Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. Then, compared to the
unwaxed capillary, the angle of contact $\theta$ and the height $h$ upto which water rises change. These changes are :
a.
$\theta$ increases and $h$ also increases
b.
$\theta$ decreases and $h$ also decreases
c.
$\theta$ increases and $h$ decreases
Correct Answer
d.
$\theta$ decreases and $h$ increases
No explanation saved for this question yet.
Q2mcq
In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as
$F = \frac{e^{2}}{4\pi \epsilon _{0}} (\frac{1}{r^{2}} + \frac{\beta}{r^{3}})$ , where $\beta$ is a constant. For this atom, the radius of the $n^{th\,}$ orbit in terms of the Bohr
radius $(a_{0} = \frac{\epsilon _{0}h^{2}}{m\pi e^{2}})$ is :
a.
$r_{n} =a_{0}n- \beta$
b.
$r_{n} =a_{0}n^{2} +\beta$
c.
$r_{n} =a_{0}n^{2} - \beta$
Correct Answer
d.
$r_{n} =a_{0}n+\beta$
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Q3mcq
Which of the four resistances $P,Q,R$ and $S$ generate the greatest amount of heat when a current flows from A
to B ?
a.
$Q$
b.
$S$
Correct Answer
c.
$P$
d.
$R$
No explanation saved for this question yet.
Q4mcq
The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the
container is $1 : 4$ . What fraction of the inner volume of the container should the liquid occupy so that the
volume of the remaining vacant space will be same at all temperatures ?
a.
$2 : 5$
b.
$1 : 4$
Correct Answer
c.
$1 : 64$
d.
$1 : 8$
No explanation saved for this question yet.
Q5mcq
A $70\,kg$ man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground
with a constant force $F$ to raise himself. The center of gravity rises by $0.5\,m$ before he leaps. After the leap the
c.g. rises by another $1\,m$ . The maximum power delivered by the muscles is : (Take $g = 10\,ms^{-2}$ )
a.
$6.26 \times 10^{3}$ Watts at the start
b.
$6.26 \times 10^{3}$ Watts at take off
Correct Answer
c.
$6.26 \times 10^{4}$ Watts at the start
d.
$6.26 \times 10^{4}$ Watts at take off
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Q6mcq
A particle of charge $16 \times 10^{-16}C$ moving with velocity $10\,ms^{-1}$ along $x$ -axis enters a region where magnetic
field of induction $\vec{B}$ is along the $y$ -axis and an electric field of magnitude $10^{4}\vec{V}m^{-1}$ is along the negative $z$ -
axis. If the charged particle continues moving along $x$ -axis, the magnitude of $B$ is :
a.
$16 \times 10^{3}\,Wb\,m^{-2}$
b.
$2 \times 10^{3}\,Wb\,m^{-2}$
c.
$1 \times 10^{3}\,Wb\,m^{-2}$
Correct Answer
d.
$4 \times 10^{3}\,Wb\,m^{-2}$
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Q7mcq
A parallel plate capacitor of area $60\,cm^{2}$ and separation $3\,mm$ is charged initially to $90\mu C$ . If the medium
between the plate gets slightly conducting and the plate loses the charge initially at the rate of $2.5 \times 10^{-8}C/s$ ,
then what is the magnetic field between the plates ?
a.
$2.5 \times 10^{-8}\,T$
b.
$2.0 \times 10^{-7}\,T$
c.
$1.63 \times 10^{-11}\,T$
d.
Zero
Correct Answer
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Q8mcq
Select the correct statement from the following :
a.
Electromagnetic waves cannot travel in vacuum.
b.
Electromagnetic waves are longitudinal waves.
c.
Electromagnetic waves are produced by charges
moving with uniform velocity.
d.
Electromagnetic waves carry both energy and
momentum as they propagate through space.
Correct Answer
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Q9mcq
A thin tube sealed at both ends is $100\,cm$ long. It lies horizontally, the middle $20\,cm$ containing mercury and
two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position,
by what amount will the mercury be displaced ?
(Given : cross-section of the tube can be assumed to be uniform)
a.
$2.95\,cm$
b.
$5.18\,cm$
Correct Answer
c.
$8.65\,cm$
d.
$0.0\,cm$
No explanation saved for this question yet.
