A solid sphere is rolling on a surface as shown in figure, with a translational velocity $v\,m\,s^{-1}$ . If it is to climb
the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is
a.
$\sqrt{2gh}$
b.
$\sqrt{\frac{7}{5}}gh$
c.
$\sqrt{\frac{7}{2}} gh$
d.
$\sqrt{\frac{10}{7}}gh$
Correct Answer
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Q2mcq
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 pure semiconductor has negative temperature coefficient
of resistance. Statement 2: On raising the temperature, more charge carriers are released into the conduction
band.
a.
Statement 1 is false, Statement 2 is true.
b.
Statement 1 is true, Statement 2 is false.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation of
Statement 1.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is the correct explanation of
Statement 1.
Correct Answer
No explanation saved for this question yet.
Q3mcq
A wave represented by the equation $y_{1} =acos (kx- \omega t)$ is superimposed with another wave to form a
stationary wave such that the point $x-0$ is node. The equation for the other wave is
a.
$acos(kx- \omega t+\pi )$
b.
$acos(kx+\omega t+\pi )$
Correct Answer
c.
$acos(kx+\omega t+ \frac{\pi}{2})$
d.
$acos(kx- \omega t+ \frac{\pi}{2})$
No explanation saved for this question yet.
Q4mcq
The maximum number of possible interference maxima for slit separation equal to $1.8\lambda$ , where $\lambda$ is the
wavelength of light used, in a Young's double slit experiment is
a.
zero
b.
3
Correct Answer
c.
infinite
d.
5
No explanation saved for this question yet.
Q5mcq
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: Bats emitting ultrasonic waves can detect the location of a
prey by hearing the waves reflected from it. Statement 2: When the source and the detector are moving, the
frequency of reflected waves is changed.
a.
Statement 1 is false, Statement 2 is true.
b.
Statement 1 is true, Statement 2 is false.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is not the correct explanation of
Statement 1.
Correct Answer
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is the correct explanation of
Statement 1.
No explanation saved for this question yet.
Q6mcq
A student measured the diameter of a wire using a screw gauge with the least count $0.001\,cm$ and listed the
measurements. The measured value should be recorded as
a.
$5.3200\,cm$
b.
$5.3\,cm$
c.
$5.32\,cm$
d.
$5.320\,cm$
Correct Answer
No explanation saved for this question yet.
Q7mcq
Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a
distance of $r$ from the centre is proportional to
a.
$r$
Correct Answer
b.
$r^{-1}$
c.
$r^{2}$
d.
$r^{-2}$
No explanation saved for this question yet.
Q8mcq
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: When moment of inertia $I$ of a body rotating about an axis
with angular speed $\omega$ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if
there is no torque applied on it. Statement 2: $L=I\omega$ , kinetic energy of rotation $= \frac{1}{2}I\omega ^{2}$
a.
Statement 1 is true, Statement 2 is true, Statement
2 is not the correct explanation of Statement 1.
b.
Statement 1 is false, Statement 2 is true.
Correct Answer
c.
Statement 1 is true, Statement 2 is true, Statement
2 is correct explanation of the Statement 1.
d.
Statement 1 is true, Statement 2 is false.
No explanation saved for this question yet.
Q9mcq
Three resistors of $4\Omega , 6\Omega$ and $12\Omega$ are connected in parallel and the combination is connected in series with a
$1.5\,V$ battery of $1\Omega$ internal resistance. The rate of Joule heating in the $4\Omega$ resistor is
a.
$0.55\,W$
b.
$0.33\,W$
c.
$0.25\,W$
Correct Answer
d.
$0.86\,W$
No explanation saved for this question yet.
Q10mcq
It is preferable to measure the e.m.f. of a cell by potentiometer than by a voltmeter because of the following
possible reasons. (i) In case of potentiometer, no current flows through the cell. (ii) The length of the
potentiometer allows greater precision. (iii) Measurement by the potentiometer is quicker. (iv) The sensitivity
of the galvanometer, when using a potentiometer is not relevant. Which of these reasons are correct?
a.
(i),(iii),(iv)
b.
