Two spheres of the same material have radii $1\,m$ and $4\,m$ and temperatures $4000\,K$ and $2000\,K$ respectively.
The ratio of the energy radiated per second by the first sphere to that by the second is
a.
1 : 1
Correct Answer
b.
16 : 1
c.
4 : 1
d.
5 : 3
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Q2mcq
If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a
a.
low resistance in parallel
b.
high resistance in parallel
c.
high resistance in series
Correct Answer
d.
low resistance in series
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Q3mcq
A particle of mass $m$ moves along line $PC$ with velocity $v$ as shown. What is the angular momentum of the
particle about $P?$
a.
mvL
b.
mvl
c.
mvr
d.
zero
Correct Answer
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Q4mcq
When forces $F_{1},F_{2},F_{3}$ are acting on a particle of mass $m$ such that $F_{2}$ and $F_{3}$ are mutually perpendicular, then
the particle remains stationary. If the force $F_{1}$ is now removed then the acceleration of the particle is
a.
$F_{1}/m$
Correct Answer
b.
$F_{2}\,F_{3}/mF_{1}$
c.
$(F_{2}- F_{3})/m$
d.
$F_{2}/m$
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Q5mcq
A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$
perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular
and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure. The
induced emf is
a.
zero
b.
RvB
c.
VBL/R
d.
VBL
Correct Answer
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Q6mcq
Infra red radiation is detected by
a.
spectrometer
b.
pyrometer
Correct Answer
c.
nanometer
d.
photometer
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Q7mcq
If $\theta _{i}$ , is the inversion temperature, $\theta _{n}$ is the neutral temperature, $\theta _{c}$ is the temperature of the cold junction, then
One end of a massless rope, which passes over a massless and frictionless pulley $P$ is tied to a hook $C$ while
the other end is free. Maximum tension that the rope can bear is $360\,N$ . With what value of maximum safe
acceleration (in $ms^{-2}$ ) can a man of $60\,kg$ climb on the rope?
a.
16
b.
6
c.
4
d.
8
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A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (vertically). If the
acceleration of the system is $g/8$ , then the ratio of the masses is
a.
8 : 1
b.
9 : 7
c.
4 : 3
d.
5 : 3
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The minimum velocity (in $ms^{-1}$ ) with which a car driver must traverse a flat curve of radius $150\,m$ and
coefficient of friction $0.6$ to avoid skidding is
a.
60
b.
30
c.
15
d.
25
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A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the
ball as observed by the man in the lift and a man standing stationary on the ground are respectively
a.
g, g
b.
g - a, g - a
c.
g - a, g
d.
a, g
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Speeds of two identical cars are $u$ and $4u$ at the specific instant. The ratio of the respective distances in which
the two cars are stopped from that instant is
a.
1 : 1
b.
1 : 4
c.
1 : 8
d.
1 : 16
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A wire when connected to $220\,V$ mains supply has power dissipation $P_{1}$ . Now the wire is cut into two equal
pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_{2}$ Then $P_{2} :P_{1}$ is
a.
1
b.
4
c.
2
d.
3
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A charged particle $q$ is placed at the centre $O$ of cube of length $L$ (A B C D E F G H). Another same charge $q$ is
placed at a distance $L$ from $O$ . Then the electric flux through $ABCD$ is
a.
$q/4\pi \epsilon _{0}L$
b.
zero
c.
$q/2\pi \epsilon _{0}L$
d.
$q/3\pi \epsilon _{0}L$
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Initial angular velocity of a circular disc of mass $M$ is $\omega _{1}$ . Then two small spheres of mass $m$ are attached
gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?
a.
$(\frac{M+m}{M})\omega _{1}$
b.
$(\frac{M+m}{m} )\omega _{1}$
c.
$(\frac{M}{M+4\,m})\omega _{1}$
d.
$(\frac{M}{M+2m} )\omega _{1}$
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A ball whose kinetic energy is E, is projected at an angle of $45^{\circ }$ to the horizontal. The kinetic energy of the ball
at the highest point of its flight will be
a.
$E$
b.
$E/\sqrt{2}$
c.
$E/2$
d.
zero
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Wires 1 and 2 carrying currents $i_{1}$ and $i_{2}$ respectively are inclined at an angle $\theta$ to each other. What is the force
on a small element dl of wire 2 at a distance of $r$ from wire 1 (as shown in the figure) due to the magnetic field
of wire 1 ?
