GATE

Q. A radioactive element X has a half-life of 30 hours. It decays via alpha, beta and gamma emissions with the branching ratio for beta decay being 0.75. The partial half-life for beta decay in unit of hours is            Ans: 40 Sol:

Q. Let 𝜃 be a variable in the range − 𝜋 ≤ 𝜃 < 𝜋.  Now consider a function If its Fourier series is written as then the value of 𝑚=−∞   𝑚 |𝐶3|2 (rounded off to three decimal places) is            Ans: 0.011

Q. A projectile of mass 1 kg is launched at an angle of 30° from the horizontal direction at 𝑡 = 0 and takes time 𝑇 before hitting the ground. If its initial speed is 10 ms−1 , the value of the action integral for the entire flight in the units of kg m2s−1 (rounded

Q. The ground state electronic configuration of the rare-earth ion (Nd3+) is [Pd] 4f 35s25p6.Assuming LS coupling, the Land𝑒́ 𝑔-factor of this ion is 8/11 . The effective magnetic 11 moment in units of Bohr magneton 𝜇B (rounded off to two decimal places) is Ans: 3.62 Sol:

Q. Low energy collision (s-wave scattering) of pion (π+) with deuteron (d) results in the production of two protons (𝜋+ + 𝑑 → 𝑝 + 𝑝). The relative orbital angular momentum (in units of ℏ) of the resulting two-proton system for this reaction is (A) 0 (B) 1 (C) 2 (D) 3 Ans: 1 Sol:

Q. An infinitely long wire parallel to the x-axis is kept at 𝑧 = 𝑑 and carries a current I in the positive x direction above a superconductor filling the region 𝑧 ≤ 0 (see figure). The magnetic  field  𝐵⃗→   inside  the  superconductor  is  zero  so  that  the  field  just  outside  the superconductor is parallel

Q. A ball bouncing off a rigid floor is described by the potential energy function Which of the following schematic diagrams best represents the phase space plot of the ball? Ans: Option B Sol:

Q. For the following circuit, the correct logic values for the entries X2 and Y2 in the truth table are (A) 1 and 0                 (B) 0 and 0                  (C) 0 and 1                  (D) 1 and 1 Ans: 1 and 0 

Q. Consider a potential barrier 𝑉(𝑥) of the form: where 𝑉0 is a constant. For particles of energy 𝐸 < 𝑉0 incident on this barrier from the left, which of the following schematic diagrams best represents the probability density |𝜓 (𝑥)|2 as a function of 𝑥. Ans: Option A

Q. A 3-bit analog-to-digital converter is designed to digitize analog signals ranging from 0 V to 10 V. For this converter, the binary output corresponding to an input of 6 V is (A) 011 (B) 101 (C) 100 (D) 010 Ans: 100 Sol: