1
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?
A
The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5
B
There is an overlap between the wavelength ranges of Balmer and Paschen series
C
The wavelengths of Lyman series are given by $$\left( {1 + {1 \over {{m^2}}}} \right){\lambda _0}$$, where $${\lambda _0}$$ is the shortest wavelength of Lyman series and m is an integer
D
The wavelength ranges of Lyman and Balmer series do not overlap
2
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at the distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure).

A resistor R = 1.4 $$\Omega$$ and a capacitor C0 = 5.0$$\mu$$F are connected in series between the rails. At time t = 0, C0 is uncharged. Which of the following statement(s) is(are) correct? [$$\mu$$0 = 4$$\pi$$ $$\times$$ 10$$-$$7 SI units. Take ln 2 = 0.7]

A
Maximum current through R is 1.2 $$\times$$ 10$$-$$6 ampere
B
Maximum current through R is 3.8 $$\times$$ 10$$-$$6 ampere
C
Maximum charge on capacitor C0 is 8.4 $$\times$$ 10$$-$$12 coulomb
D
Maximum charge on capacitor C0 is 2.4 $$\times$$ 10$$-$$12 coulomb
3
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle $$\theta$$ = 45$$^\circ$$. P1 and P2 are pressures at points 1 and 2, respectively, located at the base of the tube. Let $$\beta$$ = (P1 $$-$$ P2)/($$\rho$$gd), where $$\rho$$ is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?

A
$$\beta$$ = 0 when a = g/$$\sqrt 2$$
B
$$\beta$$ > 0 when a = g/$$\sqrt 2$$
C
$$\beta = {{\sqrt 2 - 1} \over {\sqrt 2 }}$$ when a = g/2
D
$$\beta = {1 \over {\sqrt 2 }}$$ when a = g/2
4
JEE Advanced 2021 Paper 1 Online
Numerical
+4
-0
An $$\alpha$$-particle (mass 4 amu) and a singly charged sulphur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $$\alpha$$-particle and the sulfur ion move in circular orbits of radii r$$\alpha$$ and rs, respectively. The ratio (rs/r$$\alpha$$) is __________.