Q10mcq
A system of four gates is set up as shown. The 'truth table' corresponding to this system is :
No explanation saved for this question yet.
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A projectile of mass $M$ is fired so that the horizontal range is $4\,km$ . At the highest point the projectile explodes
in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero
initial speed. The horizontal range (distance from point of firing) of the lighter part is :
a.
$16\,km$
b.
$1\,km$
c.
$10\,km$
d.
$2\,km$
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A body of mass ' $m$ ' is tied to one end of a spring and whirled round in a horizontal plane with a constant
angular velocity. The elongation in the spring is $1\,cm$ . If the angular velocity is doubled, the elongation in the
spring is $5\,cm$ . The original length of the spring is :
a.
$15\,cm$
b.
$12\,cm$
c.
$16\,cm$
d.
$10\,cm$
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Electrons are accelerated through a potential difference $V$ and protons are accelerated through a potential
difference $4\,V$ . The de-Broglie wavelengths are $\lambda _{e}$ and $\lambda _{p}$ for electrons and protons respectively. The ratio of
$\frac{\lambda _{e}}{\lambda _{p}}$ is given by: (given $m_{e}$ is mass of electron and $m_{p}$ is mass of proton).
$n$ identical waves each of intensity $I_{0}$ interfere with each other. The ratio of maximum intensities if the
interference is (i) coherent and (ii) incoherent is :
a.
$n^{2}$
b.
$\frac{1}{n}$
c.
$\frac{1}{n^{2}}$
d.
$n$
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A copper wire of length $1.0\,m$ and a steel wire of length $0.5\,m$ having equal cross-sectional areas are joined end
to end. The composite wire is stretched by a certain load which stretches the copper wire by $1\,mm$ . If the
Young's modulii of copper and steel are respectively $1.0 \times 10^{11} Nm^{-2}$ and $2.0 \times 10^{11}Nm^{-2}$ , the total extension
of the composite wire is :
a.
$1.75\,mm$
b.
$2.0\,mm$
c.
$1.50\,mm$
d.
$1.25\,mm$
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$500\,g$ of water and $100\,g$ of ice at $0^{\circ }C$ are in a calorimeter whose water equivalent is $40\,g.10\,g$ of steam at
$100^{\circ }C$ is added to it. Then water in the calorimeter is : (Latent heat of ice $= 80cal/g$ , Latent heat of steam
$= 540cal/g$ )
a.
$580\,g$
b.
$590\,g$
c.
$600\,g$
d.
$610\,g$
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If the time period $t$ of the oscillation of a drop of liquid of density $d$ , radius $r$ , vibrating under surface tension $s$
is given by the formula $t= \sqrt{r^{2}^{b}s^{c}d^{a}^{/2}}$ . It is observed that the time period is directly proportional to $\sqrt{\frac{d}{s}}$ . The
value of $b$ should therefore be :
a.
$\frac{3}{4}$
b.
$\sqrt{3}$
c.
$\frac{3}{2}$
d.
$\frac{2}{3}$
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A boy of mass $20\,kg$ is standing on a $80\,kg$ free to move long cart. There is negligible friction between cart and
ground. Initially, the boy is standing $25\,m$ from a wall. If he walks $10\,m$ on the cart towards the wall, then the
final distance of the boy from the wall will be
a.
$15\,m$
b.
$12.5\,m$
c.
$15.5\,m$
d.
$17\,m$
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Bob of a simple pendulum of length $l$ is made of iron. The pendulum is oscillating over a horizontal coil
carrying direct current. If the time period of the pendulum is $T$ then :
a.
$T < 2\pi \sqrt{\frac{l}{g}}$ and damping is smaller than in air alone.
b.
$T = 2\pi \sqrt{\frac{l}{g}}$ and damping is larger than in air alone.
c.
$T > 2\pi \sqrt{\frac{l}{g}}$ and damping is smaller than in air alone.
d.
$T < 2\pi \sqrt{\frac{l}{g}}$ and damping is larger than in air alone.
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A rectangular loop of wire, supporting a mass $m$ , hangs with one end in a uniform magnetic field $\vec{B}$ pointing
out of the plane of the paper. A clockwise current is set up such that $i>mg/Ba$ , where $a$ is the width of the
loop. Then :
a.
