21.

Assertion:  The Carnot cycle is useful in understanding the performance of heat engines. 

Reason:  The Carnot cycle provides a way of determining the maximum possible efficiency achievable with reservoirs of given temperatures.

• If both assertion and reason are true and reason is the correct explanation of the assertion

• If both assertion and reason are true but reason is not the correct explanation of the assertion

• If assertion is true, but reason is false

• Both assertion and reason are false statements

Assertion: Perspiration from human body helps in cooling the body.

Reason: A thin layer of water on the skin enhances its emissivity.

• If both assertion and reason are true and reason is the correct explanation of the assertion

• If both assertion and reason are true but reason is not the correct explanation of the assertion

• If assertion is true, but reason is false

• Both assertion and reason are false statements

Assertion:  When a glass of hot milk is placed in a room and allowed to cool, its entropy decreases. 

Reason:  Allowing hot object to cool does not violate the second law of thermodynamics.

• If both assertion and reason are true and reason is the correct explanation of the assertion

• If both assertion and reason are true but reason is not the correct explanation of the assertion

• If assertion is true, but reason is false

• Both assertion and reason are false statement

Assertion: A thin stainless steel needle can lay floating on a still water surface. 

Reason:  Any object floats when the buoyancy force balances the weight of the object.

• If both assertion and reason are true and reason is the correct explanation of the assertion

• If both assertion and reason are true but reason is not the correct explanation of the assertion

• If assertion is true, but reason is false

• Both assertion and reason are false statements

Two parallel large thin metal sheets have equal surface charge densities ( σ = 26.4 × 10^-12 C/m² ) of opposite signs. The electric field between these sheets is

• 1.5 N/C

• 1.5 × 10^-10 N/C

• 3 N/C

• 3 × 10^-10 N/C 

The magnetic moment has dimensions of

• [ LA ]

• [ L²A ]

• [ L T^-1 A ]

• [ L² T^-1 A ]

Five capacitors, each of capacitance value C are connected as shown in the figure. The ratio of
capacitance between P and R, and the capacitance between P and Q is

• 3 : 1

• 5 : 2

• 2 : 3

• 1 : 1

The spatial distribution of the electric field due to two charges (A, B) is shown in figure. Which one of the following statements is correct?

• A is +ve and +B is -ve and $\left|\mathrm{A}\right| > \left|\mathrm{B}\right|$

• A is $-$ve and B is +ve; $\left|\mathrm{A}\right| = \left|\mathrm{B}\right|$

• both are +ve but A > B

• both are $-$ve but A > B

Circular  loop  of  a  wire  and a  long  straight  wire  carry currents  I_c  and  I_e respectively  as shown in figure. Assuming  that  these  are  places  in  the same plane, the magnetic  field  will be  zero  at  the  centre of  the loop when separation  H is

• $\frac{{\mathrm{I}}_{\mathrm{e}} \mathrm{R}}{{\mathrm{I}}_{\mathrm{c}} \mathrm{\pi }}$

• $\frac{{\mathrm{I}}_{\mathrm{c}} \mathrm{R}}{{\mathrm{I}}_{\mathrm{e} }\mathrm{\pi }}$

• $\frac{\mathrm{\pi } {\mathrm{I}}_{\mathrm{c}}}{{\mathrm{I}}_{\mathrm{e}} \mathrm{R}}$

• $\frac{{\mathrm{I}}_{\mathrm{e}} \mathrm{\pi }}{{\mathrm{I}}_{\mathrm{c}} \mathrm{R}}$

A metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at I = 0 and completely emerges out at  t = T sec. The current in the ring varies as