Byju's Answer

Question Papers

WBJEE | 2011

Q. A box is moved along a straight line by machine delivering constant power. The distance moved by the body in time

t

is proportional to:

$t^{2}$
$t^{\frac{3}{2}}$
$t^{\frac{3}{4}}$
$t^{\frac{1}{2}}$

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Q. A cubical vessel of height

1 m

is full of water. What is the amount of work done in pumping water out of the vessel?
(Take

g = 10 m / s^{2}

)

$1250 J$
$5000 J$
$1000 J$
$2500 J$

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Q. An object weights

m_{1}

in a liquid of density

d_{1}

and that in liquid of density

d_{2}

m_{2}

. The density

d

of the object is

$\frac{m_{2} d_{2} - m_{1} d_{1}}{m_{2} - m_{1}}$
$\frac{m_{1} d_{1} - m_{2} d_{2}}{m_{2} - m_{1}}$
$\frac{m_{2} d_{1} - m_{1} d_{2}}{m_{1} - m_{2}}$
$\frac{m_{1} d_{2} - m_{2} d_{1}}{m_{1} - m_{2}}$

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Q. A stone of relative density

K

is released from rest on the surface of a lake. If viscous effect are ignored, the stone sinks in water with an acceleration of:

$g (1 - K)$
$g (1 + \frac{1}{K})$
$g (1 + K)$
$g (1 - \frac{1}{K})$

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Q. A material has Poisson's ratio

0.50

. If a uniform rod of it suffers a longitudinal strain of

2 \times 10^{- 3}

, then the percentage change in volume is

$0.6$
$0.4$
zero
$0.2$

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Q. The resistance across

A

and

B

in the given figure will be:

None of the above
$3 R$
$\frac{R}{3}$
$R$

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Q. Two identical cylindrical vessels, with their bases at the same level, each contain a liquid of density

ρ

. The height of liquid in one vessel in

h_{1}

and that in the other is

h_{2}

. The area of either base is

A

. What is the work done by gravity in equalising the levels when the vessels are interconnected?

$A ρ g {(\frac{h_{1} - h_{2}}{2})}^{2}$
$A ρ g {(\frac{h_{1} + h_{2}}{2})}^{2}$
$\frac{1}{2} A ρ g {(h_{1} - h_{2})}_{1}^{2}$
None of these

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Q. Tow identical springs are connected to mass

m

as shown (

k =

spring constant). IF the period of the configuration in (a) is

2 s

, the period of the configuration in (b) is

$\sqrt{2} s$
$2 \sqrt{2} s$
$\frac{1}{\sqrt{2}} s$
$1 s$

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Q. Two cells with the same emf

E

and different internal resistances

r_{1}

and

r_{2}

are connected in series to an external resistance

R

. The value of

R

so that the potential difference across the first cell be zero, is

$\sqrt{r_{1} r_{2}}$
$r_{1} - r_{2}$
$r_{1} + r_{2}$
$\frac{r_{1} + r_{2}}{2}$

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Q. If

g

is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass

m

raised from the earth's surface to a height equal to the radius

R

of the earth is

$\frac{m g R}{4}$
$\frac{m g R}{2}$
$m g R$
$2 m g R$

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Q. The charge on the capacitor of capacitance

C

shown in the figure will be :

$\frac{C E R_{1}}{R_{2} + r}$
$\frac{C E R_{1}}{R_{1} + r}$
$C E$
$\frac{C E R_{2}}{R_{2} + r}$

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Q. A shell of mass

m

is at rest initially. It explodes into three fragments having masses in the ratio

2 : 2 : 1

. The fragments having equal masses fly off along mutually perpendicular direction with speed

v

. What will be the speed of the third (lighter) fragment?

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Q. If a person can throw a stone to maximum height of

h

metre vertically, then the maximum distance through which it can be thrown horizontally by the same person is

$h$
$3 h$
$2 h$
$\frac{h}{2}$

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Q. A small spherical ball of mass

m

slides without friction from the top of a hemisphere of radius

R

. At what height will the ball lose contact with surface of the sphere?

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Q. Which type of gate the following truth table represents?