The weight rises due to a vertical force caused by
the magnetic field and work is done on the
system.
b.
The weight do not rise due to vertical for caused
by the magnetic field and work is done on the
system.
c.
The weight rises due to a vertical force caused by
the magnetic field but no work is done on the
system.
d.
The weight rises due to a vertical force caused by
the magnetic field and work is extracted from the
magnetic field.
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A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of $25.5 kVm^{-1}$ . The
density of liquid is $1.26 \times 10^{3}\,kg\,m^{-3}$ . The radius of the drop is (neglect buoyancy).
a.
$4.3 \times 10^{-7}\,m$
b.
$7.8 \times 10^{-7}\,m$
c.
$0.078 \times 10^{-7}\,m$
d.
$3.4 \times 10^{-7}\,m$
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A light ray falls on a square glass slab as shown in the diagram. The index of refraction of the glass, if total
internal reflection is to occur at the vertical face, is equal to :
a.
$\frac{(\sqrt{2}+1)}{2}$
b.
$\sqrt{\frac{5}{2}}$
c.
$\frac{3}{2}$
d.
$\sqrt{\frac{3}{2}}$
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A sonometer wire of length $114\,cm$ is fixed at both the ends. Where should the two bridges be placed so as to
divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$ ?
a.
At $36\,cm$ and $84\,cm$ from one end
b.
At $24\,cm$ and $72\,cm$ from one end
c.
At $48\,cm$ and $96\,cm$ from one end
d.
At $72\,cm$ and $96\,cm$ from one end
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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: The internal energy of a perfect gas is entirely kinetic and
depends only on absolute temperature of the gas and not on its pressure or volume. Statement 2: A perfect gas
is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature
of the gas at constant pressure is lower than that at constant volume.
a.
Statement-1 is true, Statement- 2 is true and
Statement $-2$ is the correct explanation of
Statement-1.
b.
Statement-1 is true, Statement-2 is false.
c.
Statement-1 is true, Statement-2 is true but
Statement-2 is not the correct explanation of
Statement-1.
d.
Statement-1 is false, Statement-2 is true.
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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: Very large size telescopes are reflecting telescopes instead
of refracting telescopes. Statement 2: It is easier to provide mechanical support to large size mirrors than large
size lenses.
a.
Statement-1 is true and Statement-2 is false.
b.
Statement-1 is false and Statement-2 is true.
c.
Statement-1 and statement-2 are true and
Statement-2 is correct explanation for statement-
1.
d.
Statements-1 and statement-2 are true and
Statement-2 is not the correct explanation for
statement-1.
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A particle of mass $2\,kg$ is moving such that at time $t$ , its position, in meter, is given by $\vec{r}(t) = 5\hat{i}-2t^{2}\hat{j}$ . The
angular momentum of the particle at $t= 2s$ about the origin in $kgm^{-2}\,s^{-1}$ is :
a.
$-80\hat{k}$
b.
$(10\hat{i}-16\hat{j})$
c.
$-40\hat{k}$
d.
$40\hat{k}$
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Bond distance in $HF$ is $9.17 \times 10^{-11}\,m$ . Dipole moment of $HF$ is $6.104 \times 10^{-30}Cm$ . The percentage ionic
character in $HF$ will be : (electron charge $= 1.60 \times 10^{-19}C$ )
a.
$61.0%$
b.
$38.0%$
c.
$35.5%$
d.
$41.5%$
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When a small amount of $KMnO_{4}$ is added to concentrated $H_{2}SO_{4}$ , a green oily compound is obtained which
is highly explosive in nature. Compound may be :
a.
$MnSO_{4}$
b.
$Mn_{2}O_{7}$
c.
$MnO_{2}$
d.
$Mn_{2}O_{3}$
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(1) $N_{2}(\,g) + 3H_{2}(\,g)\rightleftharpoons 2NH_{3}(\,g), K_{1}$ (2) $N_{2}(\,g) + O_{2}(\,g)\rightleftharpoons 2NO(g), K_{2}$ (3)
$H_{2}(\,g) + \frac{1}{2}O_{2}(\,g)\rightleftharpoons H_{2}O(g), K_{3}$ The equation for the equilibrium constant of the reaction
$2NH_{3}(\,g) + \frac{5}{2}O_{2}(\,g)\rightleftharpoons 2NO(g) + 3H_{2}O(g),\,$
$(K_{4})$ in terms of $K_{1}, \,K_{2}$ and $K_{3}$ is :
a.
