Charges $Q_{1}$ and $Q_{2}$ are at points $A$ and $B$ of a right-angled triangle $OAB$ . The resultant electric field at point
$O$ is perpendicular to the hypotenuse, then $Q_{1}/Q_{2}$ is proportional to:
a.
$\frac{x^{3}_{1}}{x^{3}_{2}}$
b.
$\frac{x_{2}}{x_{1}}$
c.
$\frac{x_{1}}{x_{2}}$
Correct Answer
d.
$\frac{x^{2}_{2}}{x^{2}_{1}}$
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Q2mcq
Four point masses, each of mass $m$ , are fixed at the corners of a square of side I. The square is rotating with
angular frequency $\omega ,$ about an axis passing through one of the corners of the square and parallel to tis diagonal,
as shown in the figure. The angular momentum of the square about the axis is
a.
$m\ell ^{2}\omega$
b.
$4m\ell ^{2}\omega$
c.
$3m\ell ^{2}\omega$
Correct Answer
d.
$2m\ell ^{2}\omega$
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Q3mcq
If the potential energy between two molecules is given by $U = \frac{A}{r^{6}} + \frac{B}{r^{12}},$ then at equilibrium, separation
between molecules, and the potential energy are:
A sound source S is moving along a straight track with speed $v$ , and is emitting sound of frequency $v_{0}$ .An
observer is standing at a finite distance, at the point $O,$ from the track. The time variation of frequency heard by
observer is best represented by : (to represents the instant when the distance between the source and observer is
minimum)
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Q5nat
Suppose that intensity of a laser is $(\frac{315}{\pi})\,W\,m^{-2}.$ The rms electric field, in units of $V\,m^{-1}$ associated with this
source is close to the nearest integer is $-(\epsilon _{0} = 8. 86 \times 10^{-12}\,C^{2}\,N\,m^{-2}; \,c = 3 \times 10^{8}\,m\,s^{-1})$
✓ Accepted Answer:275
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Q6mcq
For the given input voltage waveform $V_{in\,}(t),$ the output voltage waveform $V_{0}(t),$ across the capacitor is
correctly depicted by :
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Q7mcq
An insect is at the bottom of a hemispherical ditch of radius $1m$ . It crawls up the ditch but starts slipping after it
is at height h from the bottom. If the coefficient of friction between the ground and the insect is $0. 75,$ then $h$ is
$:(g= 10\,m\,s^{-2})$
a.
$0. 20\,m$
Correct Answer
b.
$0. 45\,m$
c.
$0. 60\,m$
d.
$0. 80\,m$
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Q8mcq
An electron is moving along $+x$ direction with a velocity of $6 \times 10^{6} ms^{-1}$ . It enters a region of uniform
electric field of $300\,V/cm$ pointing along $+y$ direction. The magnitude and direction of the magnetic field set
up in this region such that the electron keeps moving along the x direction will be:
a.
$3 \times 10^{-4}T,$ along $+z$ direction
b.
$5 \times 10^{-3}T,$ along $-z$ direction
c.
$5 \times 10^{-3}T,$ along $+z$ direction
Correct Answer
d.
$3 \times 10^{-4}T,$ along $-z$ direction
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Q9mcq
A satellite is in an elliptical orbit around a planet $P.$ It is observed that the velocity of the satellite when it is
farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between
the satellite and the planet at closest and farthest points is :
a.
$1 : 6$
Correct Answer
b.
$1 : 3$
c.
$1 : 2$
d.
$3 : 4$
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Q10mcq
A clock has a continuously moving second's hand of $0. 1m$ length. The average acceleration of the tip of the
hand (in units of $ms^{-2}$ ]) is of the order of :
a.
$10^{-3}$
Correct Answer
b.
$10^{-4}$
c.
$10^{-2}$
d.
$10^{-1}$
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A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale
marking, prior to use. Upon one complete rotation of the circular scale, a displacement of $0. 5 mm$ is noticed
on the pitch scale. The nature of zero error involved and the lest count of the screw gauge, are respectively:
a.
Negative, $2\mu m$
b.
Positive $10\mu m$
c.
Positive $0. 1mm$
d.
Positive, $0. 1\mu m$
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Shown in the figure is a hollow ice-cream cone (it is open at top). If its mass is $M$ , radius of its top is $R$ and
height, $H$ , then its moment of inertia about its axis is
a.
$\frac{MR^{2}}{2}$
b.
$\frac{M(R^{2}+H^{2})}{4}$
c.
$\frac{MH^{2}}{3}$
d.
