1
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
A physical quantity $$\overrightarrow S$$ is defined as $$\overrightarrow S = (\overrightarrow E \times \overrightarrow B )/{\mu _0}$$, where $$\overrightarrow E$$ is electric field, $$\overrightarrow B$$ is magnetic field and $$\mu$$0 is the permeability of free space. The dimensions of $$\overrightarrow S$$ are the same as the dimensions of which of the following quantity(ies)?
A
$${{Energy} \over {Ch\arg e \times Current}}$$
B
$${{Force} \over {Length \times Time}}$$
C
$${{Energy} \over {Volume}}$$
D
$${{Power} \over {Area}}$$
2
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
A heavy nucleus N, at rest, undergoes fission N $$\to$$ P + Q, where P and Q are two lighter nuclei. Let $$\delta$$ = MN $$-$$ MP $$-$$ MQ, where MP, MQ and MN are the masses of P, Q and N, respectively. EP and EQ are the kinetic energies of P and Q, respectively. The speeds of P and Q are vP and vQ, respectively. If c is the speed of light, which of the following statement(s) is(are) correct?
A
$${E_P} + {E_Q} = {c^2}\delta$$
B
$${E_P} = \left( {{{{M_P}} \over {{M_P} + {M_Q}}}} \right){c^2}\delta$$
C
$${{{v_P}} \over {{v_Q}}} = {{{M_Q}} \over {{M_P}}}$$
D
The magnitude of momentum for P as well Q is $$c\sqrt {2\mu \delta }$$, where $$\mu = {{{M_P}{M_Q}} \over {({M_P} + {M_Q})}}$$
3
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the larger loop carries current I2 in the clockwise direction, with I2 > 2I1. $$\overrightarrow B$$(x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?

A
$$\overrightarrow B$$(x, y) is perpendicular to the xy-plane at any point in the plane
B
| $$\overrightarrow B$$(x, y) | depends on x and y only through the radial distance $$r = \sqrt {{x^2} + {y^2}}$$
C
| $$\overrightarrow B$$(x, y) | is non-zero at all points for r < R
D
$$\overrightarrow B$$(x, y) points normally outward from the xy-plane for all the points between the two loops
4
JEE Advanced 2021 Paper 2 Online
Numerical
+2
-0
A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmosphere pressure p0 = 105 Pa so that the volume of the trapped air is v0 = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p0 + $$\Delta$$p without changing its orientation. At this pressure, the volume of the trapped air is v0 $$-$$ $$\Delta$$v. Let $$\Delta$$v = X cc and $$\Delta$$p = Y $$\times$$ 103 Pa.

The value of X is _______________.