A cylindrical tube, open at both ends, has a fundamental frequency, $f$ , in air. The tube is dipped vertically in
water so that half of it is in water. The fundamental frequency of the air-column is now
a.
$f$
Correct Answer
b.
$\frac{f}{2}$
c.
$\frac{3f}{4}$
d.
$2f$
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Q2mcq
Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant
magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_{p},r_{d}$ and $r_{\alpha }$ . Which one of the
following relations is correct?
a.
$r_{\alpha } =r_{p} =r_{d}$
b.
$r_{\alpha } =r_{p} <r_{d}$
Correct Answer
c.
$r_{\alpha } >r_{d} >r_{p}$
d.
$r_{\alpha } =r_{d} >r_{p}$
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Q3mcq
Helium gas goes through a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in
figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas)
a.
$15.4%$
Correct Answer
b.
$9.1%$
c.
$10.5%$
d.
$12.5%$
No explanation saved for this question yet.
Q4mcq
A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading:
$58.5$ degree Vernier scale reading : $09$ divisions Given that $1$ division on main scale corresponds to $0.5$ degree.
Total divisions on the vernier scale is $30$ and match with $29$ divisions of the main scale. The angle of the prism
from the above data
a.
$58.59^{\circ }$
b.
$58.77^{\circ }$
c.
$58.65^{\circ }$
Correct Answer
d.
$59^{\circ }$
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Q5mcq
A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times 10^{-2}\,N$ (see
figure). The length of the slider is $30\,cm$ and its weight negligible. The surface tension of the liquid film is
a.
$0.0125\,Nm^{-1}$
b.
$0.1\,Nm^{-1}$
c.
$0.05\,Nm^{-1}$
d.
$0.025\,Nm^{-1}$
Correct Answer
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Q6mcq
A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of
force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an
aluminium plate is placed near to the coil, it stops. This is due to :
a.
development of air current when the plate is
placed.
b.
induction of electrical charge on the plate
c.
shielding of magnetic lines of force as aluminium
is a paramagnetic material.
d.
electromagnetic induction in the aluminium plate
giving rise to electromagnetic damping.
Correct Answer
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Q7mcq
An object $2.4\,m$ in front of a lens forms a sharp image on a film $12\,cm$ behind the lens. A glass plate $1\,cm$
thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what
distance (from lens) should object be shifted to be in sharp focus on film?
a.
$7.2\,m$
b.
$2.4\,m$
c.
$3.2\,m$
d.
$5.6\,m$
Correct Answer
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Q8mcq
A particle of mass $m$ is at rest at the origin at time $t = 0$ . It is subjected to a force $F(t) = F_{0}e^{-bt}$ in the $x$
direction. Its speed $v(t)$ is depicted by which of the following curves?
No explanation saved for this question yet.
Q9mcq
A diatomic molecule is made of two masses $m_{1}$ and $m_{2}$ which are separated by a distance $r$ . If we calculate its
rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ( $n$ is
an integer)
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. An insulating solid sphere of radius $R$ has a uniformly positive charge
density $\rho$ . As a result of this uniform charge distribution there is a finite value of electric potential at the centre
of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at
infinity is zero. Statement $1$ : When a charge $q$ is taken from the centre to the surface of the sphere, its potential
energy changes by $\frac{qp}{3\epsilon _{0}}$ Statement $2$ : The electric field at a distance $r(r<R)$ from the centre of the sphere is
$\frac{\rho r}{3\epsilon _{0}}$
a.
Statement $1$ is true, Statement $2$ is true,
Statement $2$ is not the correct explanation for
statement $1$ .
b.
Statement $1$ is true, Statement $2$ is false
c.
Statement $1$ is false, Statement $2$ is true
Correct Answer
d.
Statement $1$ is true, Statement $2$ is the correct
explanation for statement $1$
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A radar has a power of $1\,Kw$ and is operating at a frequency of $10\,GHz$ . It is located on a mountain top of
height $500\,m$ . The maximum distance upto which it can detect object located on the surface of the earth
(Radius of earth $= 6.4 \times 10^{6}\,m$ ) is
a.