$\frac{MR^{2}}{3}$
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A part of a complete circuit is shown in the figure. At some instant, the value of current I is $1A$ and it is
decreasing at a rate of $10^{2} As^{-1}$ . The value of the potential difference $V_{p}-V_{Q},$ (in volts) at that instant is-
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You are given that $^{7}_{3}Li = 7. 0160u,$ Mass of Mass of $^{4}_{2}He = 4. 0026u$ and Mass of $^{1}_{1}He = 1. 0079H$ When $20g$
of $^{7}_{3}Li$ is converted into He by proton capture, the energy liberated, (in $^{4}_{2} kWh$ ), is : [Mass of nucleon
$= 1 GeV /c^{2}$ ]
a.
$4. 5 \times 10^{5}$
b.
$8 \times 10^{6}$
c.
$6. 82 \times 10^{5}$
d.
$1. 33 \times 10^{6}$
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Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a
temperature of T. The total internal energy, U of a mole of this gas, and the value of $\gamma =(\frac{C_{p}}{C_{v}})$ are given,
respectively, by
a.
$U = \frac{5}{2}RT$ and $\gamma = \frac{6}{5}$
b.
$U = 5\,R T$ and $\gamma = \frac{7}{5}$
c.
$U = \frac{5}{2}RT$ and $\gamma = \frac{7}{5}$
d.
$U = 5RT$ and $\gamma = \frac{6}{5}$
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A particle of charge $q$ and mass $m$ is moving with a velocity $-vˆi(v\neq 0)$ towards a large screen placed in the
$Y - Z$ plane at distance d. If there is magnetic field $\vec{B}=B_{0}ˆk,$ the minimum value of $v$ for which the particle
will not hit the screen is :
a.
$\frac{qdB_{0}}{3m}$
b.
$\frac{2qdB_{0}}{m}$
c.
$\frac{qdB_{0}}{m}$
d.
$\frac{qdB_{0}}{2m}$
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A point like object is placed at distance of $1m$ in front of a convex lens of focal length $0. 5m$ . A plane mirror is
placed at a distance of $2m$ behind the lens. The position and nature of the image formed by the system is
a.
$2. 6m$ from the mirror, real
b.
$1m$ from the mirror, virtual
c.
$1m$ from the mirror, real
d.
$2. 6m$ from the mirror, virtual
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An electron, a doubly ionized helium ion ( $He^{++}$ ) and proton are having the same kinetic energy. The relation
between their respective de-Broglie wavelength $\lambda _{e^{*}}\lambda _{He^{++}}$ and $\lambda _{p}$ is :
a.
$\lambda _{e} >\lambda _{He^{++}} >\lambda _{p}$
b.
$\lambda _{e} <\lambda _{He^{++}} ==\lambda _{p}$
c.
$\lambda _{e} >\lambda _{p} >\lambda _{He^{++}}$
d.
$\lambda _{e} <\lambda _{p} <\lambda _{He^{++}}$
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An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross-section, A. Young
modulus of the material of the wire is $Y$ . If the mass is pulled down slightly its frequency of oscillation along
the vertical direction is :
a.
$f = \frac{1}{2\pi}\sqrt{\frac{mL}{Y A}}$
b.
$f = \frac{1}{2\pi}\sqrt{\frac{Y A}{mL}}$
c.
$f = \frac{1}{2\pi}\sqrt{\frac{mA}{V L}}$
d.
$f = \frac{1}{2\pi}\sqrt{\frac{Y L}{mA}}$
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In the figure below, $P$ and $Q$ are two equally intense coherent sources emitting radiation of wavelength $20m.$
The separation between $P$ and $Q$ is $5m$ and the phase of $P$ is ahead of that of $Q$ by $90^{\circ}. A, B$ and C are three
distinct point of observation, each equidistant from the midpoint of PQ. The intensities of radiation at $A, B, C$
will be in the ratio :
a.
$0 : 1 : 4$
b.
$2 : 1 : 0$
c.
$0 : 1 : 2$
d.
