A mass of $50\,g$ of water in a closed vessel, with surroundings at a constant temperature takes 2 minutes to cool
from $30^{\circ }C$ to $25^{\circ }C$ . A mass of $100\,g$ of another liquid in an identical vessel with identical surroundings takes
the same time to cool from $30^{\circ }C$ to $25^{\circ }C$ . The specific heat of the liquid is : (The water equivalent of the vessel
is $30\,g$ .)
a.
$2.0kcal/kg$
b.
$7kcal/kg$
c.
$3kcal/kg$
d.
$0.5kcal/kg$
Correct Answer
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Q2mcq
One of the two small circular coils, (none of them having any self - inductance) is suspended with a V-shaped
copper wire, with plane horizontal. The other coil is placed just below the first one with plane horizontal. Both
the coils are connected in series with a dc supply. The coils are found to attract each other with a force. Which
one of the following statements is incorrect?
a.
Both the coils carry currents in the same
direction.
b.
Coils will attract each other, even if the supply is
an ac source.
c.
Force is proportional to $d^{-1}$
d.
Force is proportional to $d^{-2}$
Correct Answer
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Q3mcq
A block is placed on a rough horizontal plane. A time dependent horizontal force $F = kt$ acts on the block,
where $k$ is a positive constant. The acceleration - time graph of the block is :
No explanation saved for this question yet.
Q4mcq
In an experiment, a small steel ball falls through a liquid at a constant speed of $10\,cm/s$ . If the steel ball is
pulled upward with a force equal to twice its effective weight, how fast will it move upward ?
a.
$5\,cm/s$
b.
Zero
c.
$10\,cm/s$
Correct Answer
d.
$20\,cm/s$
No explanation saved for this question yet.
Q5mcq
This question has Statement-1 and Statements2. Of the four choices given after the Statements, choose the one
that best describes the two Statements. Statement-1 : Out of radio waves and microwaves, the radio waves
undergo more diffraction. Statement-2 : Radio waves have greater frequency compared to microwaves.
a.
Statement-1 is true, Statement-2 is true and
Statement-2 is the correct explanation of
Statement-1
b.
Statement-1 is false, Statement-2 is true.
c.
Statement-1 is true, Statement-2 is false.
Correct Answer
d.
Statement-1 is true, Statement-2 is true but
Statement-2 is not the correct explanation of
Statement-1
No explanation saved for this question yet.
Q6mcq
A series $LR$ circuit is connected to an ac source of frequency $\omega$ and the inductive reactance is equal to $2R$ . A
capacitance of capacitive reactance equal to $R$ is added in series with $L$ and $R$ . The ratio of the new power
factor to the old one is :
a.
$\frac{2}{3}$
$\sqrt{\,}$
b.
$\sqrt{\,} \sqrt{\frac{2}{5}}$
$\sqrt{\,}$
c.
$\frac{3}{2}$
d.
$\frac{5}{2}$
Correct Answer
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Q7mcq
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: No work is required to be done to move a test charge
between any two points on an equipotential surface. Statement 2 : Electric lines of force at the equipotential
surfaces are mutually perpendicular to each other.
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 true, Statement 2 is false.
Correct Answer
d.
Statement 1 is false, Statement 2 is true.
No explanation saved for this question yet.
Q8mcq
When resonance is produced in a series LCR circuit, then which of the following is not correct?
a.
Current in the circuit is in phase with the applied
voltage.
b.
Inductive and capacitive reactances are equal.
c.
If $R$ is reduced, the voltage across capacitor will
increase.
d.
Impedance of the circuit is maximum.
Correct Answer
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Q9mcq
A thin glass plate of thickness is $\frac{2500}{3}\lambda$ ( $\lambda$ is wavelength of light used) and refractive index $\mu = 1.5$ is inserted
between one of the slits and the screen in Young's double slit experiment. At a point on the screen equidistant
from the slits, the ratio of the intensities before and after the introduction of the glass plate is :
a.
$2 : 1$
b.
$1 : 4$
c.
$4 : 1$
Correct Answer
d.