$80\,km$
b.
$16\,km$
c.
$40\,km$
d.
$64\,km$
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A liquid in a beaker has temperature $\theta (t)$ at time $t$ and $\theta _{0}$ is temperature of surroundings, then according to
Newton's law of cooling the correct graph between $log_{e}(\theta - \theta _{0})$ and $t$ is
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In a uniformly charged sphere of total charge $Q$ and radius $R$ , the electric field $E$ is plotted as a function of
distance from the centre. The graph which would correspond to the above will be
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Assume that a neutron breaks into a proton and an electron. The energy released during this process is (Mass
of neutron $= 1.6725 \times 10^{-27}\,kg;$ mass of proton $= 1.6725 \times 10^{-27}\,kg;$ mass of electron $= 9 \times 10^{-31} kg)$
a.
$0.73\,MeV$
b.
$7.10\,MeV$
c.
$6.30\,MeV$
d.
$5.4\,MeV$
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Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ , respectively. Their speeds are such that
they make complete circles in the same time $t$ . The ratio of their centripetal acceleration is
a.
$m_{1}r_{1} :m_{2}r_{2}$
b.
$m_{1} :m_{2}$
c.
$r_{1} :r_{2}$
d.
$1 : 1$
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A Carnot engine, whose efficiency is $40%$ , takes in heat from a source maintained at a temperature of $500\,K$ It
is desired to have an engine of efficiency $60%$ . Then, the intake temperature for the same exhaust (sink)
temperature must be
a.
efficiency of Carnot engine cannot be made
larger than $50%$
b.
$1200\,K$
c.
$750\,K$
d.
$600\,K$
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Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied
across it. If the percentage errors in the measurement of the current and the voltage difference are $3%$ each, then
error in the value of resistance of the wire is
a.
$6%$
b.
zero
c.
$1%$
d.
$3%$
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Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4$ . Then
the number of spectral lines in the emission spectra will be
a.
$2$
b.
$3$
c.
$5$
d.
$6$
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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 : Davisson - germer experiment established the wave nature
of electrons. Statement 2 : If electrons have wave nature, they can interfere and show diffraction.
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 the correct
explanation for statement $1$
d.
Statement $1$ is true, Statement $2$ is true,
Statement $2$ is not the correct explanation for
statement $1$ .
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A charge $Q$ is uniformly distributed over the surface of non conducting disc of radius $R$ . The disc rotates about
an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$ . As a result of this
rotation a magnetic field of induction $B$ is obtained at the centre of the disc. If we keep both the amount of
charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the
variation of the magnetic induction at the centre of the disc will be represented by the figure
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A wooden wheel of radius $R$ is made of two semicircular parts (see figure); The two parts are held together by a
ring made of a metal strip of cross sectional area S and length $L$ . $L$ is slightly less than $2\pi R$ . To fit the ring on
the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to
surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the
metal is $\alpha$ , and its Youngs' modulus is $Y$ , the force that one part of the wheel applies on the other part is :
a.
$2\pi SY\alpha \Delta T$
b.
$SY\alpha \Delta T$
c.
$\pi SY\alpha \Delta T$
d.
$2SY\alpha \Delta T$
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An electromagnetic wave in vacuum has the electric and magnetic fields $\vec{E}$ and $\vec{B}$ , which are always
perpendicular to each other. The direction of polarization is given by $\vec{X}$ andthat of wave propagation by $\vec{k}$ .
Then:
a.
$\vec{X}\parallel \vec{B}$ and $\vec{k}\parallel \vec{B}\times \vec{E}$
b.
$\vec{X}\parallel \vec{E}$ and $\vec{k}\parallel \vec{E}\times \vec{B}$
c.
$\vec{X}\parallel \vec{B}$ and $\vec{k}\parallel \vec{E}\times \vec{B}$
d.
