A mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If
the string does not slip on the cylinder, with what acceleration will the mass fall on release?
a.
$\frac{2g}{3}$
b.
$\frac{g}{2}$
Correct Answer
c.
$\frac{5g}{6}$
d.
$g$
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Q2mcq
A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob
rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :
a.
Angular momentum is conserved
b.
Angular momentum changes in magnitude but not
in direction
c.
Angular momentum changes in direction but not
in magnitude
Correct Answer
d.
Angular momentum changes both in direction and
magnitude
No explanation saved for this question yet.
Q3mcq
A green light is incident from the water to the air - water interface at the critical angle $(\theta _{c})$ . Select the correct
statement.
a.
The entire spectrum of visible light will come out
o
of the water at an angle of 90 to the normal
b.
The spectrum of visible light whose frequency is
less than that of green light will come out to the
air medium
Correct Answer
c.
The spectrum of visible light whose frequency is
more than that of green light will come out to the
air medium
d.
The entire spectrum of visible light will come out
of the water at various angles to the normal
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Q4mcq
A particle moves with simple harmonic motion in a straight line. In first $τ s$ , after starting from rest it travels a
distance a, and in next $τ s$ it travels 2a, in same direction, then :
a.
Amplitude of motion is 3a
b.
Time period of oscillations is $8τ$
c.
Amplitude of motion is 4a
d.
Time period of oscillations is $6τ$
Correct Answer
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Q5mcq
A thin convex lens made from crown glass $(\mu = \frac{3}{2} )$ has focal length $f$ . When it is measured in two different
liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$ , it has the focal lengths $f_{1}$ and $f_{2}$ respectively. The correct relation
between the focal lengths is :
a.
$f_{1} =f_{2} <f$
b.
$f_{1} >f$ and $f_{2}$ becomes negative
Correct Answer
c.
$f_{2} >f$ and $f_{1}$ becomes negative
d.
$f_{1}$ and $f_{2}$ both become negative
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Q6mcq
When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude
2
F = ax + bx where a and b are constants. The work done in stretching the unstretched rubber-band by L is :
$+ bL$
The current voltage relation of diode is given by I = (e - 1) mA, where the applied voltage V is in volts
and the temperature T is in degree Kelvin. If a student makes an error measuring $\pm 0.01 V$ while measuring the
current of 5 mA at 300 K, what will be the error in the value of current in mA ?
a.
0.2 mA
Correct Answer
b.
0.02 mA
c.
0.5 mA
d.
0.05 mA
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Q8mcq
In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The
voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be:
a.
8 A
b.
10 A
c.
12 A
Correct Answer
d.
14 A
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Q9mcq
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d and d are filled in
1 2
o
the tube. Each liquid subtends 90 angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical.
Ratio $\frac{d_{1}}{\,d_{2}}$ is :
a.
$\frac{1+sin\alpha}{1-sin\alpha}$
b.
$\frac{1+cos\alpha}{1-cos\alpha}$
c.
$\frac{1+tan\alpha}{1-tan\alpha}$
Correct Answer
d.
$\frac{1+sin\alpha}{1-cos\alpha}$
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Q10mcq
The radiation corresponding to $3 \rightarrow 2\rightarrow$ transition of hydrogen atom falls on a metal surface to produce
photoelectrons. These electrons are made to enter a magnetic field of $3 \times 10^{-4} T$ . If the radius of the largest
circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :
a.
1.8 eV
b.
1.1 eV
Correct Answer
c.
0.8 eV
d.
1.6 eV
No explanation saved for this question yet.
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A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column
in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
a.
12
b.
8
c.
6
d.
4
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A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric
of dielectric constant 2.2 between them. When the electric field in the dielectric is $3 \times 10^{4}\,V/m$ , the charge
density of the positive plate will be close to :
a.
$6 \times 10^{-7}\,C/m^{2}$
b.
$3 \times 10^{-7}\,C/m^{2}$
c.
$3 \times 10^{4}\,C/m^{2}$
d.
$6 \times 10^{4}\,C/m^{2}$
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On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be
spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r << R, and the
surface tension of water is T, value of r just before bubbles detatch is :
(density of water is $\rho _{w}$ )
a.
$R^{2}\sqrt{\,} \frac{2$\rho$_{w}\,g}{3T}$
b.
$R^{2}\sqrt{\,} \frac{\rho _{w}\,g}{6T}$
c.
