A $1\, kg$ block attached to a spring vibrates with a frequency of $1\, Hz$ on a frictionless horizontal table. Two
springs identical to the original spring are attached in parallel to a $\,8\, kg \,$ block placed on the same table. So, the
frequency of vibration of the $8\, kg$ block is
a.
$2\, Hz$
b.
$\frac{1}{4}\, Hz$
c.
$\frac{1}{2\sqrt{2}}\, Hz$
d.
$\frac{1}{2}\, Hz$
Correct Answer
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Q2mcq
A small circular loop of wire of radius $a$ is located at the centre of a much larger circular wire loop of radius $b$ .
The two loops are in the same plane. The outer loop of radius $b$ carries an alternating current $I =I_{0}cos(\omega t).$
The emf induced in the smaller inner loop is nearly:
If the Earth has no rotational motion, the weight of a person on the equator is $W$ . Determine the speed with
which the earth would have to rotate about its axis so that the person at the equator will weigh $\frac{3}{4} W$ . The radius
of the Earth is $6400\, km$ and $g= 10\,m\,s^{-2}$
a.
$0.63 \times 10^{-3}\,rad\,s^{-1}$
Correct Answer
b.
$0.28 \times 10^{-3}\, rad \,s^{-1}$
c.
$1.1 \times 10^{-3}\, rad \,s^{-1}$
d.
$0.83 \times 10^{-3}\, rad \,s^{-1}$
No explanation saved for this question yet.
Q4mcq
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $10\,s^{-1}.$ At, $t= 0$ the
displacement is $5\,m.$ What is the maximum acceleration? The initial phase is $\frac{\pi}{4}$ .
a.
$500\,m\,s^{-2}$
b.
$750\,m\,s\sqrt{2}^{-2}$
c.
$750\,m\,s^{-2}$
d.
$500\,m\,s\sqrt{2}^{-2}$
Correct Answer
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Q5mcq
Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?
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Q6mcq
The energy stored in the electric field produced by a metal sphere is $4. 5\,J$ . If the sphere contains $4\,$ $\mu$ $C$ charge,
its radius will be: $[Take : \frac{1}{4\pi \in _{0}} = 9 \times 10^{9}\,N\,m^{2}\,C^{-2}]$
a.
$32\, mm$
b.
$16\, mm$
Correct Answer
c.
$28\, mm$
d.
$20\, mm$
No explanation saved for this question yet.
Q7mcq
Two deuterons undergo nuclear fusion to form a Helium nucleus. The energy released in this process is (given
binding energy per nucleon for deuteron $= 1.1\, MeV$ and for helium $= 7.0\, MeV$ )
a.
$23.6\, MeV$
Correct Answer
b.
$30.2\, MeV$
c.
$25.8\, MeV$
d.
$32.4\, MeV$
No explanation saved for this question yet.
Q8mcq
Two wires $W_{1}$ and $W_{2}$ have the same radius $r$ and respective, densities $\rho _{1}$ and $\rho _{2}$ , such that $\rho _{2} = 4\rho _{1}$ . They
are joined together at the point $O$ , as shown in the figure. The combination is used as a sonometer wire and
kept under tension $T$ . The point $O$ is midway between the two bridges. When a stationary wave is set up in the
composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in $W_{1}$ to $W_{2}$ is
a.
$4 : 1$
b.
$1 : 2$
Correct Answer
c.
$1 : 1$
d.
$1 : 3$
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Q9mcq
There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$ ,
in the region, is found to vary between the limits $589. 0\,V$ to $\,589. 8\,V$ . What is the potential at a point on the
sphere whose radius vector makes an angle of $60^{\circ}$ with the direction of the field?
a.
$589. 4\,V$
b.
$589. 5\,V$
c.
$589. 2\,V$
d.
$589. 6\,V$
Correct Answer
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Q10mcq
A signal of frequency $20\, kHz$ and peak voltage of $5\, Volt \,$ is used to modulate a carrier wave of frequency
$1. 2\, MHz \,$ and peak voltage $25\, Volts$ . Choose the correct statement.
a.
Modulation index $= 5$ , side frequency bands are
at $1400\, kHz \, and \,1000\, kHz$ .
b.