$\vec{X}\parallel \vec{E}$ and $\vec{k}\parallel \vec{B}\times \vec{E}$
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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. If two springs $S_{1}$ and $S_{2}$ of force constants $k_{1}$ and $k_{2}$ , respectively, are
stretched by the same force, it is found that more work is done on spring $S_{1}$ than on spring $S_{2}$ . Statement $1$ : If
stretched by the same amount, work done on $S_{1}$ , will be more than that on $S_{2}$ Statement $2 :k_{1} <k_{2}$
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 the correct
explanation for statement $1$
d.
Statement $1$ is true, Statement $2$ is true, Statement
$2$ is not the correct explanation for statement $1$ .
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If a simple pendulum has significant amplitude (up to a factor of $1/e$ of original) only in the period between
$t= 0s$ to $t=τs$ , then $τ$ may be called the average life of the pendulum. When the spherical bob of the
pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ' $b$ ' as the constant of
proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:
a.
$\frac{0.693}{b}$
b.
$b$
c.
$\frac{1}{b}$
d.
$\frac{2}{b}$
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The mass of a spaceship is $1000\,kg$ . It is to be launched from the earth's surface out into free space. The value
of ' $g$ ' and ' $R$ ' (radius of earth) are $10\,m/s^{2}$ and $6400\,km$ respectively. The required energy for this work will
be ;
a.
$6.4 \times 10^{11}$ Joules
b.
$6.4 \times 10^{8}$ Joules
c.
$6.4 \times 10^{9}$ Joules
d.
$6.4 \times 10^{10}$ Joules
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In Young's double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one
slit is double of that from other slit. If $I_{m}$ be the maximum intensity, the resultant intensity I when they
interfere at phase difference $\phi$ is given by
a.
$\frac{I_{m}}{9}(4 + 5 cos\phi )$
b.
$\frac{l_{m}}{3} (1 + 2 cos^{2} \frac{\phi}{2})$
c.
$\frac{I_{m}}{5}(1 + 4 cos^{2} \frac{\phi}{2} )$
d.
$\frac{I_{m}}{9} (1 + 8 cos^{2} \frac{\phi}{2})$
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For a first order reaction, $(A) \rightarrow \rightarrow$ products, the concentration of $A$ changes from $0.1\,M$ to $0.025\,M$ in $40$
minutes. The rate of reaction when the concentration of $A$ is $0.01\,M$ is :
a.
$1.73 \times 10^{-5}M/min$
b.
$3.47 \times 10^{-4}M/min$
c.
$3.47 \times 10^{-5}M/min$
d.
$1.73 \times 10^{-4}M/min$
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Which one of the following statements is correct?
(1) All amino acids except lysine are optically active (2) All amino acids are optically active
(3) All amino acids except glycine are optically (4) All amino acids except glutamic acid are
active optically active
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The standard reduction potentials for $Zn^{2+}/Zn, Ni^{2+}/Ni$ , and $Fe^{2+}/Fe$ are $-0.76, -0.23$ and $-0.44\,V$
respectively. The reaction $X + Y^{2+} \rightarrow X\rightarrow^{2+} + Y$ will be spontaneous when:
a.
$X =Ni,Y =Fe$
b.
$X =Ni,Y =Zn$
c.
$X =Fe,Y =Zn$
d.
$X =Zn,Y =Ni$
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The equilibrium constant $(K_{c})$ for the reaction $N_{2}(g) + O_{2}(\,g) \rightarrow 2NO(g)\rightarrow$ at temperature $T$ is $4 \times 10^{-4}$ . The
value of $K_{c}$ for the reaction, $NO(g) \rightarrow 1/2\,N\rightarrow_{2}(g) + 1/2\,O_{2}(g)$ at the same temperature is :
a.
$0.02$
b.
$2.5 \times 10^{2}$
c.
$4 \times 10^{-4}$
d.