$4 : 1 : 0$
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Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have
a completely inelastic collision and move together thereafter with a final speed which is half of their initial
velocities of the two bodies (in degree) is -
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The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is $(\frac{x}{100})%.$ If
the relative errors in measuring the mass and the diameter are $6. 0%$ and $1. 5%$ respectively, the value of $x$ is $-$
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Initially a gas of diatomic molecules is contained in a cylinder of volume $V_{1}$ at a pressure $P_{1}$ and temperature
$250\,K$ . Assuming that $25%$ of the molecules get dissociated causing a change in number of moles. The
pressure of the resulting gas at temperature $2000\,K,$ when contained in a volume $2V_{1}$ is given by $P_{2}$ . The
ratio $P_{2}/P_{1}$ is -
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Potassium chlorate is prepared by the electrolysis of $KCl$ in basic solution
$6 OH^{-} + Cl^{-} ClO^{-}_{3} + 3H_{2}O + 6e^{-}$ . If only $60%$ of the current is utilized in the reaction, the time
(rounded to the nearest hour) required to produce $10g$ of $KClO_{3}$ using a current of $2A$ is $… … . .$ (Given :
$F = 96, \,500C\vec{m}ol$ ; molar mass of $KClO_{3} = 122\,g\, mol^{-1}$ )
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The elevation of boiling point of $0. 10m$ aqueous $CrCl_{3}. xNH_{3}$ solution is two times that of $0. 05\,m$ aqueous
$CaCl_{2}$ solution. The value of $x$ is $… … … … . .$
[Assume $100%$ ionisation of the complex and $CaCl_{2},$ coordination number of $Cr$ as $6,$ and that all $NH_{3}$
molecules are present inside the coordination sphere]
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The variation of equilibrium constant with temperature is given below :
$Temperature EquilibriumConstant$
$T_{1} = 25^{\circ}C K_{1} = 10$
$T_{2} = 100^{\circ}C K_{2} = 100$
The values of $\Delta H^{\circ}, \,\Delta G^{\circ}$ at $T_{1}$ and $\Delta G^{\circ}$ at $T_{2}$ (in $kJ \, mol^{-1}$ ) respectively, are close to [use
$R = 8. 314 JK^{-1} mol^{-1}$ ]
a.
$28. 4, -7. 14\,and\, -5. 71$
b.
$0. 64, -7. 14\,and\, -5. 71$
c.
$28. 4, -5. 71\,and\, -14. 29$
d.
$0. 64, -5. 71\, and \, -14. 29$
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A solution of two components containing $n_{1}$ moles of the $1^{st\,}$ component and $n_{2}$ moles of the $2^{nd\,}$ component
is prepared. $M_{1}$ and $M_{2}$ are the molecular weights of component 1 and 2 respectively. If $d$ is the density of the
solution in $gmI^{-1}, \,C_{2}$ is the molarity and $x_{2}$ is the mole fraction of the $2^{nd\,}$ component, then $C_{2}$ can be
expressed as :
In an estimation of bromine by Carius method, $1. 6g$ of an organic compound gave $1. 88g$ of $AgBr$ . The mass
percentage of bromine in the compound is $… . .$
$($ Atomic mass, $Ag = 108, \,Br = 80\, gmol^{-1}$
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Consider the following reactions
$A \rightarrow P1; B \rightarrow P2; C \rightarrow P3; D \rightarrow P4\rightarrow \rightarrow \rightarrow \rightarrow$
The order of the above reactions are $a, \,b, \,c\, and \,d,$ respectively. The following graph is obtained when
log[rate] vs.log[conc.] are plotted:
Among the following, the correct sequence for the order of the reactions is :
a.
$d > a > b > c$
b.
$a > b > c > d$
c.
$c > a > b > d$
d.
$d > b > a > c$
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Consider the Assertion and Reason given below.
Assertion (A) : Ethene polymerized in the presence of Ziegler Natta Catalyst at high temperature and pressure
is used to make buckets and dustbins.
Reason (R) : High density polymers are closely packed and are chemically inert. Choose the correct answer
from the following:
a.
(A) is correct but (R) is wrong.
b.
Both (A) and (R) are correct but (R) is not the
correct explanation of (A).
c.
Both (A) and (R) are correct and (R) is the
correct explanation of (A).
d.
(A) and (R) both are wrong.
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A spherical balloon of radius $3\, cm$ containing helium gas has a pressure of $48 \times 10^{-3}$ bar. At the
same temperature, the pressure, of a spherical balloon of radius $12\, cm$ containing the same amount of gas will
be $… … … … . \times 10^{-6}$ bar.
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If $\Sigma ^{n} (x_{i}- a) =n$ and $\Sigma ^{n} (x_{i}- a)^{2} =na, \,(n, \,a> 1)$ , then the standard deviation of $n$ observations
$i=1 i=1$
$x_{1}, \,x_{2}, \, … ,x_{n}$ is
a.
$a-1$
b.
$n\sqrt{(a-1)}$
c.
$\sqrt{n(a-1)}$
d.
$\sqrt{(a-1)}$
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If $\alpha$ and $\beta$ be two roots of the equation $x^{2} -64x+ 256 = 0.$ Then the value of $( \frac{\alpha ^{3}}{\beta ^{5}})\frac{1}{8} +(\frac{\beta ^{3}}{\alpha ^{5}})\frac{1}{8}$ is :
a.
$2$
b.
$3$
c.
$1$
d.
$4$
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If $I_{1} =\int _{0}^{1} (1 - x^{50})^{100}dx$ and $I_{2} =\int _{0}^{1} (1 - x^{50})^{101}dx$ such that $I_{2} =\alpha I_{1}$ then $\alpha$ equals to :
a.
$\frac{5049}{5050}$
b.