Modulation index $= 5$ , side frequency bands are
at $21. 2\, kHz \, and \,18. 8\, kHz$ .
c.
Modulation index $= 0. 2$ , side frequency bands
are at $1220\, kHz \, and \,1180\, kHz$ .
Correct Answer
d.
Modulation index $= 5$ , side frequency bands are
at $24. 2\, kHz \, and \,18. 8\, kHz$ .
No explanation saved for this question yet.
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An object is dropped from a height $h$ from the ground. Every time it hits the ground it loses $50%$ of its kinetic
energy. The total distance covered as $t\rightarrow \infty \rightarrow$ is:
a.
$3h$
b.
$\infty$
c.
$\frac{5}{3} h$
d.
$\frac{8}{3} h$
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Time $(T)$ , velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length
and time. In terms of these, the dimensions of mass would be:
a.
$[M] =[T^{-1}C^{-2}h]$
b.
$[M]=[T^{-1}C^{2}h]$
c.
$[M] =[T^{-1}C^{-2}h^{-1}]$
d.
$[M]=[TC^{-2} h]$
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Moment of inertia of an equilateral triangular lamina $ABC$ , about the axis passing through its centre $O$ and
perpendicular to its plane is $I_{0}$ as shown in the figure. A cavity $DEF$ is cut out from the lamina, where
$D, \,E, \,F$ are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis
is:
a.
$\frac{7}{8} I_{0}$
b.
$\frac{15}{16}I_{0}$
c.
$\frac{3}{4} I_{0}$
d.
$\frac{31I_{0}}{32}$
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The maximum velocity of the photoelectrons emitted from the surface is $v$ when light of frequency $n$ falls on a
metal surface. If the incident frequency is increased to $3n$ , the maximum velocity of the ejected photoelectrons
will be:
a.
more than $\sqrt{3}v$
b.
equal to $\sqrt{3}v$
c.
$v$
d.
less than $\sqrt{3}v$
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A uniform disc of radius $R$ and mass $M$ is free to rotate only about its axis. A string is wrapped over its rim and
a body of mass $m$ is tied to the free end of the string as shown in the figure. The body is released from rest.
Then the acceleration of the body is:
a.
$\frac{2\,Mg}{2m+M}$
b.
$\frac{\,2 Mg}{2M+m}$
c.
$\frac{2\,mg}{2M+m}$
d.
$\frac{2\,mg}{2m+M}$
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In a physical balance working on the principle of moments, when $5 mg$ weight is placed on the left pan, the
beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following
statements is correct?
a.
Every object that is weighed using this balance
appears lighter than its actual weight
b.
Left arm is shorter than the right arm
c.
Both the arms are of same length
d.
Left arm is longer than the right arm
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In a certain region static electric and magnetic fields exist. The magnetic field is given by
$\vec{B}=B_{0}(ˆi + 2ˆj -4ˆk)$ . If a test charge moving with a velocity $\vec{v}=v_{0}(3ˆi -ˆj + 2ˆk)$ experiences no force in
that region, then the electric field in the region, in SI units, is:
a.
$\vec{E} = \, - v_{0} B_{0}(ˆi +ˆj + 7ˆk)$
b.
$\vec{E} = \, - υ_{0} B_{0}(3ˆi -2ˆj -4ˆk)$
c.
$\vec{E} = \,v_{0} B_{0}(14ˆj + 7ˆk)$
d.
$\vec{E} = -v_{0} B_{0}(14ˆj + 7ˆk)$
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A $9\,V$ battery with an internal resistance of $0.5\,\Omega$ is connected across an infinite network, as shown in the
figure. All ammeters $A_{1}, \,A_{2}, \,A_{3}$ and voltmeter $V$ are ideal.
Choose the correct statement.
a.
Reading of $A_{1}$ is $18\,A$ .
b.
Reading of $V$ is $9\,V$ .
c.
Reading of $V$ is $7\,V$ .
d.
Reading of $A_{1}$ is $2\,A$ .
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Let the refractive index of a denser medium with respect to rarer medium be $n_{12}$ and its critical angle be $\theta _{C}$ .
