Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is
bent into a loop and produces magnetic field $B_{1}$ , at its centre when a current $I$ passes through it. The ratio
$B_{1} : B_{2}$ is:
a.
1:1
b.
$1 : 3$
Correct Answer
c.
$1 : 9$
d.
$9 : 1$
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Q2mcq
The refractive index of the material of a concave lens is $\mu$ . It is immersed in a medium of refractive index $\mu _{1}$ .
A parallel beam of light is incident on the lens. The path of the emergent rays when $\mu _{1} >\mu$ is:
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Q3mcq
A source of sound A emitting waves of frequency $1800\,Hz$ is falling towards ground with a terminal speed $v$ .
The observer $B$ on the ground directly beneath the source receives waves of frequency $2150\,Hz$ . The source A
receives waves, reflected from ground of frequency nearly: (Speed of sound $= 343\,m/s$ )
a.
$2150\,Hz$
b.
$2500\,Hz$
Correct Answer
c.
$1800\,Hz$
d.
$2400\,Hz$
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Q4mcq
For LED's to emit light in visible region of electromagnetic light, it should have energy band gap in the range
of:
a.
$0.1eV$ to $0.4eV$
b.
$0.5eV$ to $0.8eV$
c.
$0.9eV$ to $1.6eV$
d.
$1.7eV$ to $3.0eV$
Correct Answer
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Q5mcq
Hot water cools from $60^{\circ }C$ to $50^{\circ }C$ in the first 10 minutes and to $42^{\circ }C$ in the next 10 minutes. The
temperature of the surroundings is:
a.
$25^{\circ }C$
b.
$10^{\circ }C$
Correct Answer
c.
$15^{\circ }C$
d.
$20^{\circ }C$
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Q6mcq
A spring of unstretched length 1 has a mass $m$ with one end fixed to a rigid support. Assuming spring to be
made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is:
a.
$\frac{1}{2}mv^{2}$
b.
$mv^{2}$
c.
$\frac{1}{3}mv^{2}$
d.
$\frac{1}{6} mv^{2}$
Correct Answer
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Q7mcq
A bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into $0.8\,kg$ block of wood at rest on a table. If
the coefficient of friction between the block and the table is $0.3$ , how far will the block slide approximately?
a.
$0.19\,m$
b.
$0.379\,m$
Correct Answer
c.
$0.569\,m$
d.
$0.758\,m$
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Q8mcq
Three masses $m, 2\,m$ and $3\,m$ are moving in $x -y$ plane with speed $3u, 2u$ and $u$ respectively as shown in
figure. The three masses collide at the same point at $P$ and stick together. The velocity of resulting mass will be:
A spherically symmetric charge distribution is characterised by a charge density having the following
variations: $\rho (r) =\rho _{o}(1 - \frac{r}{R})$ for $r<R \rho (r) = 0$ for $r\geq R$ Where $r$ is the distance from the centre of the
charge distribution $\rho _{o}$ is a constant. The electric field at an internal point $(r<R)$ is:
Two hypothetical planets of masses $m_{1}$ and $m_{2}$ are at rest when they are infinite distance apart. Because of the
gravitational force they move towards each other along the line joining their centres. What is their speed when
their separation is ' $d$ '? (Speed of $m_{1}$ is $v_{1}$ and that of $m_{2}$ is $v_{2}$ )
A beam of light has two wavelengths of $4972$ Åand $6216$ Åwith a total intensity of $3.6 \times 10^{-3} Wm^{-2}$ equally
distributed among the two wavelengths. The beam falls normally on an area of $1\,cm^{2}$ of a clean metallic
surface of work function $2.3eV$ . Assume that there is no loss of light by reflection and that each capable
photon ejects one electron. The number of photoelectrons liberated in $2\,s$ is approximately:
a.
$6 \times 10^{11}$
b.
$9 \times 10^{11}$
c.
$11 \times 10^{11}$
d.
$15 \times 10^{11}$
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A lamp emits monochromatic green light uniformly in all directions. The lamp is $3%$ efficient in converting
electrical power to electromagnetic waves and consumes $100\,W$ of power. The amplitude of the electric field
associated with the electromagnetic radiation at a distance of $5\,m$ from the lamp will be nearly:
a.
$1.34\,V/m$
b.
$2.68\,V/m$
c.
$4.02\,V/m$
d.