(i),(iii),(iv)
c.
(i),(ii)
Correct Answer
d.
(i),(ii),(iii),(iv)
No explanation saved for this question yet.
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A spring is compressed between two blocks of masses $m_{1}$ and $m_{2}$ placed on a horizontal frictionless surface as
shown in the figure. When the blocks are released, they have initial velocity of $v_{1}$ and $v_{2}$ as shown. The blocks
travel distances $x_{1}$ and $x_{2}$ respectively before coming to rest. The ratio $(\frac{x_{1}}{x_{2}})$ is
a.
$\frac{m_{2}}{m_{1}}$
b.
$\frac{m_{1}}{m_{2}}$
c.
$\sqrt{\,} \frac{m}{m_{1}}^{2}$
d.
$\sqrt{\,} \frac{m}{m_{2}}^{1}$
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An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the
surface is $1/3$ . If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the
vertical, the maximum possible value of $\alpha$ so that the insect does not slip is given by
a.
$cot\alpha = 3$
b.
$sec\alpha = 3$
c.
$cosec\alpha = 3$
d.
$cos\alpha = 3$
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A resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through
a key. The key is closed at $t=$ 0 . If after $t$ sec the voltage across the capacitance was seven times the voltage
across $R$ , the value of $t$ is
a.
$3RC\ell n2$
b.
$2RC\ell n2$
c.
$2RCln 7$
d.
$3RC\ell n7$
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The distance travelled by a body moving along a line in time $t$ is proportional to $t^{3}$ . The acceleration-time $(a,t)$
graph for the motion of the body will be
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A hypothetical atom has only three energy levels. The ground level has energy, $E_{1} = -8eV$ . The two excited
states have energies, $E_{2} = -6eV$ and $E_{3} = -2eV$ . Then which of the following wavelengths will not be
present in the emission spectrum of this atom?
a.
$207\,nm$
b.
$465\,nm$
c.
$310\,nm$
d.
$620\,nm$
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A given ideal gas with $\gamma = \frac{C_{p}}{C_{v}} = 1.5$ at a temperature $T$ . If the gas is compressed adiabatically to one-fourth
of its initial volume, the final temperature will be
a.
$2\sqrt{2}T$
b.
$4T$
c.
$2T$
d.
$8T$
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A doubly ionised $Li$ atom is excited from its ground $state(n= 1)$ to $n= 3$ state. The wavelengths of the
spectral lines are given by $\lambda _{32},\lambda _{31}$ and $\lambda _{21}$ . The ratio $\lambda _{32}/\lambda _{31}$ and $\lambda _{21}/\lambda _{31}$ are, respectively
a.
$8.1, 0.67$
b.
$8.1, 1.2$
c.
$6.4, 1.2$
d.
$6.4, 0.67$
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Magnetic flux through a coil of resistance $10\Omega$ is changed by $\Delta \phi$ in $0.1\,s$ . The resulting current in the coil
varies with time as shown in the figure. Then $|\Delta \phi |$ is equal to (in weber)
a.
6
b.
4
c.
2
d.
8
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The circuit in figure consists of wires at the top and bottom and identical springs as the left and right sides. The
wire at the bottom has a mass of $10\,g$ and is $5\,cm$ long. The wire is hanging as shown in the figure. The springs
stretch $0.5\,cm$ under the weight of the wire and the circuit has a total resistance of $12\Omega$ . When the lower wire
is subjected to a static magnetic field, the springs, stretch an additional $0.3\,cm$ . The magnetic field is
a.
$0.6\,T$ and directed out of page
b.
$1.2\,T$ and directed into the plane of page
c.
$0.6\,T$ and directed into the plane of page
d.
$1.2\,T$ and directed out of page
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A projectile moving vertically upwards with a velocity of $200\,ms^{-1}$ breaks into two equal parts at a height of
$490\,m$ . One part starts moving vertically upwards with a velocity of $400\,ms^{-1}$ . How much time it will take,
after the break up with the other part to hit the ground?
a.
$2\,s\sqrt{10}$
b.
$5\,s$
c.
$10\,s$
d.
