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 : Sky wave signals are used for long distance radio
communication. These signals are in general, less stable than ground wave signals. Statement-2 : The state of
ionosphere varies from hour to hour, day to day and season to season.
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation of
Statement-1.
Correct Answer
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the 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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Q2mcq
A fully charged capacitor $C$ with initial charge $q_{0}$ is connected to a coil of self inductance $L$ at $t= 0$ . The time
at which the energy is stored equally between the electric and the magnetic field is :
a.
$\frac{\pi}{4} \sqrt{LC}$
Correct Answer
b.
$2\pi \sqrt{LC}$
c.
$\sqrt{LC}$
d.
$\pi \sqrt{LC}$
No explanation saved for this question yet.
Q3mcq
A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has
mass $m$ and radius $R$ . Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m$ , if
the string does not slip on the pulley, is
a.
$g$
b.
$\frac{2}{3} \,g$
Correct Answer
c.
$\frac{g}{3}$
d.
$\frac{3}{2} g$
No explanation saved for this question yet.
Q4mcq
A mass $M$ , attached to a horizontal spring, executes S.H.M. with amplitude $A_{1}$ . When the mass $M$ passes
through its mean position then a smaller mass $m$ is placed over it and both of them move together with
amplitude $A_{2}$ . The ratio of $(\frac{A_{1}}{A_{2}})$ is :
a.
$\frac{M+m}{M}$
b.
$(\frac{M}{M+m})^{1/2}$
c.
$(\frac{M+m}{M})^{1/2}$
Correct Answer
d.
$\frac{M}{M+m}$
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Q5mcq
A Carnot engine operating between temperatures $T_{1}$ and $T_{2}$ has efficiency $\frac{1}{6}$ . When $T_{2}$ is lowered by 62 $K$ , its
efficiency increases to $\frac{1}{3}$ . Then $T_{1}$ and $T_{2}$ are, respectively :
a.
$372\,K$ and $330\,K$
b.
$330\,K$ and $268\,K$
c.
$310\,K$ and $248\,K$
d.
$372\,K$ and $310\,K$
Correct Answer
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Q6mcq
Three perfect gases at absolute temperatures $T_{1},T_{2}$ and $T_{3}$ are mixed. The masses of molecules are $m_{1}$ , $m_{2}$
and $m_{3}$ and the number of molecules are $n_{1},n_{2}$ and $n_{3}$ respectively. Assuming no loss of energy, the final
temperature of the mixture is :
A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a
point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During
the journey of the insect, the angular speed of the disc:
a.
continuously decreases
b.
continuously increases
c.
first increases and then decreases
Correct Answer
d.
remains unchanged
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Q8mcq
The transverse displacement $y(x,t)$ of a wave on a string is given by $y(x,t) =e^{-(ax^{2}+bt^{2}+2\sqrt{ab}xt)}$ . This
represents a
a.
wave moving in $-x$ direction with speed $\sqrt{\frac{b}{a}}$
Correct Answer
b.
standing wave of frequency $\sqrt{b}$
c.
standing wave of frequency $\frac{1}{\sqrt{b}}$
d.
wave moving in $+x$ direction with $\sqrt{\frac{a}{b}}$
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Q9mcq
Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}\,m$ . The water velocity as it
leaves the tap is $0.4\,ms^{-1}$ . The diameter of the water stream at a distance $2 \times 10^{-1}\,m$ below the lap is close to :
a.
$7.5 \times 10^{-3}\,m$
b.
$9.6 \times 10^{-3}\,m$
c.
$3.6 \times 10^{-3}\,m$
Correct Answer
d.
$5.0 \times 10^{-3}\,m$
No explanation saved for this question yet.
Q10mcq
A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading :
$0\,mm$ Circular scale reading : 52 divisions Given that $1\,mm$ on main scale corresponds to 100 divisions of the
circular scale. The diameter of wire from the above date is :
a.
$0.052\,cm$
Correct Answer
b.
$0.026\,cm$
c.