A solid sphere, a hallow sphere and a ring are released from top of an inclined plane (frictionless) so that they
slide down the plane. Then maximum acceleration down the plane is for (no rolling)
a.
solid sphere
b.
hollow sphere
c.
ring
d.
all same
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Wavelength of light used in an optical instrument are $\lambda _{1} = 4000$ Åand $\lambda _{2} = 5000$ Å, then ratio of their
respective resolving powers (corresponding to $\lambda _{1}$ and $\lambda _{2}$ ) is
a.
16 : 25
b.
9 : 1
c.
4 : 5
d.
5 : 4
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From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards $A$ and $B$ downwards (both
vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then
a.
$V_{B} > V_{A}$
b.
$V_{A} = V_{B}$
c.
$V_{A} > V_{B}$
d.
their velocities depend on their masses
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If in a circular coil $A$ of radius $R$ , current I is flowing and in another coil $B$ of radius $2R$ a current $2l$ is
flowing, then the ratio of the magnetic fields $B_{A}$ and $B_{B}$ , produced by them will be
a.
1
b.
2
c.
1/2
d.
4
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At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can
emit (i) electrons (ii) protons (iii) $He^{2+}$ (iv) neutrons The emission at instant can be
a.
i, ii, iii
b.
i, ii, iii, iv
c.
iv
d.
ii, iii
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In a transformer, number of turns in the primary coil are 140 and that in the secondary coil are 280. If current
in primary coil is $4\,A$ , then that in the secondary coil is
a.
4 A
b.
2 A
c.
6 A
d.
10 A
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A tuning fork arrangement (pair) produces 4 beats / sec with one fork of frequency $288cps$ . A little wax is
placed on the unknown fork and it then produces 2 beats /sec. The frequency of the unknown fork is
a.
286 cps
b.
292 cps
c.
294 cps
d.
288 cps
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A bead of weight $w$ can slide on smooth circular wire in a vertical plane. The bead is attached by a light thread
to the highest point of the wire and in equilibrium, the thread is taut and make an angle $\theta$ with the vertical then
tension of the thread and reaction of the wire on the bead are
a.
$T =wcos\theta R=wtan\theta$
b.
$T = 2w cos\theta R = w$
c.
$T = w R = w sin\theta$
d.
$T =wsin\theta R=wcot\theta$
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A cylinder of height $20\,m$ is completely filled with water. The velocity of efflux of water (in $ms^{-1}$ ) through a
small hole on the side wall of the cylinder near its bottom is
a.
10
b.
20
c.
25.5
d.
5
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Three identical blocks of masses $m = 2\,kg$ are drawn by a force $F = 10.2\,N$ with an acceleration of $0.6\,ms^{-2}$
on a frictions surface, then what is the tension (in $N$ ) in the string between the blocks $B$ and $C$ ?
a.
9.2
b.
7.8
c.
4
d.
9.8
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Two forces are such that the sum of their magnitudes is $18\,N$ and their resultant is $12\,N$ which is perpendicular
to the smaller force. Then the magnitudes of the forces are
a.
$12\,N, 6\,N$
b.
$13\,N, 5\,N$
c.
$10\,N, 8\,N$
d.
$16\,N, 2\,N$
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Uncertainity in position of a minute particle of mass $25\,g$ in space is $10^{-5}\,m$ . What is the uncertainity in its
velocity (in $ms^{-1})?(\,h = 6.6 \times 10^{-34}Js)$
a.
$2.1 \times 10^{-34}$
b.
$0.5 \times 10^{-34}$
c.
$2.1 \times 10^{-28}$
d.
$0.5 \times 10^{-23}$
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When $KMnO_{4}$ acts as an oxidising agent and ultimately forms $[MnO_{4}]^{-1}, MnO_{2}, Mn_{2}O_{3}, Mn^{+2}$ then the
number of electrons transferred in each case respectively is
a.
4, 3, 1, 5
b.
1, 5, 3, 7
c.
1, 3, 4, 5
d.
3, 5, 7, 1
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Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of Na and Mg
present in the unit cell of their respective crystal is
a.
4 and 2
b.
9 and 14
c.
14 and 9
d.
2 and 4
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Freezing point of an aqueous solution is $(-0.186)^{\circ }C$ . Elevation of boiling point of the same solution is
$K_{b} = 0.512^{\circ }C, K_{f} = 1.86^{\circ }C$ , find the increase in boiling point.
a.