$R^{2}\sqrt{\,} \frac{\rho _{w}\,g}{T}$
d.
$R^{2}\sqrt{\,} \frac{3\rho _{w}\,g}{T}$
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One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is
adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct
statement :
a.
The change in internal energy in whole cyclic
process is 250 R
b.
The change in internal energy in the process CA
is 700 R.
c.
The change in internal energy in the process AB
is - 350 R
d.
The change in internal energy in the process BC
is - 500 R
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The pressure that has to be applied to the ends of a steel wire of length $10\, cm$ to keep its length constant when
its temperature is raised by $100\,^{\circ}C$ is :
(For steel, Young's modulus is $2 \times 10^{11}\,N\,m^{-2}$ and coefficient of thermal expansion is $1. 1 \times 10^{-5}\,K^{-1}$ )
a.
$2 .2 \times 10^{8}\, Pa$
b.
$2 .2 \times 10^{9}\, Pa$
c.
$2 .2 \times 10^{7}\, Pa$
d.
$2 .2 \times 10^{6}\, Pa$
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1 2 4 + 6 ++
Hydrogen ( H ), Deuterium ( H ), singly ionised Helium ( He ) and doubly ionised lithium ( Li ) all have
1 1 2 3
one electron around the nucleus. Consider an electron transition from $n= 2$ to $n= 1$ . If the wave lengths of
emitted radiation are $\lambda _{1},\,\lambda _{2},\,\lambda _{3}$ and $\lambda _{4}$ respectively then approximately which one of the following is correct ?
The coercivity of a small magnet, where the ferromagnet gets demagnetised is $3 \times 10^{3}\,A/m$ . The current
required to be passed in a solenoid of length $10\, cm$ and number of turns $100$ , so that the magnet gets
demagnetised when inside the solenoid is
a.
30 mA
b.
60 mA
c.
3 A
d.
6 A
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An open glass tube is immersed in mercury in such a way that a length of $8\, cm$ extends above the mercury
level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional
$46\, cm$ . What will be length of the air column above mercury in the tube now ?
(Atmospheric pressure = $76\, cm$ of Hg)
a.
$16\, cm$
b.
$22\, cm$
c.
$38\, cm$
d.
$6\, cm$
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Assume that an electric field $\vec{E}= 30x^{2}ˆi$ exists in space. Then the potential difference $V$ , where V
$_{A}-V_{O}$ O
is the potential at the origin and V the potential at x = 2 m is :
A
a.
$120\,J\,C^{-1}$
b.
$-120\,J\,C^{-1}$
c.
$-80\,J\,C^{-1}$
d.
$80\,J\,C^{-1}$
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Four particles, each of mass $M$ and equidistant from each other, move along a circle of radius $R$ under the
action of their mutual gravitational attraction. The speed of each particle is
a.
$\sqrt{\frac{GM}{R}}$
b.
$\sqrt{2}\sqrt{2}\frac{GM}{R}$
c.
$\sqrt{\frac{GM}{R}}(1 + 2\sqrt{2})$
d.
$\frac{1}{2}\sqrt{\frac{GM}{R}} (1 + 2\sqrt{2})$
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Two beams, A and B of plane polarized light with mutually perpendicular planes of polarization are seen
through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero
o
intensity), a rotation of polaroid through 30 makes the two beams appear equally bright. If the initial
intensities of the two beams are I and I respectively, then $\frac{I_{A}}{I_{B}}$ equals :
A B
a.
3
b.
$\frac{3}{2}$
c.
1
d.
$\frac{1}{3}$
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A conductor lies along the z-axis at $-1.5 \leq z < 1.5 m$ and carries a fixed current of 10.0 A in $-ˆa_{z}$ direction
(see figure). For a field $\vec{B}= 3.0 \times 10^{-4}\,e^{-0.2x\,}ˆa_{y}$ T, find the power required to move the conductor at constant
speed to x = 2.0 m, y = 0 m in $5 \times 10^{-3}\,s$ . Assume parallel motion along the x-axis.
a.
1.57 W
b.
2.97 W
c.
14.85 W
d.
29.7 W
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In the circuit shown here, the point ' $C$ ' is kept connected to point $A$ '' till the current flowing through the circuit
becomes constant. Afterward, suddenly, point ' $C$ ' is disconnected from point $A$ '' and connected to point ' $B$ ' at
time $t= 0$ . Ratio of the voltage across resistance and the inductor at $t= \frac{L}{R}$ will be equal to :
a.