$\frac{K_{1}\cdot K_{2}}{\,K_{3}}$
b.
$\frac{K_{1}\cdot K^{2}_{3}}{\,K_{2}}$
c.
$K_{1}\,K_{2}\,K_{3}$
d.
$\frac{K_{2}\cdot K^{3}_{3}}{\,K_{1}}$
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Vapour pressure of pure benzene is 119 torr and that of toluene is $37.0$ torr at the same temperature. Mole
fraction of toluene in vapour phase which is in equilibrium with a solution of benzene and toluene having a
mole fraction of toluene $0.50$ , will be :
a.
$0.137$
b.
$0.237$
c.
$0.435$
d.
$0.205$
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Given :
$E\frac{o_{1}}{2}_{Cl_{2}/Cl^{-}} = 1.36\,V, E^{o}_{Cr^{3+}/Cr} = -0.74\,V$
$E^{o}_{Cr_{2}O^{2-}_{7}}_{/Cr^{3+}} = 1.33\,V, E^{o}_{MnO^{-}_{4}}_{/Mn^{2+}} = 1.51\,V$
The correct order of reducing power of the species $(Cr, Cr^{3+}, Mn^{2+}$ and $Cl^{-})$ will be:
a.
$Mn^{2+} < Cl^{-} < Cr^{3+} < Cr$
b.
$Mn^{2+} < Cl^{3+} < Cl^{-} < Cr$
c.
$Cr^{3+} < Cl^{-} < Mn^{2+} < Cr$
d.
$Cr^{3+} < Cl^{-} < Cr < Mn^{2+}$
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In a face centred cubic lattice, atoms of A form the corner points and atoms of B form the face centred points.
If two atoms of $A$ are missing from the corner points, the formula of the ionic compound is :
a.
$AB_{3}$
b.
$AB_{4}$
c.
$A_{2}\,B_{5}$
d.
$AB_{2}$
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The rate constant of a zero order reaction is $2.0\times 10^{-2}\,mol\,L^{-1}\,s^{-1}$ . If the concentration of the reactant after
25 seconds is $0.5M$ . What is the initial concentration?
a.
$0.5M$
b.
$1.25M$
c.
$12.5M$
d.
$1.0M$
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Let $\theta _{1}$ be the angle between two lines $2x+ 3y+c_{1} = 0$ and $-x+ 5y+c_{2} = 0$ and $\theta _{2}$ be the angle between
two lines $2x+ 3y+c_{1} = 0$ and $-x+ 5y+c_{3} = 0$ , where $c_{1},c_{2},c_{3}$ are any real numbers : Statement-1: If $c_{2}$
and $c_{3}$ are proportional, then $\theta _{1} =\theta _{2}$ . Statement-2: $\theta _{1} =\theta _{2}$ for all $c_{2}$ and $c_{3}$ .
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is a correct explanation of
Statement-1.
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not a correct explanation of
Statement-1.
c.
Statement-1 is false; Statement- 2 is true.
d.
Statement-1 is true; Statement- 2 is false.
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$A, B, C$ try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets
are $\frac{3}{4}, \frac{1}{2}, \frac{5}{8}$ . The probability that the target is hit by A or B but not by $C$ is :
a.
$21/64$
b.
$7/8$
c.
$7/32$
d.
$9/64$
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If two lines $L_{1}$ and $L_{2}$ in space, are defined by
$L_{1} = {x= \sqrt{\lambda}y+ (\sqrt{\lambda}-1),$
$z= (\sqrt{\lambda}-1)y+ \sqrt{\lambda}}\,and\,$
$L_{2} = {x= \sqrt{\mu}y+ (1 - \sqrt{\mu}),$
$z= (1 - \sqrt{\mu})y+ \sqrt{\mu}}$
then $L_{1}$ is perpendicular to $L_{2}$ , for all nonnegative reals $\lambda$ and $\mu$ , such that :
a.
$\sqrt{\lambda}+ \sqrt{\mu}= 1$
b.
$\lambda \neq \mu$
c.
$\lambda +\mu = 0$
d.