$0.186^{\circ }C$
b.
$0.0512^{\circ }C$
c.
$0.092^{\circ }C$
d.
$0.2372^{\circ }C$
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A metal $M$ readily forms its sulphate $MSO_{4}$ which is water - soluble. It forms its oxide MO which becomes
inert on heating. It forms an insoluble hydroxide $M(OH)_{2}$ which is soluble in $NaOH$ solution. Then $M$ is
a.
Mg
b.
Ba
c.
Ca
d.
Be
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Conductivity (unit Siemen’s S) is directly proportional to area of the vessel and the concentration of the
solution in it and is inversely proportional to the length of the vessel then the unit of the constant of
proportionality is
a.
$Sm\,mol^{-1}$
b.
$Sm^{2}\,mol^{-1}$
c.
$S^{-2}\,m^{2}\,mol$
d.
$S^{2}\,m^{2}\,mol^{-2}$
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A heat engine absorbs heat $Q_{1}$ at temperature $T_{1}$ and heat $Q_{2}$ at temperature $T_{2}$ . Work done by the engine is
$J(Q_{1}+Q_{2})$ . This data
(1) violates $1^{st\,}$ law of thermodynamics (2) violates $1^{st\,}$ law of thermodynamics if $Q_{1}$ is $-ve$
(3) violates $1^{st\,}$ law of thermodynamics if $Q_{2}$ is $-$ ve(4) does not violate $1^{st\,}$ law of thermodynamics
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Arrangement of $(CH_{3})_{3}-C-, (CH_{3})_{2}-CH-, CH_{3}-CH_{2}$ - when attached to benzyl or an unsaturated
group in increasing order of inductive effect is
$\vec{a}= 3\hat{i}-5\hat{j}$ and $\vec{b}= 6\hat{i}+ 3\hat{j}$ are two vectors and $\vec{c}$ is a vector such that $\vec{c}= \vec{a}\times \vec{b}$ then
$|\vec{a}| : |\vec{b}| : |\vec{c}|$
a.
$\sqrt{34}: : \sqrt{45} \sqrt{39}$
b.
$\sqrt{34}: : 39\sqrt{45}$
c.
$34 : 39 : 45$
d.
$39 : 35 : 34$
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In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of
the complete class is 72, then what is the average of the girls?
a.
73
b.
65
c.
68
d.
74
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If $\alpha \neq \beta$ but $\alpha ^{2} = 5\alpha -3$ and $\beta ^{2} = 5\beta -3$ then the equation having $\alpha /\beta$ and $\beta /\alpha$ as its roots is
a.
$3x^{2} -19x+ 3 = 0$
b.
$3x^{2} + 19x-3 = 0$
c.
$3x^{2} -19x-3 = 0$
d.
$x^{2} -5x+ 3 = 0$
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If $y=f(x)$ makes $+ve$ intercept of 2 and 0 unit on $x$ and $y$ axes and encloses an area of $3/4$ square unit with
the axes then $\int _{0}^{2} xf'(x)dx is$
a.
3/2
b.
1
c.
5/4
d.
-3/4
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$f(x)$ and $g(x)$ are two differentiable functions on $[0, 2]$ such that $f''(x) - g''(x) = 0$
$f'(1) = 2g'(1) = 4f(2) = 3g(2) = 9$ then $f(x) - g(x)$ at $x= 3/2$ is
a.
0
b.
2
c.
10
d.
5
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$r$ and $n$ are positive integers $r> 1,n> 2$ and coefficient of $(r+ 2)^{th\,}$ term and $3r^{th\,}$ term in the expansion of
$(1 +x)^{2n}$ are equal, then $n$ equals
a.
3r
b.
3r + 1
c.
2r
d.
2r + 1
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The locus of the centre of a circle which touches the circle $|z- z_{1}| =a$ and $|z- z_{2}| =b$ externally ( $z,z_{1}$ and
$z_{2}$ are complex numbers) will be
a.
an ellipse
b.
a hyperbola
c.
a circle
d.
none of these
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A problem in mathematics is given to three students $A, B, C$ and their respective probability of solving the
problem is $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ . Probability that the problem is solved is
a.
$\frac{3}{4}$
b.
$\frac{1}{2}$
c.
$\frac{2}{3}$
d.
$\frac{1}{3}$
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