$0.005\,cm$
d.
$0.52\,cm$
No explanation saved for this question yet.
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A car is fitted with a convex side-view mirror of focal length $20\,cm$ . A second car $2.8\,m$ behind the first car is
overtaking the first car at relative speed of $15\,m/s$ . The speed of the image of the second car as seen in the
mirror of the first one is :
a.
$\frac{1}{15}\,m/s$
b.
$10\,m/s$
c.
$15\,m/s$
d.
$\frac{1}{10} \,m/s$
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A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is
$v$ , the total area around the fountain that gets wet is :
a.
$\pi \frac{v^{4}}{g^{2}}$
b.
$\frac{\pi}{2} \frac{v^{4}}{g^{2}}$
c.
$\pi \frac{v^{2}}{g^{2}}$
d.
$\pi \frac{v^{4}}{g}$
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Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $\omega$ along the $x$ -
axis. Their mean position is separated by distance $X_{0}(X_{0} >A)$ . If the maximum separation between them is
$(X_{0}+A)$ , the phase difference between their motion is :
a.
$\frac{\pi}{3}$
b.
$\frac{\pi}{4}$
c.
$\frac{\pi}{6}$
d.
$\frac{\pi}{2}$
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A resistor 'R' and $2\mu F$ capacitor in series is connected through a switch to $200\,V$ direct supply. Across the
capacitor is a neon bulb that lights up at $120\,V$ . Calculate the value of $R$ to make the bulb light up $5\,s$ after the
switch has been closed. $(log_{10}2.5 = 0.4)$
a.
$1.7 \times 10^{5}\Omega$
b.
$2.7 \times 10^{6}\Omega$
c.
$3.3 \times 10^{7}\Omega$
d.
$1.3 \times 10^{4}\Omega$
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A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius $R$ .
The magnitude of the magnetic induction along its axis is
a.
$\frac{\mu _{0}I}{2\pi ^{2}R}$
b.
$\frac{\mu _{0}I}{2\pi R}$
c.
$\frac{\mu _{0}I}{4\pi ^{2}R}$
d.
$\frac{\mu _{0}l}{\pi ^{2}R}$
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Two bodies of masses $m$ and $4\,m$ are placed at a distance $r$ . The gravitational potential at a point on the line
joining them where the gravitational field is zero is:
a.
$- \frac{4Gm}{r}$
b.
$- \frac{6Gm}{r}$
c.
$- \frac{9Gm}{r}$
d.
zero
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Let the $x- z$ plane be the boundary between two transparent media. Medium 1 in $z\geq 0$ has a refractive index
of $\sqrt{2}$ and medium 2 with $z< 0$ has a refractive index of $\sqrt{3}$ . A ray of light in medium 1 given by the vector
$\vec{A}= 6\sqrt{3}\hat{i}+ 8\sqrt{3}\hat{j}-10\hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is
a.
$45^{\circ }$
b.
$60^{\circ }$
c.
$75^{\circ }$
d.
$30^{\circ }$
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A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$ . It is
moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its
temperature increases by :
a.
$\frac{(\gamma -1)}{2\gamma R}Mv^{2}\,K$
b.
$\frac{\gamma Mv^{2}}{2R}K$
c.
$\frac{(\gamma -1)}{2R}Mv^{2}\,K$
d.
$\frac{(\gamma -1)}{2(\gamma +1)R} Mv^{2}\,K$
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The half life of a radioactive substance is 20 minutes. The approximate time interval $(t_{2}- t_{1})$ between the
time $t_{2}$ when $\frac{2}{3}$ of it has decayed and time $t_{1}$ and $\frac{1}{3}$ of it had decayed is :
a.
$14\,min$
b.
$20\,min$
c.
$28\,min$
d.
$7\,min$
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An object, moving with a speed of $6.25\,m/s$ , is decelerated at a rate given by :
$\frac{dv}{dt} = -2.5\sqrt{v}$
where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be:
a.
$2\,s$
b.
$4\,s$
c.