$50.0$
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$K_{f}$ for water is $1.86\,K\,kg\,mol^{-1}$ . If your automobile radiator holds $1.0\,kg$ of water, how many grams of
ethylene glycol $(C_{2}H_{6}O_{2})$ must you add to get the freezing point of the solution lowered to $-2.8^{\circ }C$ ?
a.
$72\,g$
b.
$93\,g$
c.
$39\,g$
d.
$27\,g$
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The density of a solution prepared by dissolving $120\,g$ of urea (mol. Mass $= 60u$ ) in $1000\,g$ of water is
$1.15\,g/mL$ . The molarity of this solution is :
a.
$0.50\,M$
b.
$1.78\,M$
c.
$1.02\,M$
d.
$2.05\,M$
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Which method of purification is represented by the following equation:
$Ti(s) + 2I_{2}(g)^{523\,K}\longrightarrow TiI_{4}(g)^{1700\,K}\longrightarrow Ti(s) + 2I_{2}(g)$
a.
zone refining
b.
cupellation
c.
Poling
d.
Van Arkel
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The electrons identified by quantum numbers $n$ and $I$ : (a) $n= 4,I = 1$ (b) $n= 4,l= 0$ (c) $n= 3,I = 2$ (d)
$n= 3,I = 1$ Can be placed in order of increasing energy as:
a.
(c) $<$ (d) $<$ (b) $<$ (a)
b.
(d) $<$ (b) $<$ (c) $<$ (a)
c.
(b) $<$ (d) $<$ (a) $<$ (c)
d.
(a) $<$ (c) $<$ (b) $<$ (d)
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Three numbers are chosen at random without replacement from ${1, 2, 3, … . .8}$ . The probability that their
minimum is $3$ , given that their maximum is $6$ , is
a.
$\frac{3}{8}$
b.
$\frac{1}{5}$
c.
$\frac{1}{4}$
d.
$\frac{2}{5}$
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If $f : R \rightarrow R\rightarrow$ is a function defined by $f(x) = [x] cos(\frac{2x-1}{2})\pi$ , where $[x]$ denotes the greatest integer function,
then $f$ is
a.
continuous for every real $x$
b.
discontinuous only at $x= 0$
c.
discontinuous only at non-zero integral values of
$x$
d.
continuous only at $x= 0$
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Statement $1$ : An equation of a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} +y^{2} = 4$ is
$y= 2x+ 2\sqrt{3}$ . Statement $2$ : If the line $y=mx+ \frac{4\sqrt{3}}{m} , (m\neq 0)$ is a common tangent to the parabola
$y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} +y^{2} = 4$ , then $m$ satisfies $m^{4} + 2m^{2} = 24$ .
a.
Statement $1$ is false, statement $2$ is true
b.
Statement $1$ is true, statement $2$ is true; statement
$2$ is a correct explanation for statement $1$
c.
Statement $1$ is true, statement $2$ is true; statement
$2$ is not a correct explanation for statement $1$
d.
Statement $1$ is true, statement $2$ is false
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A line is drawn through the point $(1, 2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle
$OPQ$ , where $O$ is the origin. If the area of the triangle $OPQ$ is least, then the slope of the line $PQ$ is
a.
$-\frac{1}{4}$
b.
$-4$
c.
$-2$
d.
$- \frac{1}{2}$
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A spherical balloon is filled with $4500\,\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to
escape at the rate of $72\,\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of
the balloon decreases $49$ minutes after the leakage began is
a.
$\frac{9}{7}$
b.
$\frac{7}{9}$
c.
$\frac{2}{9}$
d.
$\frac{9}{2}$
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Let $x_{1}, x_{2}, … … , x_{n}$ be $n$ observations, and let $-x$ be their arithematic mean and $\sigma ^{2}$ be their variance.
Statement $1$ : Variance of $2x_{1}, 2x_{2}, … … , 2x_{n}$ is $4\sigma ^{2}$ . Statement $2$ : Arithmetic mean of $2x_{1}, 2x_{2}, … . . , 2x_{n}$ is
$-$ .