$\frac{e}{1-e}$
b.
1
c.
- 1
d.
$\frac{1-e}{e}$
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A block of mass $m$ is placed on a surface with a vertical cross section given by $y= \frac{x^{3}}{6}$ . If the coefficient of
friction is $0. 5$ , the maximum height above the ground at which the block can be placed without slipping is
a.
$\frac{1}{6}\,m$
b.
$\frac{2}{3}\,m$
c.
$\frac{1}{3}\,m$
d.
$\frac{1}{2}\,m$
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Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section
of each rod is $4\, cm^{2}$ . End of copper rod is maintained at $100^{\circ}C$ . Where as ends of brass and steel are kept at
$0^{\circ}C$ . Lengths of the copper, brass and steel rods are $46, \,13\,$ and $12\, cms$ respectively. The rods are thermally
insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are $0. 92, \,0. 26$
and $0. 12$ CGS units respectively. Rate of heat flow through copper rod is :
a.
$1. 2\, Cal /s$
b.
$2. 4\, Cal /s$
c.
$4. 8\, Cal /s$
d.
$6. 0\, Cal /s$
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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle,
to hit the ground, is n times that taken by it to reach the highest point of its path.The relation between H, u and n
is :
a.
2 g H = n2 2
u
b.
g H = (n - 2)2 2
u
c.
2g H = nu2
(n - 2)
d.
g H = (n - 2)u2
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Match List - I(Electromagnetic wave type) with List - II(Its association/application) and select the correct
option from the choices given below the lists :
List - I List - II
(a) Infrared waves (i) To treat muscular strain
(b) Radio waves (ii) For broadcasting
(c) X - rays (iii) To detect fracture of bones
(d) Ultraviolet rays (iv) Absorbed by the ozone layer of the atmosphere
$a b c d a b c d$
a.
$( ) ( ) ( ) ( )$
$(iv) (iii) (ii) (i)$
$a b c d$
b.
$( ) ( ) ( ) ( )$
$(i) (ii) (iv) (iii)$
$a b c d$
c.
$( ) ( ) ( ) ( )$
$(iii) (ii) (i) (iv)$
d.
$( ) ( ) ( ) ( )$
$(i) (ii) (iii) (iv)$
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For complete combustion of ethanol,
$C_{2}H_{5}OH(l) + 3O_{2}(g) \rightarrow 2CO\rightarrow_{2}(g) + 3H_{2}O(l)$ ,
the amount of heat produced as measured in bomb calorimeter, is $1364.47 kJ mol^{-1}$ at $25$ ℃. Assuming
ideality the Enthalpy of combustion, $\Delta _{c}H$ , for the reaction will be: $(R = 8.314 kJ mol^{-1})$
a.
$-1366.95 kJ mol^{-1}$
b.
$-1361.95 kJ mol^{-1}$
c.
$-1460.50 kJ mol^{-1}$
d.
$-1350.50 kJ mol^{-1}$
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For the non-stoichiometry reaction, $2A + B \rightarrow C + D\rightarrow$ , the following kinetic data were obtained in three
separate experiments, all at $298\,K$ .
Initial Concentration Initial Concentration Initial rate of formation of C
(A) (B) $(mol L^{-} S^{-})$
$0.1 M 0.1 M 1.2 \times 10^{-3}$
$0.1 M 0.2 M 1.2 \times 10^{-3}$
$0.2 M 0.1 M 2.4 \times 10^{-3}$
The rate law for the formation of $C$ is
a.
$\frac{dc}{dt} = k[A][B]$
b.
$\frac{dc}{dt} = k[A]^{2}[B]$
c.
$\frac{dc}{dt} = k[A][B]^{2}$
d.
$\frac{dc}{dt} = k[A]$
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In which of the following reactions $H_{2}O_{2}$ acts as a reducing agent ?
$(a)\,\,H_{2}O_{2}+ 2H^{+} + 2e^{-} \rightarrow 2H\rightarrow_{2}O$
$(b)\,\,H_{2}O_{2}-2e^{-} \rightarrow O\rightarrow_{2}+ 2H^{+}$
$(c)\,\,H_{2}O_{2}+ 2e^{-} \rightarrow 2OH\rightarrow^{-}$
$(d)\,\,H_{2}O_{2}+ 2OH^{-} -2e^{-} \rightarrow O\rightarrow_{2}+ 2H_{2}O$
a.