At an angle of incidence $A$ when light is travelling from denser medium to rarer medium, a part of the light is
reflected and the rest is refracted and the angle between reflected and refracted rays is $90^{o}$ . Angle $A$ is given
by
a.
$tan^{-1}(sin\theta _{C})$
b.
$\frac{1}{tan^{-1}(sin\theta _{C})}$
c.
$cos^{-1}(sin\theta _{C})$
d.
$\frac{1}{cos^{-1}(sin\theta _{C})}$
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A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that
its temperature increases by $\Delta T$ . The net change in its length is zero. Let $l$ be the length of the rod, A its area of
cross-section, $Y$ its Young's modulus, and $\alpha$ its coefficient of linear expansion. Then, $F$ is equal to:
a.
$lAY \alpha \,\Delta T$
b.
$A\,Y\alpha \,\Delta T$
c.
$\frac{AY}{\alpha \Delta T}$
d.
$l^{2}\,Y\alpha \,\Delta T$
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The conductivity of a semiconductor sample having electron concentration of $5 \times 10^{18}\, electrons \,m^{-3}$ , hole
concentration of $5 \times 10^{19}\, holes \,m^{-3}$ , electron mobility of $2 .0 \,m^{2}\,V^{-1}\,s^{-1}$ and hole mobility of
$0. 01\,m^{2}\,V^{-1}\,s^{-1}$ is
(Take charge of an electron as $1 .6 \times 10^{-19}\,C$ )
a.
$1 .83 \,(\Omega \,m)^{-1}$
b.
$1 .65 \,(\Omega \,m)^{-1}$
c.
$1 .20 \,(\Omega \,m)^{-1}$
d.
$0 .59 \,(\Omega \,m)^{-1}$
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In an experiment, a sphere of aluminium of mass $0. 20\, kg$ is heated up to $150^{\circ}C$ . Immediately, it is put into
water of volume $150\, cc \,$ at $27^{o}C$ kept in a calorimeter of water equivalent to $\,0. 025\, kg$ . The final temperature
of the system is $40^{o}C$ . The specific heat of the aluminium is(take $4. 2\,Joule = 1\, calorie$ )
a.
$434\,J\,kg^{-1}^{o}C$
b.
$378\,J\,kg^{-1}^{\circ}C$
c.
$315\,\,J\,kg^{-1}^{o}C$
d.
$476\,\,J\,kg^{-1}^{o}C$
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A single slit of width $b$ is illuminated by a coherent monochromatic light of wavelength $\lambda .$ If the second and
fourth minima in the diffraction pattern at a distance $1\, cm$ from the slit are at $3\, cm$ and $6\, cm$ respectively
from the central maximum, what is the width of the central maximum? (i.e. distance between first minimum on
either side of the central maximum)
a.
$4. 5\, cm$
b.
$1. 5\, cm$
c.
$6. 0\, cm$
d.
$3. 0\, cm$
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An engine operates by taking $n$ moles of an ideal gas through the cycle $ABCDA$ shown in figure. The thermal
efficiency of the engine is:
(Take $C_{v} = 1.5R$ , where $R$ is gas constant)
a.
$0. 24$
b.
$0. 15$
c.
$0. 32$
d.
$0. 08$
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A potentiometer $PQ$ is set up to compare two resistances, as shown in the figure. The ammeter $A$ in the circuit
reads $1. 0\,A\,$ when the two-way key $K_{3}$ is open. The balance point is at a length $l_{1}\, cm$ from $P$ when the two-
way key $K_{3}$ is plugged in between $2\, and \,1$ , while the balance point is at a length $l_{2}\, cm$ from $P$ when the key
$K_{3}$ is plugged in between $3\, and \,1$ . The ratio of two resistances $\frac{R_{1}}{R_{2}} ,$ is found to be
a.
$\frac{l_{1}}{l_{1}-l_{2}}$
b.
$\frac{l_{2}}{l_{2}-l_{1}}$
c.
$\frac{l}{l_{1}+l_{2}}^{1}$
d.
$\frac{l}{l_{2}-l_{1}}^{1}$
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According to Bohr's theory, the time averaged magnetic field at the centre (i.e., nucleus) of a hydrogen atom
due to the motion of electrons in the $n^{th}$ orbit is proportional to: ( $n=$ principal quantum number)
a.