$8\,s$
d.
$1\,s$
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Direction: The question has a paragraph followed by two statements, Statement $-1$ and statement $-2$ . Of the
given four alternatives after the statements, choose the one that describes the statements. A thin air film is
formed by putting the convex surface of a plane - convex lens over a plane glass plate. With monochromatic
light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom
(glass plate) surface of the film. Statement-1 : When light reflects from the air-glass plate interface, the
reflected wave suffers a phase change of $\pi$ . Statement-2 : The centre of the interference pattern is dark.
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation of
Statement-1.
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the 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 pulley of radius $2\,m$ is rotated about its axis by a force $F =(20t -5t^{2})$ Newton (where $t$ is measured in
seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley
before its direction of motion if reversed, is :
a.
more than 3 but less than 6
b.
more than 6 but less than 9
c.
more than 9
d.
less than 3
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$100\,g$ of water is heated from $30^{\circ }C$ to $50^{\circ }C$ . Ignoring the slight expansion of the water, the change in its
internal energy is (specific heat of water is $4148\,J/kg/K$ ):
a.
$8.4\,kJ$
b.
$84\,kJ$
c.
$2.1\,kJ$
d.
$4.2\,kJ$
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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 : A metallic surface is irradiated by a monochromatic
light of frequency $v>v_{0}$ (the threshold frequency). The maximum kinetic energy and the stopping potential
are $K_{max}$ and $V_{0}$ respectively. If the frequency incident on the surface doubled, both the $K_{max}$ and $V_{0}$ are also
doubled. Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from
a surface are linearly dependent on the frequency of incident light.
a.
Statement-1 is true, Statement-2 is true;
Statement-2 is the correct explanation of
Statement-1.
b.
Statement-1 is true, Statement-2 is true;
Statement-2 is not the 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 boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5}NA^{-1}\,m^{-1}$ due north and
horizontal. The boat carries a vertical aerial $2\,m$ long. If the speed of the boat is $1.50\,ms^{-1}$ , the magnitude of
the induced emf in the wire of aerial is :
a.
$0.75mV$
b.
$0.50mV$
c.
$0.15mV$
d.
$1mV$
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The electrostatic potential inside a charged spherical ball is given by $\phi =\alpha \rho ^{2} +b$ where $r$ is the distance from
the centre; $a,b$ are constants. Then the charge density inside ball is
a.
$-6a\epsilon _{0}r$
b.
$-24\pi a\epsilon _{0}r$
c.
$-6a\epsilon _{0}$
d.
$-24\pi a\epsilon _{0}r$
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Two identical charged spheres suspended from a common point by two massless strings of length I are initially
a distance $d(d<< 1)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres
at a constant rate. As a result the charges approach each other with a velocity $v$ . Then as a function of distance
$x$ between them,
a.
$v\propto x^{-1}$
b.
$v\propto x^{1/2}$
c.
$v\propto x$
d.
$v\propto x^{-1/2}$
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In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre
positions. If one atom of $B$ is missing from one of the face centred points, the formula of the compound is
a.
$AB_{2}$
b.
$A_{2}B_{3}$
c.
$A_{2}\,B_{5}$
d.
$A_{2}B$
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The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume
of $10dm^{3}$ to a volume of $100dm^{3}$ at $27^{\circ }C$ is :
a.
$35.8\,J\,mol^{-1}\,K^{-1}$
b.
$32.3\,J\,mol^{-1}\,K^{-1}$
c.
$42.3\,J\,mol^{-1}\,K^{-1}$
d.
$38.3\,J\,mol^{-1}\,K^{-1}$
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Trichloroacetaldehyde was subjected to Cannizzaro's reaction by using $NaOH$ . The mixture of the products
contains sodium trichloroacetate and another compound. The other compound is :
a.
Trichloromethanol
b.
2, 2, 2-Trichloropropanol
c.
Chloroform
d.