Input	Input	Output
$A$	$B$	$Q$
$0$	$0$	$1$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$0$

NOT
OR
AND
NAND

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Q. A body of mass

6 k g

is acted upon by a force which causes a displacement in it given by

x = \frac{t^{2}}{4}

metre, where

t

is the time in second. The work done by the force in

2 s

$12 J$
$9 J$
$6 J$
$3 J$

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Q. In the nuclear reaction,

_{7}^{14} N + X ⟶_{6}^{14} C +_{1}^{1} H

, the

X

will be

$_{- 1}^{0} e$
$_{0}^{1} n$
$_{1}^{1} H$
$_{1}^{2} H$

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Q. Current through

A B C

and

A^{'} B^{'} C^{'}

I

. What is the magnetic field at

P

(Given,

B P = P B^{'} = r

and

C^{'} B^{'} P B C

are colinear)

$B = \frac{1}{4 π} (\frac{2 I}{r})$
$B = \frac{μ_{0}}{4 π} (\frac{2 I}{r})$
$B = \frac{μ_{0}}{4 π} (\frac{I}{r})$
Zero

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Q. A body floats in water with

40

% of its volume outside water. When the same body floats in an oil

60

% of its volume remains outside oil. The relative density of oil is:

$0.9$
$1.2$
$1.0$
$1.5$

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Q. The magnetic field at the point of intersection of diagonals of a square wire loop side

L

carrying a current

I

$\frac{μ_{0} I}{π L}$
$\frac{{2 μ}_{0} I}{π L}$
$\frac{\sqrt{2} μ_{0} I}{π L}$
$\frac{2 \sqrt{2} μ_{0} I}{π L}$

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Q. Given

\to A = 2^i + 3^j

and

\to B =^i +^j

. The component of vector

\to A

along vector

\to B

is:

$\frac{1}{\sqrt{2}}$
$\frac{5}{\sqrt{2}}$
$\frac{7}{\sqrt{2}}$
$\frac{3}{\sqrt{2}}$

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Q. A particle is moving with constant speed

v

in circle. What is the magnitude of average velocity after half rotation?

$2 \frac{v}{π}$
$2 v$
$\frac{v}{2}$
$\frac{v}{2 π}$

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Q. A radioactive nucleus of mass number

A

, initially at rest, emits an

α

-particle with a speed

v

. The recoil speed of the daughter nucleus will be

$\frac{2 v}{A + 4}$
$\frac{2 v}{A - 4}$
$\frac{4 v}{A - 4}$
$\frac{4 v}{A + 4}$

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Q. A battery of emf

E

and identical resistance

r

is connected across a pure resistive device (such as an electric heater) of resistance

R

. Prove that the power output of the device will be maximum if

R = r

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Q. Two soap bubbles of radii

x

and

y

coalesce to constitute a bubble of radius

z

. Then

z

is equal to:

$\sqrt{x^{2} + y^{2}}$
$\sqrt{x + y}$
$\frac{x + y}{2}$
$x + y$

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Q. A cricket ball of mass

0.25 k g

with speed

10 m / s

collides with a bat and returns with same speed within

0.01 s

. The force acted on bat is

$25 N$
$250 N$
$50 N$
$500 N$

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Q. Five equal resistance, each of resistance

R

are connected as shown in figure. A battery of

V

volt is connected between

A

and

B

. The current flowing in

F C

will be

$\frac{3 V}{R}$
$\frac{V}{2 R}$
$\frac{2 V}{R}$
$\frac{V}{R}$

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Q. In an inelastic collision an electron excites a hydrogen atom from its ground state to a M-shell state. A second electron collides instantaneously with the excited hydrogen atom in the M-shell state and ionizes it. At least how much energy the second electron transfers to the atom in the M-shell state?

$+ 3.4 e V$
$+ 1.51 e V$
$- 3.4 e V$
$- 1.51 e V$

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Q. A radioactive isotope

X

with half life

1.5 \times 10^{9}

yr decays into a stable nucleus

Y

. A rock sample contains both elements

X

and

Y

in ratio

1 : 15

. Find the age of the rock

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Q. If the earth were to suddenly contract to

\frac{1}{n} t h

if its present radius without any change in its mass, the duration of the new day will be nearly

$\frac{24}{n}$ $h r$
$\frac{24}{n^{2}} h r$
$24 n^{2} h r$
$24 n h r$

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