$\sqrt{10}\,s$
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The magnetic force acting on charged particle of charge $2\mu C$ in magnetic field of $2T$ acting in $y-$ direction,
when the particle velocity is $(2\hat{i}+ 3\hat{j}) \times 10^{6}\,ms^{-1}$ is
a.
$8\,N$ in z-direction
b.
$8\,N$ in y-direction
c.
$4\,N$ in y-direction
d.
$4\,N$ in z-direction
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Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a
spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity
$v_{0}$ along the line joining $A$ and $B$ and collides elastically with $A$ . At a certain time after the collision it is found
that the instantaneous velocities of $A$ and $B$ are same and the compression of the spring is $x_{0}$ . The spring
constant $k$ will be
a.
$m\frac{v^{2}_{0}}{x^{2}_{0}}$
b.
$m\frac{v_{0}}{2x_{0}}$
c.
$2m \frac{v_{0}}{x_{0}}$
d.
$2$
$\frac{2}{3} m(\frac{v_{0}}{x_{0}})$
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The first diffraction minimum due to the single slit diffraction is seen at $\theta = 30^{\circ }$ for a light of wavelength
$5000$ Åfalling perpendicularly on the slit. The width of the slit is
a.
$2.5 \times 10^{-5}\,cm$
b.
$1.25 \times 10^{-5}\,cm$
c.
$10 \times 10^{-5}\,cm$
d.
$5 \times 10^{-5}\,cm$
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Water is flowing through a horizontal tube having cross-sectional areas of its two ends being $A$ and $A'$ such
that the ratio $A/A'$ is 5 . If the pressure difference of water between the two ends is $3\times 10^{5}\,N\,m^{-2}$ , the
velocity of water with which it enters the tube will be (neglect gravity effects)
a.
$5\,m\,s^{-1}$
b.
$10\,m\,s^{-1}$
c.
$25\,m\,s^{-1}$
d.
$50\,m\,s\sqrt{10}^{-1}$
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We wish to make a microscope with the help of two positive lenses both with a focal length of 20 $mm$ each
and the object is positioned $25\,mm$ from the objective lens. How far apart the lenses should be so that the final
image is formed at infinity?
a.
$20\,mm$
b.
$100\,mm$
c.
$120\,mm$
d.
$80\,mm$
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A series combination of $n_{1}$ capacitors, each of capacity $C_{1}$ is charged by source of potential difference $4\,V$ .
When another parallel combination of $n_{2}$ capacitors each of capacity $C_{2}$ is charged by a source of potential
difference $V$ , it has the same total energy stored in it as the first combination has. The value of $C_{2}$ in terms of
$C_{1}$ is then
a.
$16\frac{n_{2}}{n_{1}} C_{1}$
b.
$\frac{2C_{1}}{n_{1}n_{2}}$
c.
$2\frac{n_{2}}{n_{1}}C_{1}$
d.
$\frac{16C_{1}}{n_{1}n_{2}}$
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A metal $M$ on heating in nitrogen gas gives $Y$ . $Y$ on treatment with $H_{2}O$ gives a colourless gas which when
passed through $CuSO_{4}$ solution gives a blue colour. $Y$ is
a.
$NH_{3}$
b.
$Mg(NO_{3})_{2}$
c.
$Mg_{3}\,N_{2}$
d.
$MgO$
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In a chemical reaction $A$ is converted into $B$ . The rates of reaction, starting with initial concentrations of $A$ as
$2 \times 10^{-3}M$ and $1 \times 10^{-3} M$ , are equal to $2.40 \times 10^{-4}Ms^{-1}$ and $0.60 \times 10^{-4}Ms^{-1}$ respectively. The order of
reaction with respect to reactant $A$ will be
a.
0
b.
$1.5$
c.
1
d.
2
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An aqueous solution of oxalic acid dihydrate contains its $6.3\,g$ in $250ml$ . The volume of $0.1\,N NaOH$ required
to completely neutralize $10ml$ of this solution
a.
$4ml$
b.
$20ml$
c.
$2ml$
d.