$5.36\,V/m$
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Interference pattern is observed at ' $P$ ' due to superimposition of two rays coming out from a source ' $S$ ' as
shown in the figure. The value of ' $l$ ' for which maxima is obtained at ' $P$ ' is: ( $R$ is perfect reflecting surface)
The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant'
varies with distance as per the relation:
$K(x) = K_{o}+\lambda x(\lambda = a\,constant\,)$
The capacitance $C$ , of the capacitor, would be related to its vacuum capacitance $C_{o}$ for the relation :
A Carnot engine absorbs $1000\,J$ of heat energy from a reservoir at $127^{\circ }C$ and rejects $600\,J$ of heat energy
during each cycle. The efficiency of engine and temperature of sink will be:
a.
$20%$ and $-43^{\circ }C$
b.
$40%$ and $-33^{\circ }C$
c.
$50%$ and $-20^{\circ }C$
d.
$70%$ and $-10^{\circ }C$
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A person climbs up a stalled escalator in $60\,s$ . If standing on the same but escalator running with constant
velocity he takes $40\,s$ . How much time is taken by the person to walk up the moving escalator?
a.
$37\,s$
b.
$27\,s$
c.
$24\,s$
d.
$45\,s$
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The circuit shown here has two batteries of $8.0\,V$ and $16.0\,V$ and three resistors $3\Omega , 9\Omega$ and $9\Omega$ and a
capacitor of $5.0\mu F$ .
How much is the current $I$ in the circuit in steady state?
a.
$1.6\,A$
b.
$0.67\,A$
c.
$2.5\,A$
d.
$0.25\,A$
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In the experiment of calibration of voltmeter, a standard cell of e.m.f. $1.1$ volt is balanced against $440\,cm$ of
potential wire. The potential difference across the ends of resistance is found to balance against $220\,cm$ of the
wire. The corresponding reading of voltmeter is $0.5$ volt. The error in the reading of volmeter will be:
a.
$-0.15$ volt
b.
$0.15$ volt
c.
$0.5$ volt
d.
$-0.05$ volt
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A piece of bone of an animal from a ruin is found to have $^{14}C$ activity of 12 disintegrations per minute per gm
of its carbon content. The $^{14}C$ activity of a living animal is 16 disintegrations per minute per gm. How long
ago nearly did the animal die? (Given half life of $^{14}C$ is $t_{1/2} = 5760$ years)
a.
1672 years
b.
2391 years
c.
3291 years
d.
4453 years
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Steel ruptures when a shear of $3.5 \times 10^{8}\,N\,m^{-2}$ is applied. The force needed to punch a $1\,cm$ diameter hole in a
steel sheet $0.3\,cm$ thick is nearly:
a.
$1.4 \times 10^{4}\,N$
b.
$2.7 \times 10^{4}\,N$
c.
$3.3 \times 10^{4}\,N$
d.
$1.1 \times 10^{4}\,N$
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A positive charge ' $q$ ' of mass ' $m$ ' is moving along the $+x$ axis. We wish to apply a uniform magnetic field B
for time $\Delta t$ so that the charge reverses its direction crossing the $y$ axis at a distance $d$ . Then:
a.
$B = \frac{mv}{qd}$ and $\Delta t = \frac{\pi d}{v}$
b.
$B = \frac{mv}{2qd}$ and $\Delta t = \frac{\pi d}{2v}$
c.
$B = \frac{2mv}{qd}$ and $\Delta t = \frac{\pi d}{2v}$
d.
$B= \frac{2mv}{qd}$ and $\Delta t = \frac{\pi d}{v}$
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In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of
some other wavelength. If wavelength of red light is $6600$ Å, then wavelength of first maximum will be:
a.
$3300$ Å
b.
$4400$ Å
c.
$5500$ Å
d.
$6600$ Å
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A cylindrical vessel of cross-section A contains water to a height $h$ . There is a hole in the bottom of radius ' $a$ '.
The time in which it will be emptied is:
A particle is moving in a circular path of radius a, with a constant velocity $v$ as shown in the figure. The centre
of circle is marked by ' $C$ '. The angular momentum from the origin $O$ can be written as:
a.
va $(1 + cos 2\theta )$
b.
va $(1 + cos\theta )$
c.
va $cos 2\theta$
d.
va
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From the following combinations of physical constants (expressed through their usual symbols) the only
combination, that would have the same value in different systems of units, is:
Which of the following expressions corresponds to simple harmonic motion along a straight line, where $x$ is
the displacement and $a, b, c$ are positive constants?
a.