2, 2, 2-Trichloroethanol
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A vessel at $1000\,K$ contains $CO_{2}$ with a pressure of $0.5\,atm$ . Some of the $CO_{2}$ is converted into $CO$ on the
addition of graphite. If the total pressure at equilibrium is $0.8\,atm$ , the value of $K$ is
a.
$3\,atm$
b.
$0.3\,atm$
c.
$0.18\,atm$
d.
$1.8\,atm$
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Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to
$4\,kg$ of water to prevent it from freezing at $-6^{\circ }C$ will be : $[K_{t}$ for water $= 1.86\,K\,kg\,mol^{-1}$ , and molar mass
of ethylene glycol $= 62\,g\,mol^{-1}$ )
a.
$204.30\,g$
b.
$400.00\,g$
c.
$304.60\,g$
d.
$804.32\,g$
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The rate of a chemical reaction doubles for every $10^{\circ }C$ rise of temperature. If the temperature is raised by
$50^{\circ }C$ , the rate of the reaction increases by about :
a.
24 times
b.
32 times
c.
64 times
d.
10 times
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$\{\frac{sin(p+1)x+sinx}{x} x< 0$
The value of $p$ and $q$ for which the function $f(x) = q ,x= 0$ is continuous for all $x$ in $R$ , is
$\{$
$\frac{\sqrt{x+x^{2}}-\sqrt{x}}{x^{3/2}} ,x> 0$
a.
$p= \frac{5}{2},q= \frac{1}{2}$
b.
$p= - \frac{3}{2},q= \frac{1}{2}$
c.
$p= \frac{1}{2},q= \frac{3}{2}$
d.
$p= \frac{1}{2} ,q= - \frac{3}{2}$
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If the angle between the line $x= \frac{y-1}{2} = \frac{z-3}{\lambda}$ and the plane $x+ 2y+ 3z= 4$ is $cos^{-1} (\sqrt{\frac{5}{14}} )$ , then $\lambda$ equals
a.
$\frac{3}{2}$
b.
$\frac{2}{5}$
c.
$\frac{5}{3}$
d.
$\frac{2}{3}$
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Let $A$ and $B$ be two symmetric matrices of order 3 . 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 $-1$ :
$A(BA)$ and $(AB)A$ are symmetric matrices. Statement - 2 : $AB$ is symmetric matrix if matrix multiplication
of $A$ and $B$ is commutative.
a.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is not a correct explanation for
Statement $-1$
b.
Statement $-1$ is true, Statement $-2$ is false.
c.
Statement $-1$ is false, Statement- 2 is true.
d.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is a correct explanation for
Statement $-1$
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Let $\alpha ,\beta$ be real and $z$ be a complex number. If $z^{2} +\alpha z+\beta = 0$ has two distinct roots on the line $Rez= 1$ ,
then it is necessary that
a.
$\beta \in (-1, 0)$
b.
$|\beta | = 1$
c.
$\beta \in (1, \infty )$
d.
$\beta \in (0, 1)$
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If $\vec{a}= \frac{1}{\sqrt{10}}(3\hat{i}+ \hat{k})$ and $\vec{b}= \frac{1}{7}(2\hat{i}+ 3\hat{j}-6\hat{k})$ , then the value of $(2\vec{a}- \vec{b}) \cdot [(\vec{a}\times \vec{b}) \times (\vec{a}+ 2\vec{b})]$ is
a.
$-3$
b.
$5$
c.
$3$
d.
$-5$
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Consider the following statements $P$ : Suman is brilliant Q : Suman is rich $R$ : Suman is honest The negation
of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as
a.
$\sim (Q \leftrightarrow (P\wedge \sim R))$
b.
$\sim Q\leftrightarrow \sim P \wedge R$
c.
$\sim (P\wedge \sim R) \leftrightarrow Q$
d.
$\sim P \wedge (Q\leftrightarrow \sim R)$
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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 point $A(1, 0, 7)$ is the mirror image of the point
$B(1, 6, 3)$ in the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ . Statement-2 : The line: $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ bisects the line segment
joining $A(1, 0, 7)$ and $B(1, 6, 3)$ .
a.