(a) , (b)
b.
(c) , (d)
c.
(a) , (c)
d.
(b) , (d)
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For the estimation of nitrogen, $1. 4\,g$ of an organic compound was digested by the Kjeldahl method and the
evolved ammonia was absorbed in $60\, ml$ of $\frac{M}{10}$ sulphuric acid. The unreacted acid required $20\, ml$ of $\frac{M}{10}$
sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is
a.
$6%$
b.
$10%$
c.
$3%$
d.
$5%$
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In the reaction,
$^{LiAlH_{4}}^{PCl_{5}}^{Alc. KOH}C$ ,
$---CH_{3}COOH \rightarrow \rightarrow A \rightarrow \rightarrow B \rightarrow \rightarrow$
the product C is :
a.
Acetaldehyde
b.
Acetylene
c.
Ethylene
d.
Acetyl chloride
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Resistance of 0.2 M solution of an electrolyte is $50\,\Omega$ . The specific conductance of the solution is $1.4 S m^{-1}$ .
The resistance of 0.5 M solution of the same electrolyte is $280\,\Omega$ . The molar conductivity of 0.5 M solution of
the electrolyte in $S m^{2} mol^{-1}$ is :
a.
$5 \times 10^{-4}$
b.
$5 \times 10^{-3}$
c.
$5 \times 10^{3}$
d.
$5 \times 10^{2}$
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For the reaction $SO_{2}(g) + \frac{1}{2} O_{2}(g) \rightleftharpoons SO_{3}(g)$ , if $K_{P} = K_{C}(RT)^{x}$ where the symbols have usual meaning
then the value of $x$ is:
(assuming ideality)
a.
$-1$
b.
$-\frac{1}{2}$
c.
$\frac{1}{2}$
d.
$1$
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Consider separate solutions of $0. 500\,M\,C_{2}H_{5}OH \,(aq), \,0. 100\,M\, Mg_{3}(PO_{4})_{2}\,(aq), \,0. 250\,M\, KBr \,(aq)$
and $0. 125\,M\, Na_{3}PO_{4}\,(aq)$ at $25^{\circ}C$ . Which statement is true about these solutions, assuming all salts to be
strong electrolytes?
a.
They all have the same osmotic pressure.
b.
$0. 100\,M\, Mg_{3}(PO_{4})_{2}\,(aq)$ has the highest
osmotic pressure.
c.
$0. 125\,M\, Na_{3}PO_{4}\,(aq)$ has the highest osmotic
pressure.
d.
$0. 500\,M\,C_{2}H_{5}OH \,(aq)$ has the highest osmotic
pressure.
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The octahedral complex of a metal ion $M^{3+}$ with four monodentate ligands $\vec{L}_{1}, \,L_{2}, \,L_{3}\, and \,L_{4}$ absorb
wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength
of the four ligands is
a.
$L_{4}\, < \,L_{3}\, < \,L_{2}\, < \,L_{1}$
b.
$L_{1}\, < \,L_{3}\, < \,L_{2}\, < \,L_{4}$
c.
$L_{3}\, < \,L_{2}\, < \,L_{4}\, < \,L_{1}$
d.
$L_{1}\, < \,L_{2}\, < \,L_{4}\, < \,L_{3}$
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The equivalent conductance of $NaCl$ at concentration C and at infinite dilution are $\lambda _{C}$ and $\lambda _{\infty }$ , respectively.
The correct relationship between $\lambda _{C}$ and $\lambda _{\infty }$ is given as :
(where the constant B is positive)
a.
$\lambda _{C} =\lambda _{\infty } + (B)C$
b.
$\lambda _{C} =\lambda _{\infty } -(B)C$
c.
$\lambda _{C} =\lambda _{\infty } -(B)\sqrt{C}$
d.
$\lambda _{C} =\lambda _{\infty } + (B)\sqrt{C}$
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$--_{LetAandBbe two events such thatP(A\cup }_{B)=} \frac{1}{6}_{, \,P(A\cap }_{B) =} \frac{1}{4}_{andP(A)=} \frac{1}{4}_{,whereAstands for}$
the complement of the event $A\bar{. Then the events}A$ and $B$ are
a.
Independent but not equally likely.
b.
