,m$
b.
$2.8\,m$
c.
$2.5\,m$
d.
$5.1\,m$
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In a Young's double slit experiment, the path difference, at a certain point on the screen, betwen two interfering
waves is $\frac{1}{8}$ th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is
close to:
a.
0.74
b.
0.85
c.
0.94
d.
0.8
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A particle undergoing simple harmonic motion has time dependent displacement given by $x(t) = A sin \frac{\pi t}{90}$ .
The ratio of kinetic to potential energy of this particle at $t = 210\,s$ will be
a.
$\frac{1}{9}$
b.
1
c.
2
d.
$\frac{1}{3}$
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Three charges $Q, +y$ and $+q$ are placed at the vertices of a right-angle isosceles triangle as shown below. The
net electrostatic energy of the configuration is zero, if the value of $Q$ is
a.
$+q$
b.
$\frac{-\sqrt{2}q}{\sqrt{2}+1}$
c.
$\frac{-q}{1+\sqrt{2}}$
d.
$-2q$
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In the circuit shown,
the switch $S_{1}$ is closed at time $t= 0$ and the switch $S_{2}$ is kept open. At some later time $(t_{0})$ , the switch $S_{1}$ is
opened and $S_{2}$ is closed. the behaviour of the current I as a function of time ' $t$ ' is given by:
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A slab is subjected to two forces and of same magnitude as shown in the figure. Force is in XY-
$\vec{F}_{1} \vec{F}_{2} F \vec{F}_{2}$
plane while force $F_{1}$ acts along $z$ -axis at the point $(2\vec{i}+ 3\vec{j})$ . The moment of these forces about point $O$ will be:
a.
$(3\hat{i}-2\hat{j}+ 3\hat{k})$ F
b.
$(3\hat{i}-2\hat{j}-3\hat{k})F$
c.
$(3\hat{i}+ 2\hat{j}-3\hat{k})F$
d.
$(3\hat{i}+ 2\hat{j}+ 3\hat{k})F$
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An electromagnetic wave of intensity $50Wm^{-2}$ enters in a medium of refractive index 'n' without any loss.
The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic fields of the wave
before and after entering into the medium are respectively, given by :
a.
$(\frac{1}{\sqrt{n}}, \frac{1}{\sqrt{n}})$
b.
$(\sqrt{n}, \sqrt{n})$
c.
$(\sqrt{n}, \frac{1}{\sqrt{n}} )$
d.
$(\frac{1}{\sqrt{n}}, \sqrt{n})$
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A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $980$ Ã $…$ . The
radius of the atom in the excited state, in terms of Bohr radius $a_{0}$ , will be:
a.
$25a_{0}$
b.
$9a_{0}$
c.
$16a_{0}$
d.
None of the above
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A particle is moving along a circular path with a constant speed of $10\,ms^{-1}$ . What is the magnitude of the
change in velocity of the particle, when it moves through an angle of $60^{\circ }$ around the centre of the circle?
a.
$10\sqrt{3}\,m/s$
b.
zero
c.
$10\sqrt{2}\,m/s$
d.
$10\,m/s$
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An object is at a distance of $20\,m$ from a convex lens of focal length $0.3\,m$ . The lens forms an image of the
object. If the object moves away from the lens at a speed of $5\,m/s$ the speed and direction of the image will be
a.
$2.26 \times 10^{-3}\,m/s$ away from the lens
b.
$0.92 \times 10^{-3}\,m/s$ away from the lens
c.
$3.22 \times 10^{-3}\,m/s$ towards the lens
d.
$1.16 \times 10^{-3}\,m/s$ towards the lens
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Two equal resistances when connected in series to a battery, consume electric power of $60\,W$ . If these
resistance are now connected in parallel combination to the same battery, the electric power consumed will be :
a.
$60\,W$
b.
$240\,W$
c.
$120\,W$
d.
$30\,W$
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A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only
translational and rotational modes, the total internal energy of the system is
a.
$15RT$
b.
$12RT$
c.
$4RT$
d.