$4x$
a.
Statement $1$ is false, statement $2$ is true
b.
Statement $1$ is true, statement $2$ is true; statement
$2$ is a correct explanation for statement $1$
c.
Statement $1$ is true, statement $2$ is true; statement
$2$ is not a correct explanation for statement $1$
d.
Statement $1$ is true, statement $2$ is false
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If $100$ times the $100^{th\,}$ term of an $AP$ with non zero common difference equals the $50$ times its $50^{th\,}$ term, then
the $150^{th\,}$ term of this $AP$ is
a.
$-150$
b.
$150$ times its $50^{th\,}$ term
c.
$150$
d.
zero
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$--$
Let $ABCD$ be a parallelogram such that $A\vec{B}= \vec{q},A\vec{D}= \vec{p}$ and $\angle BAD$ be an acute angle. If $\vec{r}$ is the vector
that coincides with the altitude directed from the vertex $B$ to the side $AD$ , then $\vec{r}$ is given by
Let $a,b\in R$ be such that the function $f$ given by $f(x) = ln |x| +bx^{2} +ax,x\neq 0$ has extreme values at
$x= -1$ and $x= 2$ . Statement 1: $f$ has local maximum at $x= -1$ and at $x= 2$ . Statement 2: $a = \frac{1}{2}$ and
$b = \frac{-1}{4}$
a.
Statement $1$ is false, statement $2$ is true
b.
Statement $1$ is true, statement $2$ is true; statement
$2$ is a correct explanation for statement $1$
c.
Statement $1$ is true, statement $2$ is true; statement
$2$ is not a correct explanation for statement $1$
d.
Statement $1$ is true, statement $2$ is false
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The population $p(t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{dp(t)}{dt} = 0.5\,p(t)$
$-450$ . If $p(0) = 850$ , then the time at which the population becomes zero is
a.
$2 ln 18$
b.
$ln 9$
c.
$\frac{1}{2}ln 18$
d.
$ln 18$
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$1 0 0 1 0$
$( ) ( ) ( )$
Let $A= 2 1 0$ . If $u_{1}$ and $u_{2}$ are column matrices such that $Au_{1} = 0$ and $Au_{2} = 1$ , then
$( ) ( ) ( )$
$3 2 1 0 0$
$u_{1}+u_{2}$ is equal to
a.
$-1$
$( )$
$1$
$( )$
$0$
b.
$-1$
$( )$
$1$
$( )$
$-1$
c.
$-1$
$( )$
$-1$
$( )$
$0$
d.
$1$
$( )$
$-1$
$( )$
$-1$
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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more
balls can be selected from $10$ white, $9$ green and $7$ black balls is
a.
$880$
b.
$629$
c.
$630$
d.
$879$
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Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c}= \hat{a}+ 2\hat{b}$ and $\vec{d}= 5\hat{a}-4\hat{b}$ are perpendicular to each other,
then the angle between $\hat{a}$ and $\hat{b}$ is
a.
$\frac{\pi}{6}$
b.
$\frac{\pi}{2}$
c.
$\frac{\pi}{3}$
d.
$\frac{\pi}{4}$
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An ellipse is drawn by taking a diameter of the circle $(x-1)^{2} +y^{2} = 1$ as its semiminor axis and a diameter
of the circle $x^{2} + (y-2)^{2} = 4$ as its semi-major axis. If the centre of the ellipse is the origin and its axes are
the coordinate axes, then the equation of the ellipse is
a.
$4x^{2} +y^{2} = 4$
b.
$x^{2} + 4y^{2} = 8$
c.
$4x^{2} +y^{2} = 8$
d.
$x^{2} + 4y^{2} = 16$
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If the line $2x+y=k$ passes through the point which divides the line segment joining the points $(1, 1)$ and
$(2, 4)$ in the ratio $3 : 2$ , then $k$ equals
a.
$\frac{29}{5}$
b.
$5$
c.
$6$
d.
$\frac{11}{5}$
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