JEE Advanced 2021 · Paper 1

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

1. A50
2. B75
3. C350
4. D525

A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = −l, y = −h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s² along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by L⃗ and τ, respectively. î, ĵ and k̂ are unit vectors along the positive x, y and z-directions, respectively. If k̂ = î × ĵ then which of the following statement(s) is(are) correct?

1. AThe particle arrives at the point (x = l, y = −h) at time t = 2 s
2. Bτ = 2 k̂ when the particle passes through the point (x = l, y = −h)
3. CL⃗ = 4 k̂ when the particle passes through the point (x = l, y = −h)
4. Dτ = k̂ when the particle passes through the point (x = 0, y = −h)

Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?

1. AThe ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5
2. BThere is an overlap between the wavelength ranges of Balmer and Paschen series
3. CThe wavelengths of Lyman series are given by (1 + 1/m²) λ₀, where λ₀ is the shortest wavelength of Lyman series and m is an integer
4. DThe wavelength ranges of Lyman and Balmer series do not overlap