$\lambda =\mu$
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A tangent to the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{2} = 1$ meets $x$ -axis at $P$ and $y$ -axis at $Q$ . Lines $PR$ and $QR$ are drawn such
that OPRQ is a rectangle (where $O$ is the origin). Then $R$ lies on :
a.
$\frac{4}{x^{2}} + \frac{2}{y^{2}} = 1$
b.
$\frac{2}{x^{2}} - \frac{4}{y^{2}} = 1$
c.
$\frac{2}{x^{2}} + \frac{4}{y^{2}} = 1$
d.
$\frac{4}{x^{2}} - \frac{2}{y^{2}} = 1$
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On the sides $AB, BC, CA$ of a $\triangle ABC, 3, 4, 5$ distinct points (excluding vertices $A, B, C$ ) are respectively
chosen. The number of triangles that can be constructed using these chosen points as vertices are :
a.
210
b.
205
c.
215
d.
220
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If the extremities of the base of an isosceles triangle are the points $(2a, 0)$ and $(0,a)$ and the equation of one of
the sides is $x= 2a$ , then the area of the triangle, in square units, is :
a.
$\frac{5}{4}a^{2}$
b.
$\frac{5}{2}a^{2}$
c.
$\frac{25a^{2}}{4}$
d.
$5a^{2}$
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If a curve passes through the point $(2, \frac{7}{2})$ and has slope $(1 - \frac{1}{x^{2}})$ at any point $(x,y)$ on it, then the ordinate of
the point on the curve whose abscissa is $-2$ is :
a.
$-\frac{3}{2}$
b.
$\frac{3}{2}$
c.
$\frac{5}{2}$
d.
$-\frac{5}{2}$
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Let $f$ be a composite function of $x$ defined by $f(u) = \frac{1}{u^{2}+u-2} ,u(x) = \frac{1}{x-1}$ . Then the number of points $x$
where $f$ is discontinuous is :
a.
4
b.
3
c.
2
d.
1
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If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of $\alpha$ for which the vectors $\vec{u}= (\alpha -2)\vec{a}+ \vec{b}$ and
$\vec{v}= (2 + 3\alpha )\vec{a}-3\vec{b}$ are collinear is :
a.
$\frac{3}{2}$
b.
$\frac{2}{3}$
c.
$-\frac{3}{2}$
d.
$-\frac{2}{3}$
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Statement-1: The system of linear equations
$x+ (sin\alpha )y+ (cos\alpha )z= 0$
$x+ (cos\alpha )y+ (sin\alpha )z= 0$
$x-(sin\alpha )y-(cos\alpha )z= 0$
has a non-trivial solution for only one value of $\alpha$ lying in the interval $(0, \frac{\pi}{2})$ . Statement-2: The equation in $\alpha$
$cos\alpha sin\alpha cos\alpha$
$sin\alpha cos\alpha sin\alpha = 0$
$cos\alpha -sin\alpha -cos\alpha$
has only one solution lying in the interval $(0, \frac{\pi}{2} )$
a.
Statement-1 is true, Statement-2 is true,
Statement-2 is not correct explantion for
Statement-1.
b.
Statement-1 is true, Statement-2 is true,
Statement-2 is a correct explantion for
Statement-1.
c.
Statement-1 is true, Statement- 2 is false.
d.
Statememt-1 is false, Statement-2 is true.
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Let $A$ , other than $I$ or $-I$ , be a $2 \times 2$ real matrix such that $A^{2} = I$ , I being the unit matrix. Let $Tr(A)$ be the
sum of diagonal elements of A. Statement-1: $Tr(A) = 0$ Statement-2: $det(A) = -1$
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 true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
d.
Statement-1 is false; Statement- 2 is true.
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The cost of running a bus from A to B is $Rs. (av+b/v)$ where $vkm/h$ is the average speed of the bus. When
the bus travels at $30\,km/h$ , the cost comes out to be Rs. 75 while at $40\,km/h$ , it is Rs. 65. Then the most
economical speed (in km/h) of the bus is :
a.
45
b.
50
c.
60
d.
40
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If the projections of a line segment on the $x,y$ and $z$ -axes in 3-dimensional space are 2, 3 and 6 respectively,
then the length of the line segment is :
a.
12
b.
7
c.
9
d.
6
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