$\frac{5050}{5049}$
c.
$\frac{5050}{5051}$
d.
$\frac{5051}{5050}$
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The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the
hill is found to be $45^{\circ}$ . After walking a distance of $80$ meters towards the top, up a slope inclined at angle of
$30^{\circ}$ to the horizontal plane the angle of elevation of the top of the hill becomes $75^{\circ}$ . Then the height of the hill
(in meters) is _____.
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$cos^{2} x 1 + sin^{2} x sin 2x$
Let m and M be respectively the minimum and maximum value values of $1 + cos^{2} x sin^{2} x sin 2x$
$cos^{2} x sin^{2} x 1 + sin 2x$
Then the ordered pair (m, M) is equal to:
a.
$(3, 3)$
b.
$(-3, -1)$
c.
$(4, 1)$
d.
$(1, 3)$
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Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the
ellipse, $\frac{x^{2}}{4} + \frac{y^{2}}{2} = 1$ from any of its foci?
a.
$(-2, \sqrt{3})$
b.
$(-1, \sqrt{2})$
c.
$(-1, \sqrt{3})$
d.
$(1, 2)$
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Two families with three members each and one family with four members are to be seated in a row. In how
many ways can they be seated so that the same family members are not separated ?
a.
$2!\,3!\,4!$
b.
$(3!)^{3} \cdot (4!)$
c.
$\,(3!)2. (4!)$
d.
$\,3!\,(4!)^{3}$
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The position of a moving car at time $t$ is given by $f(t)=at^{2} +bt+c, \,t> 0$ , where $a, \,b\,and\,c$ are real
numbers greater than $1$ . Then the average speed of the car over the time interval $[t_{1},t_{2}]$ is attained at the point:
a.
$\frac{(t_{2}-t_{1})}{2}$
b.
$a(t_{2}- t_{1}) +b$
c.
$\frac{(t_{1}+t_{2})}{2}$
d.
$2a(t_{1}+t_{2}) +b$
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Out of 11 consecutive natural number if three numbers are selected at random (without repetition), then the
probability that they are in A.P. with positive common difference is :
a.
$\frac{15}{101}$
b.
$\frac{5}{101}$
c.
$\frac{5}{33}$
d.
$\frac{10}{99}$
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$\{x^{5} sin(\frac{1}{x} )+ 5x^{2} , x< 0$
Let $f :R\rightarrow \rightarrow R$ be defined as $f(x) = 0 , x= 0$ . The value of $\lambda$ for which $f''(0)$ exists,
$\{_{5}_{2}$
$x cos( \frac{1}{x})+\lambda x , x> 0$
is___.
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Let $AD$ and $BC$ be two vertical poles at $A\,and\,B$ respectively on a horizontal ground. If $AD= 8m$ ,
$BC = 11m$ , $AB = 10m;$ then the distance (in meters) of a point $M$ lying in between $AB$ from the point $A$
such that $MD^{2} + MC^{2}$ is minimums, is__
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A ray of light coming from the point $(2, 2\sqrt{3})$ is incident at an angle $30^{\circ}$ on the line $x= 1$ at the point $A$ . The
ray gets reflected on the line $x= 1$ and meets $x$ -axis at the point $B$ . Then, the line $AB$ passes through the
point
a.
$(3, -\frac{1}{\sqrt{3}} )$
b.
$(4, -\frac{\sqrt{3}}{2})$
c.
$(3, -\sqrt{3})$
d.
$(4, -\sqrt{3})$
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Set $A$ has $m$ elements and set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total
number of subsets of $B$ , then the value of $m\cdot n$ is___.
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If $f(x+y) =f(x)\,f(y)$ and $\Sigma ^{\infty } f(x) = 2, \,x,y\in N$ , where $N$ is the set of all natural numbers, then the value
$x=1$
of $\frac{f(4)}{f(2)}$ is
a.
$\frac{2}{3}$
b.
$\frac{1}{9}$
c.
$\frac{1}{3}$
d.
$\frac{4}{9}$
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Let $L_{1}$ be a tangent to the parabola $y^{2} = 4(x+ 1)$ and $L_{2}$ be a tangent to the parabola $y^{2} = 8(x+ 2)$ such
that $L_{1}$ and $L_{2}$ intersect at right angles. Then $L_{1}$ and $L_{2}$ meet on the straight line:
a.
x + 3 = 0
b.
2x + 1 = 0
c.
x + 2 = 0
d.
x + 2y = 0
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The values of $\lambda$ and $\mu$ for which the system of linear equations $x+y+z= 2$ , $x+ 2\,y+ 3\,z= 5$ ,
$x+ 3y+\lambda z=\mu$ has infinitely many solutions, are respectively
a.
6 and 8
b.
5 and 7
c.
5 and 8
d.
4 and 9
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