$20RT$
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The force of interaction between two atoms is given by $F =\alpha \beta exp(-_{\alpha kT} );$ where $x$ is the distance, $k$ is the
Boltzmann constant and T is temperature and $\alpha$ and $\beta$ are two constants. The dimensions of $\beta$ is:
a.
$M^{0}\,L^{2}\,T^{-4}$
b.
$M^{2}LT^{-4}$
c.
$MLT^{-2}$
d.
$M^{2}\,L^{2}\,T^{-2}$
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A satellite is revolving in a circular orbit at a height h from the carth surface, such that $h << R$ where $R$ is the
radius of the earth. Assuming that the effect of earth"s atmosphere can be neglected the minimum increase in
the speed required so that the satellite could escape from the gravitational field of earth is
b.
$\sqrt{gR}$
c.
$\frac{\sqrt{2gR}}{gR}$
$\sqrt{\,} _{2}$
d.
$\sqrt{gR}( -1)\sqrt{2}$
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The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown.
Which of the following graphs is the correct one, if $D_{m}$ is the angle of minimum deviation?
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There are two long co-axial solenoids of same length $l$ . The inner and outer coils have radii $r_{1}$ and $r_{2}$ and
number of turns per unit length $n_{1}$ and $n_{2}$ , respectively. The ratio of mutual inductance to the self-inductance
of the inner-coil is :
An equilateral triangle $ABC$ is cut from a thin solid sheet of wood. (See figure) $D, E$ and $F$ are the mid-points
of its sides as shown and $G$ is the centre of the triangle. The moment of inertia of the triangle about an axis
passing through $G$ and perpendicular to the plane of the triangle is $I_{0}$ . If the smaller triangle $DEF$ is removed
from $ABC$ , the moment of inertia of the remaining figure about the same axis is $I$ . Then
a.
$I = \frac{15}{16}I_{0}$
b.
$I = \frac{3}{4} I_{0}$
c.
$I = \frac{9}{16}I_{0}$
d.
$I = \frac{I_{0}}{4}$
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The correct statements among (a) to (d) regarding $H_{2}$ as a fuel are : (i) It produces less pollutants than petrol.
(ii) A cylinder of compressed dihydrogen weighs $\sim 30$ times more than a petrol tank producing the same
amount of energy. (iii) Dihydrogen is stored in tanks of metal alloys like $NaNi_{5}$ (iv) On combustion, values of
energy released per gram of liquid dihydrogen and LPG are 50 and $142\,kJ,$ respectively.
a.
$(ii)and(iv)only$
b.
$(i)and(iii)only$
c.
$(ii), (iii)and(iv)only$
d.
$(i), (ii)and(iii)only$
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A $10mg$ effervescent tablet containing sodium bicarbonate and oxalic acid releases $0.25\,mL$ of $CO_{2}$ at
$T = 298.15\,K$ and $P = 1$ bar. If molar volume of $CO_{2}$ is $25.0\,L$ under such condition, what is the percentage
of sodium bicarbonate in each tablet? [Molar mass of $NaHCO_{3} = 84\,g\,mol^{-1}]$
a.
0.84
b.
33.6
c.
16.8
d.
8.4
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If a reaction follows the Arrhenius equation, the plot $lnk$ vs $\frac{1}{(RT)}$ gives straight line with a gradient $(-y)$ unit.
The energy required to activate the reactant is:
a.
$y/R$ unit
b.
y unit
c.
yR unit
d.
$-y$ unit
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Two blocks of the same metal having same mass and at temperature $T_{1},$ and $T_{2}$ , respectively, are brought in
contact with each other and allowed to attain thermal equilibrium at constant pressure. The change in entropy,
$\Delta S$ , for this process is :
Heat treatment of muscular pain involves radiation of wavelength of about $900nm$ . Which spectral line of $H$
atom is suitable for this purpose? $[R_{H} = 1 \times 10^{5}\,cm^{-1} \cdot h = 6.6 \times 10^{-34}Js, c = 3 \times 10^{8}\,ms^{-1}]$
a.
Paschen, $\infty \rightarrow 3\rightarrow$
b.
Paschen, $5 \rightarrow 3\rightarrow$
c.
Balmer, $\infty \rightarrow 2\rightarrow$
d.