$4 : 3$
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Q10mcq
A metal sample carrying a current along $X-$ axis with density $J_{x}$ is subjected to a magnetic field $B_{z}$ (along $z-$
axis). The electric field $E_{y}$ developed along $Y$ -axis is directly proportional to $J_{x}$ as well as $B_{z}$ . The constant of
proportionality has SI unit.
a.
$\frac{m^{2}}{A}$
b.
$\frac{m^{3}}{As}$
Correct Answer
c.
$\frac{m^{2}}{As}$
d.
$\frac{As}{m^{3}}$
No explanation saved for this question yet.
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A printed page is pressed by a glass of water. The refractive index of the glass and water is $1.5$ and $1.33$ ,
respectively. If the thickness of the bottom of glass is $1\,cm$ and depth of water is $5\,cm$ , how much the page
will appear to be shifted if viewed from the top ?
a.
$1.033\,cm$
b.
$3.581\,cm$
c.
$1.3533\,cm$
d.
$1.90\,cm$
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The surface charge density of a thin charged disc of radius $R$ is $\sigma$ . The value of the electric field at the centre
of the disc is $\frac{\sigma}{2\in _{0}}$ . With respect to the field at the centre, the electric field along the axis at a distance $R$ from
the centre of the disc:
a.
reduces by $70.7%$
b.
reduces by $29.3%$
c.
reduces by $9.7%$
d.
reduces by $14.6%$
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The gravitational field in a region is given by: $\vec{E} = (5N/kg)\hat{i}+ (12N/kg)\hat{j}$ If the potential at the origin is
taken to be zero, then the ratio of the potential at the points $(12\,m, 0)$ and $(0, 5\,m)$ is :
a.
Zero
b.
1
c.
$\frac{144}{25}$
d.
$\frac{25}{144}$
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A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length
vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at
equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically
with a small amplitude. The time period $T$ of the oscillations of the cylinder will be :
a.
Smaller than $2\pi [ \frac{M}{(k+A\sigma g)}]^{1/2}$
b.
$2\pi \sqrt{\frac{M}{k}}$
c.
Larger than $2\pi [\frac{M}{(k+A\sigma g)} ]^{1/2}$
d.
$1/2$
$2\pi [\frac{M}{(k+A\sigma g)} ]$
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In the isothermal expansion of $10\,g$ of gas from volume $V$ to $2\,V$ the work done by the gas is $575\,J$ . What is the
root mean square speed of the molecules of the gas at that temperature?
a.
$398\,m/s$
b.
$520\,m/s$
c.
$499\,m/s$
d.
$532\,m/s$
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The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R_{0} = 40\,m$ . What will be the
acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with
uniform velocity $v = 20\,m/s$ on a horizontal surface? $(g = 10\,m/s^{2})$
a.
$30^{\circ }$
b.
$60^{\circ }$
c.
$75^{\circ }$
d.
$45^{\circ }$
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A copper ball of radius $1\,cm$ and work function $4.47\,eV$ is irradiated with ultraviolet radiation of wavelength
$2500\,$ Å. The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire
charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is
:
a.
$5.5 \times 10^{-13}\,C$
b.
$7.5 \times 10^{-13}\,C$
c.
$4.5 \times 10^{-12}\,C$
d.
$2.5 \times 10^{-11}\,C$
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The source that illuminates the double $-$ slit in 'double - slit interference experiment' emits two distinct
monochromatic waves of wavelength $500\,nm$ and $600\,nm$ , each of them producing its own pattern on the
screen. At the central point of the pattern when path difference is zero, maxima of both the patterns coincide
and the resulting interference pattern is most distinct at the region of zero path difference. But as one moves
out of this central region, the two fringe systems are gradually out of step such that maximum due to on
wavelength coincides with the minimum due to the other and the combined fringe system becomes completely
indistinct. This may happen when path difference in $nm$ is:
a.
$2000$
b.
$3000$
c.
$1000$
d.
$1500$
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In a transverse wave the distance between a crest and neighbouring trough at the same instant is $4.0\,cm$ and the
distance between a crest and trough at the same place is $1.0\,cm$ . The next crest appears at the same place after
a time interval of $0.4\,s$ . The maximum speed of the vibrating particles in the medium is:
a.