$a+bx- cx^{2}$
b.
$bx^{2}$
c.
$a- bx+cx^{2}$
d.
$-bx$
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Two soap bubbles coalesce to form a single bubble. If $V$ is the subsequent change in volume of contained air
and $S$ change in total surface area, $T$ is the surface tension and $P$ atmospheric pressure, then which of the
following relation is correct?
a.
$4PV + 3ST = 0$
b.
$3PV + 4ST = 0$
c.
$2PV + 3ST = 0$
d.
$3PV + 2ST = 0$
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Hydrogen peroxide acts both as an oxidising and as a reducing agent depending upon the nature of the reacting
species. In which of the following cases $H_{2}O_{2}$ acts as a reducing agent in acid medium?
a.
$MnO^{-}_{4}$
b.
$Cr_{2}O^{2-}_{7}$
c.
$SO^{2-}_{3}$
d.
KI
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Which of the following arrangements represents the increasing order (smallest to largest) of ionic radii of the
given species $O^{2-}, S^{2-}, N^{3-}, P^{3-}$ ?
a.
$O^{2-} < N^{3-} < S^{2-} < P^{3-}$
b.
$O^{2-} < P^{3-} < N^{3-} < S^{2-}$
c.
$N^{3} < O^{2-} < P^{3-} < S^{2-}$
d.
$N^{3-} < S^{2-} < O^{2-} < P^{3-}$
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The amount of $BaSO_{4}$ formed upon mixing 100 $mL$ of $20.8%BaCl_{2}$ solution with $50\,mL$ of $9.8% H_{2}SO_{4}$
solution will be: $(Ba = 137, Cl = 35.5, \,S = 32, H = 1$ and $O = 16$ )
a.
$23.3\,g$
b.
$11.65\,g$
c.
$30.6\,g$
d.
$33.2\,g$
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The rate coefficient $(k)$ for a particular reactions is $1.3 \times 10^{-4}M^{-1}\,s^{-1}$ at $100^{\circ }C$ , and $1.3 \times 10^{-3} M^{-1}\,s^{-1}$ at
$150^{\circ }C$ . What is the energy of activation $(E_{A})$ (in $kJ)$ for this reaction? $(R =$ molar gas constant
$= 8.314JK^{-1}\,mol^{-1}$ )
a.
16
b.
60
c.
99
d.
132
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The standard enthalpy of formation $(\Delta _{f}H^{\circ }_{298})$ for methane, $CH_{4}$ is $-74.9\,kJ\,mol^{-1}$ . In order to calculate the
average energy given out in the formation of a $C -H$ bond from this it is necessary to know which one of the
following?
a.
The dissociation energy of the hydrogen
molecule, $H_{2}$ .
b.
The first four ionisation energies of carbon.
c.
The dissociation energy of $H_{2}$ and enthalpy and
sublimation of carbon (graphite).
d.
The first four ionisation energies of carbon and
electron affinity of hydrogen.
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If $m$ and $e$ are the mass and charge of the revolving electron in the orbit of radius $r$ for hydrogen atom, the
total energy of the revolving electron will be:
a.
$\frac{1}{2} \frac{e^{2}}{r}$
b.
$- \frac{e^{2}}{r}$
c.
$\frac{me^{2}}{r}$
d.
$- \frac{1}{2} \frac{e^{2}}{r}$
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The $(S^{\circ })$ of the following substances are: $CH_{4}\,g)186.2JK^{-1}\,mol^{-1} O_{2}$ (g) $205.2JK^{-1}\,mol^{-1}$
$CO_{2}(\,g)213.6JK^{-1}\,mol^{-1} H_{2}O(g)$ 69.9.JK $^{-1}\,mol^{-1}$ The entropy change $(\Delta S^{\circ })$ for the reaction
$CH_{4}(\,g) + 2O_{2}(\,g) CO_{2}(\,g) + 2H_{2}O$ (l) is:
a.
$-312.5\,J\,K^{-1}\,m\vec{o}l^{-1}$
b.
$-242.8JK^{-1}\,mol^{-1}$
c.
$-108.1JK^{-1}\,mol^{-1}$
d.
$-37.6\,J\,K^{-1}\,mol^{-1}$
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How many electrons would be required to deposit $6.35\,g$ of copper at the cathode during the electrolysis of an
aqueous solution of copper sulphate? (Atomic mass of copper $= 63.5u, N_{A} =$ Avogadro's constant):
a.