Lyman, $\infty 1$
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The freezing point of a diluted milk sample is found to be $-0.2^{\circ }C,$ while it should have been $-0.5^{\circ }C$ for pure
milk. How much water has been added to pure milk to make the diluted sample?
a.
1 cup of water to 2 cups of pure milk
b.
3 cups of water to 2 cups of pure milk
c.
1 cup of water to 3 cups of pure milk
d.
2 cups of water to 3 cups of pure milk
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Consider the reaction $N_{2}(\,g) + 3H_{2}(\,g)\rightleftharpoons 2NH_{3}(\,g)$ The equilibrium constant of the above reaction is $K_{P}$ . If
pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that
$P_{NH_{3}} << P_{total\,}$ at equilibrium)
a.
$\frac{3^{3/2}\,K^{1/2}_{P}P^{2}}{16}$
b.
$\frac{K_{P}}{16}^{1/2P2}$
c.
$\frac{K_{P}}{4}^{1/2P2}$
d.
$\frac{3^{3/2}\,K^{1/2}_{P}P^{2}}{4}$
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A solid having density of $9 \times 10^{3}\,kg\,m^{-3}$ forms face centred cubic crystals of edge length $200\sqrt{2}pm.$ What is
the molar mass of the solid? [Avogadro constant $≈6 \times 10^{23}\,mol^{-1},\pi ≈3]$
a.
$0.0432\,kg\,mol^{-1}$
b.
$0.0216\,kg\,mol^{-1}$
c.
$0.0305\,kg\,mol^{-1}$
d.
$0.4320\,kg\,mol^{-1}$
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For the chemical reaction $X\rightleftharpoons Y,$ the standard reaction Gibbs energy depends on temperature $T$ (in $K$ ) as
$\Delta _{r}G^{\circ } ($ in $kJmol^{-1})= 120 - \frac{3}{8}\,T$ The major component of the reaction mixture at $T$ is :
a.
$Y$ if $T = 300K$
b.
$Y$ if $T = 280\,K$
c.
X if $T = 350\,K$
d.
$X$ if $T = 315K$
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An organic compound is estimated through Dumas method and was found to evolve 6 moles of $CO_{2}, 4$ moles
of $H_{2}O$ and 1 mole of nitrogen gas. The formula of the compound is:
a.
$C_{12}H_{8}\,N$
b.
$C_{12}H_{8}\,N_{2}$
c.
$C_{6}H_{8}\,N_{2}$
d.
$C_{6}H_{8}\,N$
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$||$
For the cell $Zn(s) Zn^{2+}(aq)\parallel M^{x+}(aq) M(s),$ different half cells and their standard electrode potentials are
given below:
If $E^{\circ }_{Zn^{2+}/Zn} = -0.76\,V,$ which cathode will give a maximum value of $E_{cell\,}^{0}$ per electron transferred?
a.
$Ag^{+}/Ag$
b.
$Fe^{3+}/Fe^{2+}$
c.
$Au^{3+}/Au$
d.
$Fe^{2+}/Fe$
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The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is $\frac{27}{19}$ .
Then the common ratio of this series is:
a.
$\frac{1}{3}$
b.
$\frac{2}{3}$
c.
$\frac{2}{9}$
d.
$\frac{4}{9}$
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Let $a= \hat{i}+ 2\hat{j}+ 4\hat{k}, \vec{b}= \hat{i}+\lambda \hat{j}+ 4\hat{k}$ and $\vec{c}= 2\hat{i}+ 4\hat{j}+(\lambda ^{2} -1)\hat{k}$ be coplanar vectors. Then the non-zero
vector $\vec{a}\times \vec{c}$ is:
a.
$-10\hat{i}-5\hat{j}$
b.
$-14\hat{i}-5\hat{j}$
c.
$-14\hat{i}+ 5\hat{j}$
d.
$-10\hat{i}+ 5\hat{j}$
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The direction ratios of normal to the plane through the points (0,-1,0) and (0,0,1) and making an angle $\frac{\pi}{4}$ with
the plane $y- z+ 5 = 0$ are; 2,-1,1 $2, \sqrt{2}- \sqrt{2}\sqrt{2}, 1, -1 2, 1, -1\sqrt{3}$
a.
option 1 and 2
b.
option 2 and 3
c.
option 3 and 4
d.
all the options
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The plane containing the line $\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z-1}{3}$ and also containing its projection on the plane
$2x + 3y -z = 5$ , contains which one of the following points?
a.