$\frac{3\pi}{2}\,cm/s$
b.
$\frac{5\pi}{2}\,cm/s$
c.
$\frac{\pi}{2}\,cm/s$
d.
$2\,\pi \,cm/s$
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Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area A passing over a
frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2\,m$ , then the stress
produced in the wire is:
a.
$\frac{2mg}{3\,A}$
b.
$\frac{4mg}{3\,A}$
c.
$\frac{mg}{A}$
d.
$\frac{3mg}{4\,A}$
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In an experiment on photoelectric effect, a student plots stopping potential $V_{0}$ against reciprocal of the
wavelength $\lambda$ of the incident light for two different metals $A$ and $B$ . These are shown in the figure.
Looking at the graphs, you can most appropriately say that:
a.
Work function of metal $B$ is greater than that of
metal $A$
b.
For light of certain wavelength falling on both
metal, maximum kinetic energy of electrons
emitted from A will be greater than those emitted
from $B$ .
c.
Work function of metal $A$ is greater than that of
metal $B$
d.
Students data is not correct
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A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a
fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $v$ , the electrical
power output will be most likely proportional to
a.
$v^{4}$
b.
$v^{2}$
c.
$v$
d.
$v^{3}$
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A ring of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$ . Two identical bodies each of
mass $m$ are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy
loss will be :
a.
$\frac{m(M+2m)}{M}\omega ^{2}R^{2}$
b.
$\frac{Mm}{(M+m)}\omega ^{2}R^{2}$
c.
$\frac{Mm}{(M+2m)}\omega ^{2}R^{2}$
d.
$\frac{(M+m)M}{(M+2m)}\omega ^{2}R^{2}$
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The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of
this dipole is close to $8 \times 10^{22}Am^{2}$ , the value of earth's magnetic field near the equator is close to (radius of
the earth $= 6.4 \times 10^{6}\,m)$
a.
$0.6$ Gauss
b.
$1.2$ Gauss
c.
$1.8$ Gauss
d.
$0.32$ Gauss
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A parallel plate capacitor having a separation between the plates $d$ , plate area $A$ and material with dielectric
constant $K$ has capacitance $C_{0}$ . Now one-third of the material is replaced by another material with dielectric
constant $2\,K$ , so that effectively there are two capacitors one with area $\frac{1}{3}\,A$ , dielectric constant $2\,K$ and
another with area $\frac{2}{3} \,A$ and dielectric constant $K$ . If the capacitance of this new capacitor is $C$ then $\frac{C}{C_{0}}$ is
a.
$1$
b.
$\frac{4}{3}$
c.
$\frac{2}{3}$
d.
$\frac{1}{3}$
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Which one of the following is the wrong assumption of kinetic theory of gases ?
(1) Momentum and energy always remain conserved.(2) Pressure is the result of elastic collision of
molecules with the container's wall.
(3) Molecules are separated by great distances (4) All the molecules move in straight line between
compared to their sizes. collision and with same velocity.
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In nucleophilic substitution reaction, order of halogens as incoming (attacking) nucleophile is:
$I^{-} > Br^{-} > Cl^{-}$ The order of halogens as departing nucleophile should be :
a.
$Br^{-} > I^{-} > Cl^{-}$
b.
$I^{-} > Br^{-} > Cl^{-}$
c.
$Cl^{-} > Br^{-} > I^{-}$
d.
$Cl^{-} > I^{-} > Br^{-}$
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A solution of copper sulphate $(CuSO_{4})$ is electrolysed for $10$ minutes with a current of $1.5$ amperes. The mass
of copper deposited at the cathode (at. mass of $Cu = 63u$ ) is :
a.
$0.3892\,g$
b.
$0.2938\,g$
c.
$0.2398\,g$
d.
$0.3928\,g$
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How many grams of methyl alcohol should be added to $10$ litre tank of water to prevent its freezing at $268\,K$ ?
( $K_{f}$ for water is $1.86\,K\,kg mol^{-1})$
a.
$880.07\,g$
b.
$899.04\,g$
c.
$886.02\,g$
d.
