DIRECTION: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following-

Statement-1: A paramagnetic sample display greater magnetisation (for the same magnetic field) when cooled.

Statement-2 : The magnetisation does not depend ontemperature.

(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 true; Statement-2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(d)Statement -1 is true, Statement-2 is false

A paramagnetic sampled is play greater magnetisation when cooled, this is because at lower temperature, the tendency to disrupt the alignment of dipoles (due to magnetising field) decreases on account of reduced random thermal motion.

In a RLC circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to

Solution

We know that \(f=\frac{1}{2\pi \sqrt{(LC)}}\)

when C is doubled, L should be halved so that resonant frequency remains unchanged.

The area of the acceleration-displacement curve of a body gives

impulse
change in momentum per unit mass
change in KE per unit mass
total change in energy

A thick uniform rope of length L is hanging from a rigid support. A transverse wave of wavelength λ₀ is set up at the middle of rope as shown in figure. The wavelength of the wave as it reaches to the topmost point is

2λ₀
√2λ₀
^λ₀⁄_√2
λ₀

Solution

Directions: Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer(ONLY ONE option is correct ) from the following

Statement -1 :The escape speed does not depend on the direction in which the projectile is fired.

Statement -2 :Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.

(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 true; Statement -2 is not a correct explanation for Statement-1
(d)Statement -1 is true, Statement-2 is false

Solution

(c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1

The efficiency of carnot engine when source temperature is T₁ and sink temperature is T₂ will be

\(\frac{T_{1}-T_{2}}{T_{1}}\)
\(\frac{T_{1}-T_{2}}{T_{1}}\)
\(\frac{T_{1}-T_{2}}{T_{2}}\)
\(\frac{T_{1}-T_{2}}{T_{2}}\)

Solution

Efficiency of carnot engine\(\eta =\frac{T_{1}-T_{2}}{T_{1}}\)

where T₁ =source temperature
T₂ =sink temperature.

A monkey is climbing up a rope, then the tension in the rope

must be equal to the force applied by the monkey on the rope
must be less than the force applied by the monkey on the rope.
must be greater than the force applied by the monkey on the rope.
may be equal to, less than or greater the force applied by the monkey on the rope.

A machine, which is 75% efficient, uses 12 J of energy in lifting up a 1kg mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in m/s)

\(\sqrt{24}\)
\(\sqrt{12}\)
\(\sqrt{18}\)
√9

Solution

If the linear momentum is increased by 5%, the kinetic energy will increase by

50%
100%
125%
10%

Solution

Frequency of oscillation is proportional to

\(\sqrt{\frac{3k}{m}}\)
\(\sqrt{\frac{k}{m}}\)
\(\sqrt{\frac{2k}{m}}\)
\(\sqrt{\frac{m}{3k}}\)

Solution

A man wants to see two poles, separately, situated at 11 km.The minimum distance (approximately) between these poles will be

5 m
0.5 m
1 m
3 m

In a pure capacitive A.C. circuit current and voltage differ in phase by

0°
45°
90°
180°

Elastomers are the materials which

are not elastic at all
have very small elastic range
do not obey Hooke’s law
None of these

DIRECTION: Each of these question contains two statements: Statement-1 (Assertion) and Statement-2(Reason). Answer these questions from the following fouroptions.

Statement- 1 :The ionising power of β-particle is less compared to α-particles but their penetrating power is more.

Statement- 2 :The mass of β-particle is less than the mass of α-particle.

(a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement -1
(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1
(c)Statement-1 is True, Statement- 2 is False
(d)Statement-1 is False, Statement -2 is True

Solution

(b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1

b-particles, being emitted with very high speed compared to a-particles, pass for very little time near the atoms of the medium. So the probability of the atoms being ionised is comparatively less. But due to this reason, their loss of energy is very slow and they can penetrate the medium through a sufficient depth.

The terminal velocity v_r of a small steel ball of radius r falling under gravity through a column of a viscous liquid of coefficient of viscosity η depends on mass of the ball m,acceleration due to gravity g, coefficient of viscosity η and radius r. Which of the following relations is dimensionally correct ?

v_r α \(\frac{mgr}{\eta }\)
v_r α mgηr
v_r α \(\frac{mg}{r\eta }\)
v_r α \(\frac{\eta mg}{r}\)

Solution

Note that according to Stoke’s law

6πηrv_r= mg

Hence, the valid relation is v_r α mg/rη

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