$\frac{N_{A}}{20}$
b.
$\frac{N_{A}}{10}$
c.
$\frac{N_{A}}{5}$
d.
$\frac{N_{A}}{2}$
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Excited hydrogen atom emits light in the ultraviolet region at $2.47 \times 10^{15}\,Hz$ . With this frequency, the energy
of a single photon is: $(h = 6.63 \times 10^{-34}Js)$
a.
$8.041 \times 10^{-40}\,J$
b.
$2.680 \times 10^{-19}\,J$
c.
$1.640 \times 10^{-18}\,J$
d.
$6.111 \times 10^{-17}\,J$
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If for a continuous function $f(x)$ , $\int _{-}^{t}_{\pi }(f(x) +xdx) =\pi ^{2}- t^{2}$ , for all $t\geq -\pi$ , then $f(-\frac{\pi}{3})$ is equal to:
a.
$\pi$
b.
$\frac{\pi}{2}$
c.
$\frac{\pi}{3}$
d.
$\frac{\pi}{6}$
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A relation on the set $A = {x : |x| < 3, x \in Z}$ , where $Z$ is the set of integers is defined by
$R = {(x, y) : y = |x|, x \neq -1}$ . Then the number of elements in the power set of $R$ is:
a.
32
b.
16
c.
8
d.
64
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Let $X-$ and M.D. be the mean and the mean deviation about $X-$ of $n$ observations $x_{i}, i = 1, 2$ ,n. If each of the
observations is increased by 5 , then the new mean and the mean deviation about the new mean, respectively,
are :
$-$
a.
$X$ , M.D.
b.
$X + 5$ , M.D.
$-$
c.
$\bar{X}-$ , M.D. $+5$
d.
$X + 5$ , M.D. $+5$
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Let $G$ be the geometric mean of two positive numbers $a$ and $b$ , and $M$ be the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{\,b}$ . If
$\frac{1}{M} : G$ is $4 : 5$ , then $a : b$ can be:
a.
$1 : 4$
b.
$1 : 2$
c.
$2 : 3$
d.
$3 : 4$
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If $\hat{x}, \hat{y}$ and $\hat{z}$ are three unit vectors in threedimensional space, then the minimum value of
$|\hat{x}+ \hat{y}|^{2} + |\hat{y}+ \hat{z}|^{2} + |\hat{z}+ \hat{x}|^{2}$
a.
$\frac{3}{2}$
b.
3
c.
$3\sqrt{3}$
d.
6
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$1 cos\theta 1$
If $f(\theta ) = -sin\theta 1 -cos\theta$ and $A$ and $B$ are respectively the maximum and the minimum values of
$-1 sin\theta 1$
$f(\theta )$ , then $(A,B)$ is equal to:
a.
$(3, -1)$
b.
$(4, 2 - \sqrt{2})$
c.
$(2 + \sqrt{2}, 2 - \sqrt{2})$
d.
$(2 + \sqrt{2}, -1)$
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If $(2 + \frac{x}{3})^{55}$ is expanded in the ascending powers of $x$ and the coefficients of powers of $x$ in two consecutive
terms of the expansion are equal, then these terms are:
a.
$7^{th\,}$ and $8^{th\,}$
b.
$8^{th\,}$ and $9^{th\,}$
c.
$28^{th\,}$ and $29^{th\,}$
d.
$27^{th\,}$ and $28^{th\,}$
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A number $x$ is chosen at random from the set ${1$ , $2, 3, 4, … . , 100}$ . Define the event: $A =$ the chosen number
$x$ satisfies $\frac{(x-10)(x-50)}{(x-30)} \geq 0$ Then $P(A)$ is:
a.
$0.71$
b.
$0.70$
c.
$0.51$
d.
$0.20$
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$xsin(\frac{1}{x} ) ,x\neq 0$
Let $f, g : R \rightarrow R\rightarrow$ be two functions defined by $f(x) ={$ and $g(x) =xf(x)$ Statement I: $f$ is
$0, ,x= 0$
a continuous function at $x = 0$ . Statement II: $g$ is a differentiable function at $x= 0$ .
a.
Both statement I and II are false.
b.
Both statement I and II are true.
c.
Statement $I$ is true, statement $II$ is false.
d.
Statement $I$ is false, statement $II$ is true.
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