$868.06\,g$
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The catenation tendency of $C, Si$ and $Ge$ is in the order $Ge < Si < C$ . The bond energies (in $kJ\,mol^{-1}$ ) of
$C -C, Si -Si$ and $Ge -Ge$ bonds are respectively ;
a.
$348, 297, 260$
b.
$297, 348, 260$
c.
$348, 260, 297$
d.
$260, 297, 348$
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A radioactive isotope having a half - life period of $3$ days was received after $12$ days. If $3\,g$ of the isotope is
left in the container, what would be the initial mass of the isotope ?
a.
$12\,g$
b.
$36\,g$
c.
$48\,g$
d.
$24\,g$
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Given (A) $n = 5, \,m_{\ell } = +1$ (B) $n = 2, \ell = 1, \,m_{\ell } = -1, \,m_{s} = -l/2$ The maximum number of electron(s) in
an atom that can have the quantum numbers as given in (A) and (B) are respectively:
a.
$25$ and $1$
b.
$8$ and $1$
c.
$2$ and $4$
d.
$4$ and $1$
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Given that: (i) $\Delta _{f}\vec{H}^{\circ }$ of $N_{2}O$ is $82\,kJ\,mol^{-1}$ (ii) Bond energies of $N \equiv \vec{N}, N = N, O = O$ and $N = O$ are
$946, 418, 498$ and $607\,kJ\,mol^{-1}$ respectively, The resonance energy of $N_{2}O$ is :
a.
$-88\,kJ$
b.
$-66\,kJ$
c.
$-62\,kJ$
d.
$-44\,kJ$
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The Gibbs energy for the decomposition of $Al_{2}O_{3}$ at $500\,C$ is as follows :
$\frac{2}{3}Al_{2}O_{3} \rightarrow \rightarrow \frac{4}{3}Al + O_{2}, \Delta _{r}G= +940\,kJ\,mol^{-1}$ The potential difference needed for the electrolytic reduction
of aluminium oxide at $500^{\circ }C$ should be at least :
a.
$4.5\,V$
b.
$3.0\,V$
c.
$5.0\,V$
d.
$2.5\,V$
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What would be the $pH$ of a solution obtained by mixing $5\,g$ of acetic acid and $7.5\,g$ of sodium acetate and
making the volume equal to $500\,mL$ ? $(K_{a} = 1.75 \times 10^{-5}, pK_{a} = 4.76)$
a.
$pH = 4.70$
b.
$pH < 4.70$
c.
$pH$ of solution will be equal to $pH$ of acetic acid
d.
$4.76 < pH < 5.0$
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If for positive integers $r> 1,n> 2$ , the coefficients of the $(3r)^{th\,}$ and $(r+ 2)^{th\,}$ powers of $x$ in the expansion
of $(1 +x)^{2n}$ are equal, then $n$ is equal to:
a.
$2r+ 1$
b.
$2r-1$
c.
$3r$
d.
$r+ 1$
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Let $A(-3, 2)$ and $B(-2, 1)$ be the vertices of a triangle $ABC$ . If the centroid of this triangle lies on the line
$3x+ 4y+ 2 = 0$ , then the vertex $C$ lies on the line :
a.
$4x+ 3y+ 5 = 0$
b.
$3x+ 4y+ 3 = 0$
c.
$4x+ 3y+ 3 = 0$
d.
$3x+ 4y+ 5 = 0$
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Statement 1: The only circle having radius $\sqrt{10}$ and a diameter along line $2x+y= 5$ is $x^{2} +y^{2} -6x$
$+2y= 0$ . Statement $2 : 2x+y= 5$ is a normal to the circle $x^{2} +y^{2} -6x+ 2y= 0$ .
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 false.
d.
Statement 1 is true; Statement 2 is true;
Statement 2 is not a correct explanation for
Statement 1.
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If a circle of unit radius is divided into two parts by an arc of another circle subtending an angle $60^{\circ }$ on the
circumference of the first circle, then the radius of the arc is:
a.
$\sqrt{3}$
b.
$\frac{1}{2}$
c.
1
d.
None of these
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5 - digit numbers are to be formed using $2, 3, 5, 7$ , 9 without repeating the digits. If $p$ be the number of such
numbers that exceed 20000 and $q$ be the number of those that lie between 30000 and 90000 , then $p:q$ is:
a.