$40ml$
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Given (i) $HCN(aq) + H_{2}O(b)\rightleftharpoons H_{3}O^{+}(aq) + CN^{-}(aq)K_{a} = 6.2 \times 10^{-10}$ (ii)
$CN^{-}(aq) + H_{2}O(l)\rightleftharpoons HCN(aq) + OH^{-}(aq)K_{b} = 1.6 \times 10^{-5}$ . These equilibria show the following order of
the relative base strength,
a.
$OH^{-} > H_{2}O > CN^{-}$
b.
$OH^{-} > CN^{-} > H_{2}O$
c.
$H_{2}O > CN^{-} > OH$
d.
$CN^{-} > H_{2}O > OH^{-}$
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$\alpha ,v$ and $u$ represent most probable velocity, average velocity and root mean square velocity respectively of a
gas at a particular temperature. The correct order among the following is
a.
$u>v>\alpha$
b.
$v>u>\alpha$
c.
$\alpha >u>v$
d.
$u>\alpha >v$
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The difference between the reaction enthalpy change $(\Delta _{r}H)$ and reaction internal energy change $(\Delta _{r}U)$ for the
reaction:
$2C_{6}H_{6}(l) + 15O_{2}(\,g)\longrightarrow$
at $300\,K$ is $(R = 8.314\,J\,mol^{-1}\,K^{-1})$
a.
$0\,J\,mol^{-1}$
b.
$2490\,J\,mol^{-1}$
c.
$-2490\,J\,mol^{-1}$
d.
$-7482\,J\,mol^{-1}$
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$8\,mol$ of $AB_{3}(\,g)$ are introduced into a $1.0dm^{3}$ vessel. If it dissociates as $2AB_{3}(g)\rightleftharpoons A_{2}(g) + 3B_{2}(g)$ . At
equilibrium, $2\,mol$ of $A_{2}$ are found to be present. The equilibrium constant of this reaction is
a.
2
b.
3
c.
27
d.
36
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A solution containing $0.85\,g$ of $ZnCl_{2}$ in $125.0\,g$ of water freezes at $-0.23^{\circ }C$ . The apparent degree of
dissociation of the salt is $(K_{f}$ for water $= 1.86\,K\,kg\,mol^{-1}$ , atomic mass: $Zn = 65.3$ and $Cl = 35.5)$
a.
$1.36%$
b.
$73.5%$
c.
$7.35%$
d.
$2.47%$
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Statement 1: If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q>p$ . Then the total number
of functions from set $A$ to set $B$ is $q^{p}$ Statement 2: The total number of selections of $p$ different objects out of $q$
objects is $^{q}C_{p}$ .
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 of
Statement 1.
c.
Statement 1 is false, Statement 2 is true
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation of Statement
1.
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Statement 1: The degrees of the differential equations $\frac{dy}{dx} +y^{2} =x$ and $\frac{d^{2}y}{dx^{2}} +y= sinx$ are equal. Statement
2: The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive
integral power of the highest order derivative involved in the differential equation, otherwise degree is not
defined.
a.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation of
Statement 1.
b.
Statement 1 is false, Statement 2 is true.
c.
Statement 1 is true, Statement 2 is false.
d.
Statement 1 is true, Statement 2 is true;
Statement 2 is a correct explanation of Statement
1.
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If $P_{1}$ and $P_{2}$ are two points on the ellipse $\frac{x^{2}}{4} +y^{2} = 1$ at which the tangents are parallel to the chord joining
the points $(0, 1)$ and $(2, 0)$ , then the distance between $P_{1}$ and $P_{2}$ is
a.
$2\sqrt{2}$
b.
$\sqrt{5}$
c.
$2\sqrt{3}$
d.
$\sqrt{10}$
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A unit vector which is perpendicular to the vector $2\hat{i}- \hat{j}+ 2\hat{k}$ and is coplanar with the vectors $\hat{i}+ \hat{j}- \hat{k}$ and
$2\hat{i}+ 2\hat{j}- \hat{k}$ is
a.
$\frac{2\hat{j}+\hat{k}}{\sqrt{5}}$
b.
$\frac{3\hat{i}+2\hat{j}-2\hat{k}}{\sqrt{17}}$
c.