Independent and equally likely.
c.
Mutually exclusive and independent.
d.
Equally likely but not independent.
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If $[\vec{a}\times \vec{b}^{\,\,} \vec{b}\times \vec{c}^{\,\,} \vec{c}\times \vec{a}]=\lambda [ \vec{a}^{\,\,\,} \vec{b}^{\,\,\,} \vec{c}]^{2}$ then $\lambda$ is equal to
a.
$0$
b.
$1$
c.
$2$
d.
$3$
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Let $PS$ be the median of the triangle with vertices $P(2, 2), \,Q(6, -1)$ and $R(7, 3)$ . The equation of the line
passing through $(1, -1)\,$ and parallel to $PS$ is
a.
$4x+ 7y+ 3 = 0$
b.
$2x-9y-11 = 0$
c.
$4x-7y-11 = 0$
d.
$2x+ 9y+ 7 = 0$
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Let $C$ be the circle with center at $(1, 1)$ and radius $= 1$ . If $T$ is the circle centered at $(0,y)$ , passing through the
origin and touching the circle $C$ externally, then the radius of $T$ is equal to
a.
$\frac{1}{2}$
b.
$\frac{1}{4}$
c.
$\frac{\sqrt{3}}{\sqrt{2}}$
d.
$\frac{\sqrt{3}}{2}$
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Let the population of rabbits surviving at a time $t$ be governed by the differential equation
$\frac{dp(t)}{dt} = \frac{1}{2}{p(t) -400}$ . If $p(0) = 100$ , then $p(t)$ equals
a.
$600\, -\,500\,e \frac{t}{2}$
b.
$400 -300\,e\frac{-t}{2}$
c.
$400\, -\,300\,e^{t/2}$
d.
$300 -200\,e\frac{-t}{2}$
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If $a\, \in \,R$ and the equation $-3(x\, -\,[x])^{2} + 2(x\, -\,[x])+a^{2}\, = \,0$ (where $[x]$ denotes the greatest integer
$\leq \,x$ ) has no integral solution, then all possible values of $a$ lie in the interval
a.
$(-2, \, -1)$
b.
$( -\infty , -2) \cup (2,\infty )$
c.
$(-1,\,0) \cup (0,\,1)$
d.
$(1, 2)$
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If $A$ is a $3 \times 3$ non-singular matrix such that $AA' =A'A$ and $B=A^{-1}A',$ then $BB'$ equals, where $X'$ denotes
the transpose of the matrix $X$ .
a.
$B^{-1}$
b.
$(B^{-1})'$
c.
$I+B$
d.
$I$
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Three positive numbers form an increasing $G.P.$ If the middle term in this $G.P.$ is doubled, the new numbers
are in $A.P.$ Then the common ratio of the $G.P.$ is :
a.
$2 - \sqrt{3}$
b.
$2 + \sqrt{3}$
c.
$\sqrt{2}+ \sqrt{3}$
d.
$3 + \sqrt{2}$
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A bird is sitting on the top of a vertical pole $20\,m$ high and its elevation from a point $O$ on the ground is $45^{\circ}$ . It
flies off horizontally straight away from the point $O$ . After one second, the elevation of the bird from $O$ is
reduced to $30^{\circ}$ . Then the speed (in $m/s$ ) of the bird is
a.
$20\sqrt{2}$
b.
$20(\sqrt{3}-1)$
c.
$40(\sqrt{2}-1)$
d.
$40(\sqrt{3}- \sqrt{2})$
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Let $a, \,b, \,c$ and $d$ be non-zero numbers. If the point of intersection of the lines
$4ax+ 2ay+c= 0\,&\,5bx+ 2by+d= 0$ lies in the fourth quadrant and is equidistant from the two axes then
a.
$3bc-2ad= 0$
b.
$3bc+ 2ad= 0$
c.
$2bc-3ad= 0$
d.
$2bc+ 3ad= 0$
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Let $\alpha \,and\,\beta$ be the roots of equation $px^{2} +qx+r\, = \,0$ , $p\neq 0$ . If $p, \,q, \,r$ are in A.P. and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$ , then the
value of $|\alpha - \beta |$ is
a.
$\frac{\sqrt{34}}{9}$
b.
$\frac{2\sqrt{13}}{9}$
c.
$\frac{\sqrt{61}}{9}$
d.
$\frac{2\sqrt{17}}{9}$
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