$6 : 5$
b.
$3 : 2$
c.
$4 : 3$
d.
$5 : 3$
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Let $\vec{a}= 2\hat{i}+ \hat{j}-2\hat{k}, \vec{b}= \vec{i}+ \vec{j}$ . If $\vec{c}$ is a vector such that $\vec{a}\cdot \vec{c}= |\vec{c}|, |\vec{c}- \vec{a}| = 2\sqrt{2}$ and the angle between
$\vec{a}\times \vec{b}$ and $\vec{c}$ is $30^{\circ }$ , then $|(\hat{a}\times \hat{b}) \times \vec{c}|$ equals:
a.
$\frac{1}{2}$
b.
$\frac{3\sqrt{3}}{2}$
c.
3
d.
$\frac{3}{2}$
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In a set of $2n$ observations, half of them are equal to ' $a$ ' and the remaining hall are equal to ' $-a'$ '. If the
standard deviation of all the observations is 2 ; then the value of $|a|$ is :
a.
2
b.
$\sqrt{2}$
c.
4
d.
$2\sqrt{2}$
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Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common
difference six. If first and last terms of this sequence are equal, then the last term is :
a.
16
b.
8
c.
4
d.
2
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If $p$ and $q$ are non-zero real numbers and $\alpha ^{3} +\beta ^{3} = -p,\alpha \beta =q$ , then a quadratic equation whose roots are
$\frac{\alpha ^{2}}{\beta} , \frac{\beta ^{2}}{\alpha}$ is :
a.
$px^{2} - qx+p^{2} = 0$
b.
$qx^{2} +px+q^{2} = 0$
c.
$px^{2} +qx+p^{2} = 0$
d.
$qx^{2} - px+q^{2} = 0$
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A spherical balloon is being inflated at the rate of $35cc/min$ . The rate of increase in the surface area (in
$cm^{2}/min$ .) of the balloon when its diameter is $14\,cm$ , is :
a.
10
b.
$\sqrt{10}$
c.
100
d.
$10\sqrt{10}$
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Let $f : [-2, 3] \rightarrow [0, \infty )\rightarrow$ be a continuous function such that $f(1 - x) =f(x)$ for all $x\in [-2, 3]$ . If $R_{1}$ is the
numerical value of the area of the region bounded by $y=f(x),x= -2,x= 3$ and the axis of $x$ and
$R_{2} =\int _{-2}^{3} xf(x)dx$ , then :
a.
$3R_{1} = 2R_{2}$
b.
$2R_{1} = 3R_{2}$
c.
$R_{1} = R_{2}$
d.
$R_{1} = 2R_{2}$
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Let $ABC$ be a triangle with vertices at points $A (2, 3, 5)$ , B $(-1, 3, 2)$ and $C(\lambda , 5,\mu )$ in three dimensional
space. If the median through $A$ is equally inclined with the axes, then $(\lambda ,\mu )$ is equal to:
a.
$(10, 7)$
b.
$(7, 5)$
c.
$(7, 10)$
d.
$(5, 7)$
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Consider the system of equations : $x+ay= 0,y+az= 0$ and $z+ax= 0$ . Then the set of all real values of '
$a$ ' for which the system has a unique solution is:
a.
$R -{1}$
b.
$R -{-1}$
c.
${1, -1}$
d.
${1, 0, -1}$
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If the events $A$ and $B$ are mutually exclusive events such that $P(A) = \frac{3x+1}{3}$ and $P(B) = \frac{1-x}{4}$ , then the set of
possible values of $x$ lies in the interval :
a.
$[0, 1]$
b.
$[\frac{1}{3} , \frac{2}{3}]$
c.
$[-\frac{1}{3} , \frac{5}{9}]$
d.
$[- \frac{7}{9}, \frac{4}{9}]$
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Let $p$ and $q$ be any two logical statements and $r : p \rightarrow (\sim \rightarrow p\vee q)$ . If $r$ has a truth value $F$ , then the truth values
of $p$ and $q$ are respectively:
a.
$F, F$
b.
$T, T$
c.
T, F
d.
F, T
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