$\frac{3\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{17}}$
d.
$\frac{2\hat{i}+2\hat{j}-\hat{k}}{3}$
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A number $n$ is randomly selected from the set ${1, 2, 3, … . , 1000}$ . The probability that $\frac{\sum ^{n}_{i}_{=1}i^{2}}{\sum ^{n}_{i}_{=1}i}$ is an integer is
a.
$0.331$
b.
$0.333$
c.
$0.334$
d.
$0.332$
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If $A= {x\in z^{+} :x< 10$ and $x$ is a multiple of 3 or $4}$ , where $z^{+}$ is the set of positive integers, then the total
number of symmetric relations on $A$ is
a.
$2^{5}$
b.
$2^{15}$
c.
$2^{10}$
d.
$2^{20}$
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If $\vec{u}= \hat{j}+ 4\hat{k}, \vec{v}= ^\wedge\vec{i}+ 3\hat{k}$ and $\vec{w}= cos\theta \hat{i}+ sin\theta \hat{j}$ are vectors in 3-dimensional space, then the maximum
possible value of $|u\times \vec{v}\cdot \vec{w}|$ is
a.
$\sqrt{3}$
b.
5
c.
$\sqrt{14}$
d.
7
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$||$
$||$
Statement 1: If the points $(1, 2, 2), (2, 1, 2)$ and $(2, 2,z)$ and $(1, 1, 1)$ are coplanar, then $z= 2$ . Statement 2: If
the 4 points $P,Q,R$ and $S$ are coplanar, then the volume of the tetrahedron $PQRS$ is 0.
a.
Statement 1 is false,, Statement 2 is true.
b.
Statement 1 is true, Statement 2 is false.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation of Statement
1.
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation of
Statement 1.
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If a straight line $y- x= 2$ divides the region $x^{2} +y^{2} \leq 4$ into two parts, then the ratio of the area of the
smaller part to the area of the greater part is
a.
$3\pi -8 :\pi + 8$
b.
$\pi -3 : 3\pi + 3$
c.
$3\pi -4 :\pi + 4$
d.
$\pi -2 : 3\pi + 2$
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Consider a rectangle whose length is increasing at the uniform rate of $2\,m/sec$ , breadth is decreasing at the
uniform rate of $3\,m/sec$ and the area is decreasing at the uniform rate of $5\,m^{2}/sec$ . If after some time the
breadth of the rectangle is $2\,m$ then the length of the rectangle is
a.
$2\,m$
b.
$4\,m$
c.
$1\,m$
d.
$3\,m$
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$\alpha 0 0 \gamma$
Let $A$ and $B$ be real matrices of the form $[ ]$ and $[ ]$ , respectively. Statement 1: $AB- BA$ is always
$0 \beta \delta 0$
an invertible matrix. Statement $2 :AB- BA$ is never an identity matrix.
a.
Statement 1 is true, Statement 2 is false.
b.
Statement 1 is false, Statement 2 is true.
c.
Statement 1 is true, Statement 2 is true;
Statement 2 is a correct explanation of Statement
1 .
d.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation of
Statement 1.
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Statement 1: A function $f :R\rightarrow \rightarrow R$ is continuous at $x_{0}$ if and only if $lim_{x\rightarrow \rightarrow x_{0}}f(x)$ exists and
$lim_{x\rightarrow \rightarrow x_{0}}f(x) =f(x_{0}\cdot )$ Statement 2: A function $f :R\rightarrow \rightarrow R$ is discontinuous at $x_{0}$ if and only if, $lim_{x\rightarrow \rightarrow x_{0}}f(x)$
exists and $lim_{x\rightarrow \rightarrow x_{0}}f(x) \neq f(x_{0}. )$
a.
Statement 1 is true, Statement 2 is true,
Statement 2 is not a correct explanation of
Statement 1.
b.
Statement 1 is false, Statement 2 is true.
c.
Statement 1 is true, Statement 2 is true,
Statement 2 is a correct explanation of Statement
1.
d.
Statement 1 is true, Statement 2 is false.
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