Statement $-1$ is true, Statement-2 is true;
Statement $-2$ is not a correct explanation for
Statement $-1$
b.
Statement $-1$ is true, Statement $-2$ is false.
c.
Statement $-1$ is false, Statement $-2$ is true.
d.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is a correct explanation for
Statement $-1$
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Equation of the ellipse whose axes are the axes of coordinates and which passes through the point $(-3, 1)$ and
has eccentricity $\sqrt{\frac{2}{5}}$ is
a.
$5x^{2} + 3y^{2} -48 = 0$
b.
$3x^{2} + 5y^{2} -15 = 0$
c.
$5x^{2} + 3y^{2} -32 = 0$
d.
$3x^{2} + 5y^{2} -32 = 0$
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A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his
saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start
of service will be Rs. 11040 after
a.
19 months
b.
20 months
c.
21 months
d.
18 months
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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 number of ways of distributing 10 identical
balls in 4 distinct boxes such that no box is empty is $^{9}C_{3}$ Statement-2: The number of ways of choosing any 3
places from 9 different places is $^{9}C_{3}$ .
a.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is not a correct explanation for
Statement $-1$
b.
Statement $-1$ is true, Statement $-2$ is false.
c.
Statement $-1$ is false, Statement- 2 is true.
d.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is a correct explanation for
Statement $-1$
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Let $R$ be the set of real numbers 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 :
$A= {(x,y) \in R\times R:y- x$ is an integer $}$ is an equivalence relation on $R$ . Statement-2 :
$B= {(x,y) \in R\times R:x=\alpha y$ for some rational number $\alpha }$ is an equivalence relation on $R$ .
a.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is not a correct explanation for
Statement $-1$
b.
Statement $-1$ is true, Statement- 2 is false.
c.
Statement $-1$ is false, Statement $-2$ is true.
d.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is a correct explanation for
Statement $-1$
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Let I be the purchase value of an equipment and $V(t)$ be the value after it has been used for t years. The value
$V(t)$ depreciates at a rate given by differential equation $\frac{dV(t)}{dt} = -k(T -t)$ , where $k > 0$ is a constant and $T$
is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is
a.
$I - \frac{kT}{2}$
b.
$1 - \frac{k(T-t)^{2}}{2}$
c.
$e^{-kT}$
d.
$T^{2} - \frac{1}{k}$
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Consider 5 independent Bernoulli's trials each with probability of success $p$ . If the probability of at least one
failure is greater than or equal to $\frac{31}{32}$ , then $p$ lies in the interval
a.
$(\frac{3}{4} , \frac{11}{12}]$
b.
$[0, \frac{1}{2} ]$
c.
$(\frac{11}{12}, 1]$
d.
$(\frac{1}{2}, \frac{3}{4} ]$
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The lines $L_{1} :y- x= 0$ and $L_{2} : 2x+y= 0$ intersect the line $L_{3} :y+ 2 = 0$ at $P$ and $Q$ respectively. The
bisector of the acute angle between $L_{1}$ and $L_{2}$ intersect $L_{3}$ at $R$ . 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 ratio $PR:RQ$ equals $2\sqrt{2}: \sqrt{5}$ . Statement-2 : In any triangle, bisector of an
angle divides the triangle into two similar triangles.
a.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is not a correct explanation for
Statement $-1$
b.
Statement $-1$ is true, Statement- 2 is false.
c.
Statement $-1$ is false, Statement- 2 is true.
d.
Statement $-1$ is true, Statement $-2$ is true;
Statement $-2$ is a correct explanation for
Statement $-1$
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The vector $\vec{a}$ and $\vec{b}$ are not perpendicular and $\vec{c}$ and $\vec{d}$ are two vectors satisfying: $\vec{b}\times \vec{c}= \vec{b}\times \vec{d}$ and $\vec{a}\cdot \vec{d}= 0$ .
Then the vector $\vec{d}$ is equal to