$n^{-3}$
b.
$n^{-2}$
c.
$n^{-4}$
d.
$n^{-5}$
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Magnetic field in a plane electromagnetic wave is given by,
$\vec{B}=B kx+\omega t)ˆj\,T$ . Expression for corresponding electric field will be:
$_{0}sin($
(Where $c$ is speed of light)
An ideal gas has molecules with $5$ degrees of freedom. The ratio of specific heats at constant pressure $(C_{p})$ and
at constant volume $(C_{V})$ is:
a.
$\frac{7}{5}$
b.
$6$
c.
$\frac{7}{2}$
d.
$\frac{5}{2}$
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A metal $M\,$ reacts with nitrogen gas to afford $M_{3}N$ , $M_{3}N$ on heating at high temperature gives back $M\,$ and on
reaction with water produces a gas $B$ . Gas $B\,$ reacts with an aqueous solution of $CuSO_{4}$ to form a deep blue
compound. $M\, and \,B$ respectively are
a.
$Li$ and $NH_{3}$ .
b.
$Ba$ and $NH_{3.}$
c.
$Na$ and $N_{2}.$
d.
$Al$ and $N_{2.}$
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The enthalpy change on freezing of $1\, mol$ of water at $5^{\circ}C$ to ice at $-5^{\circ}C$ is:
(Given $\Delta _{fus}\,H = 6\, kJ \, mol^{-1}$ at $0^{\circ}C,$
$C_{p}(H_{2}O, \,l) = 75 .3 \,J\, mol^{-1} K^{-1}$
$C_{p}(H_{2}O, \,s) = 36 .8 \,J\, mol^{-1} K^{-1}$ )
a.
$6 .00 \, kJ \, mol^{-1}$
b.
$5 .81 \, kJ \, mol^{-1}$
c.
$5 .44 \, kJ \, mol^{-1}$
d.
$6 .56 \, kJ \, mol^{-1}$
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Excess of $NaOH \,(aq)$ was added to $100\, mL$ of $FeCl_{3}\,(aq)$ resulting into $2. 14\,g$ of $Fe (OH)_{3}$ . The molarity
of $FeCl_{3}(aq)$ is:
(Given the molar mass of $\,Fe = 56\,g\,mol^{-1}$ and molar mass of $Cl = 35 .5 \,g\, mol^{-1}$ )
a.
$0. 3\,M$
b.
$0. 2\,M$
c.
$0. 6\,M$
d.
$1. 8\,M$
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Consider the following ionization enthalpies of two elements 'A' and 'B'.
Element Ionization enthalphy $(kJ / mol)$
$1^{st} 2^{nd} 3^{rd}$
A 899 1757 14847
B 737 1450 7731
Which of the following statements is correct?
a.
Both 'A' and 'B' belong to group-1 where 'A'
comes below 'B'.
b.
Both 'A' and 'B' belong to group-2 where 'A'
comes below 'B'.
c.
Both 'A' and 'B' belong to group-1 where 'B'
comes below 'A'.
d.
Both 'A' and 'B' belong to group-2 where 'B'
comes below 'A'.
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$5g$ of $Na_{2}SO_{4}$ was dissolved in $x\,g$ of $H_{2}O$ . The change in freezing point was found to be $3 .82^{o} C$ . If
$Na_{2}SO_{4}$ is $81. 5%$ ionised, the value of $x$
( $K_{f}$ for water $= 1 .86^{o} C\, kg \, mol^{-1}$ ) is approximately:
(molar mass of $S = 32\,g\, mol^{-1}$ and that of $Na = 23\,g\, mol^{-1}$ )
a.
$25\,g$
b.
$65\,g$
c.
$15\,g$
d.
$45\,g$
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Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of pH 6. If ionization constant
of HA is $10^{-5}$ , the ratio of salt to acid concentration in the buffer solution will be:
a.
10 : 1
b.
4 : 5
c.
5 : 4
d.
1 : 10
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Consider the following standard electrode potentials ( $E^{o}$ in volts) in aqueous solution:
$Element M^{3+}/M M^{+}/M$
$Al -1.66 +0.55$
$Tl +1.26 -0.34$
Based on these data, which of the following statements is correct?
a.