(2,2,0)
b.
(-2,2,2)
c.
(0,-2,2)
d.
(2,0,-2)
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The value of the integral $\int _{-2}^{2} \frac{sin^{2}x}{[^{x}_{\pi }]+^{1}}_{2} dx$ (where $[x]$ denotes the greatest integer less than or equal to x) is
a.
0
b.
$sin 4$
c.
4
d.
$4 -sin 4$
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Two integers are selected at random from the set ${1, 2, … , 11}$ . Given that the sum of selected numbers is
even, the conditional probability that both the numbers are even is :
a.
$\frac{7}{10}$
b.
$\frac{1}{2}$
c.
$\frac{2}{5}$
d.
$\frac{3}{5}$
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A square is inscribed in the circle $x^{2} +y^{2} -6x+ 8y-103 = 0$ with its sides parallel to the coordinate axes.
Then the distance of the vertex of this square which is nearest to the origin is:
a.
6
b.
$\sqrt{137}$
c.
$\sqrt{41}$
d.
13
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If tangents are drawn to the ellipse $x^{2} + 2y^{2} = 2$ at all points on the ellipse other than its four vertices then the
mid points of the tangents intercepted between the coordinate axes lie on the curve :
a.
$\frac{1}{4x^{2}} + \frac{1}{2y^{2}} = 1$
b.
$\frac{x^{2}}{4} + \frac{y^{2}}{2} = 1$
c.
$\frac{1}{2x^{2}} + \frac{1}{4y^{2}} = 1$
d.
$\frac{x^{2}}{2} + \frac{y^{2}}{4} = 1$
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Two circles with equal radii are intersecting at the points (0,1) and (0,-1) . The tangent at the point (0,1) to one
of the circles passes through the centre of the other circle. Then the distance between the centres of these
circles is:
a.
1
b.
2
c.
$2\sqrt{2}$
d.
$\sqrt{2}$
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If $\int \frac{\sqrt{1-x^{2}}}{x^{4}}dx=A(x)(\sqrt{1 -x^{2}})^{m} +C,$ for a suitable chosen integer $m$ and a function $A(x)$ , where $C$ is a
constant of integration, then $(A(x))^{m}$ equals :
a.
$\frac{-1}{27x^{9}}$
b.
$\frac{-1}{3x^{3}}$
c.
$\frac{1}{27x^{6}}$
d.
$\frac{1}{9x^{4}}$
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In a triangle, the sum of lengths of two sides is $x$ and the product of the lengths of the same two sides is $y$ . if
$x^{2} - c^{2} =y,$ where $c$ is the length of the third side of the triangle, then the circumradius of the triangle is
a.
$\frac{3}{2}y$
b.
$\frac{c}{\sqrt{3}}$
c.
$\frac{c}{3}$
d.
$\frac{y}{\sqrt{3}}$
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Let $[x]$ denote the greatest integer less than or equal to $X$ . Then : $lim_{x\rightarrow 0\rightarrow } \frac{tan(\pi sin^{2}x)+(|x|-sin(x[x]))^{2}}{x^{2}}$
a.
does not exist
b.
equals $\pi$
c.
equals $\pi + 1$
d.
equals 0
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The outcome of each of 30 items was observed; 10 items gave an outcome $\frac{1}{2} -d$ each, 10 items gave outcome
$\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$ then
$|d|$ equals:
a.
$\frac{2}{3}$
b.
2
c.
$\frac{\sqrt{5}}{2}$
d.
$\sqrt{2}$
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The straight line $x+ 2y= 1$ meets the coordinate axes at $A$ and $B$ . A circle is drawn through $A, B$ and the
origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is:
a.
$\frac{\sqrt{5}}{2}$
b.
$2\sqrt{5}$
c.
$\frac{\sqrt{5}}{4}$
d.
$4\sqrt{5}$
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