$Tl^{+}$ is more stable than $Al^{3+}$
b.
$Al^{+}$ is more stable than $Al^{3+}$
c.
$Tl^{3+}$ is more stable than $Al^{3+}$
d.
$Tl^{+}$ is more stable than $Al^{+}$
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A solution containing a period $-IV$ cation gives a precipitate on passing $H_{2}S.$ A solution of this precipitate in
dil. $HCl \,$ produces a white precipitate with $NaOH$ solution and bluish-white precipitate with basic potassium
ferrocyanide. The cation is
a.
$Mn^{2+}$
b.
$Zn^{2+}$
c.
$Ni^{2+}$
d.
$CO^{2+}$
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The rate of a reaction A doubles on increasing the temperature from $\,300\, to \,310\,K$ . By how much, the
temperature of reaction B should be increased from $300\,K$ so that rate doubles if activation energy of the
reaction B is twice to that of reaction A.
a.
$4. 92\,K$
b.
$9. 84\,K$
c.
$19. 67\,K$
d.
$2. 45\,K$
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The coordinates of the foot of the perpendicular from the point $(1, -2, \,1)$ on the plane containing the lines
$\frac{x+1}{6} = \frac{y-1}{7} = \frac{z-3}{8}$ and $\frac{x-1}{3} = \frac{y-2}{5} = \frac{z-3}{7},$ is:
a.
$(2, -4, \,2)$
b.
$(1, \,1, \,1)$
c.
$(0, \,0, \,0)$
d.
$(-1, \,2, -1)$
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The number of real values of $\lambda$ for which the system of linear equations, $2x+ 4y- \lambda z= 0$ , $4x+\lambda y+ 2z= 0$
and $\lambda x+ 2y+ 2z= 0$ , has infinitely many solutions, is:
a.
$3$
b.
$1$
c.
$2$
d.
$0$
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The mean age of $25$ teachers in a school is $40$ years. A teacher retires at the age of $60$ years and a new teacher
is appointed in his place. If the mean age of the teachers in this school now is $39$ years, then the age (in years)
of the newly appointed teacher is
a.
$35$
b.
$40$
c.
$25$
d.
$30$
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Let $p(x)$ be a quadratic polynomial such that $p(0) = 1.$ If $p(x)$ leaves remainder $4$ when divided by $x-1$ and
it leaves remainder $6$ when divided by $x+ 1$ then:
a.
$p(-2) = 19$
b.
$p(2) = 19$
c.
$p(-2) = 11$
d.
$p(2) = 11$
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If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as
in English dictionary, then the position of the word QUEEN is:
a.
$47^{th}$
b.
$45^{th}$
c.
$46^{th}$
d.
$44^{th}$
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Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are
$\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by P or Q but not by R is:
a.
$\frac{39}{64}$
b.
$\frac{21}{64}$
c.
$\frac{9}{64}$
d.
$\frac{15}{64}$
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If two parallel chords of a circle, having diameter $4$ units, lie on the opposite sides of the center and subtend
angles $cos^{-1}(\frac{1}{7})$ and $sec^{-1}(7)$ at the center respectively, then the distance between these chords is:
a.
$\frac{8}{\sqrt{7}}$
b.
$\frac{16}{7}$
c.
$\frac{4}{\sqrt{7}}$
d.
$\frac{8}{7}$
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Consider an ellipse, whose center is at the origin and its major axis is along the $x$ -axis. If its eccentricity is $\frac{3}{5}$
and the distance between its foci is $6$ , then the area (in sq. units) of the quadrilateral inscribed in the ellipse,
with the vertices as the vertices of the ellipse, is:
a.
$32$
b.
$80$
c.
$40$
d.
$8$
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If the common tangents to the parabola, $x^{2} = 4y$ and the circle, $x^{2} +y^{2} = 4$ intersect at the point $P$ , then the
distance of $P$ from the origin (units), is:
a.
$2(3 + 2\sqrt{2})$
b.
$3 + 2\sqrt{2}$
c.
$\sqrt{2}+ 1$
d.
$2(\sqrt{2}+ 1)$
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