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Saturday, 31 October

JEE Main 2021 · PhysicsMultiple choiceDiagram basedHardData or graph

JEE Main 26 August 2021, Shift 2, Physics Q6

Question 6 of 90 in this shift, Physics question 6 of 30, Section A.

At time t=0t=0, a material is composed of two radioactive atoms A and B, where NA(0)=2NB(0)\mathrm{N_A(0)=2N_B(0)}. The decay constant of both kind of radioactive atoms is λ\lambda. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of NB(t)/NB(0)\mathrm{N_B(t)/N_B(0)} with respect to time t ? [NA(0)= No. of A atoms at t=0NB(0)= No. of B atoms at t=0]\left[\begin{array}{l}\mathrm{N_A(0)=}\text{ No. of A atoms at }t=0\\ \mathrm{N_B(0)=}\text{ No. of B atoms at }t=0\end{array}\right]

The figure, in words

Four graphs of N_B(t)/N_B(0) (y-axis) vs t, each with dashed horizontal line at 1 and dashed vertical line at 1/(2λ) or 1/λ; see options. Given: N_A(0) = No. of A atoms at t=0, N_B(0) = No. of B atoms at t=0.
  1. (1)[figure: graph of N_B(t)/N_B(0) vs t, curve starts at 1 at t=0 and decreases in a concave-up curve reaching zero on the t axis at t = 1/(2λ) (dashed vertical line there; dashed horizontal line at 1)]
  2. (2)[figure: graph of N_B(t)/N_B(0) vs t, curve starts at 1, rises above 1 to a maximum at t = 1/(2λ) (dashed vertical line), then falls toward zero at large t; dashed horizontal line at 1]Official answer
  3. (3)[figure: graph of N_B(t)/N_B(0) vs t, curve starts at 1 and decreases monotonically, flattening toward the t axis without touching it; dashed vertical line at t = 1/(2λ) where the curve is still above the axis; dashed horizontal line at 1]
  4. (4)[figure: graph of N_B(t)/N_B(0) vs t, curve starts at 1, rises above 1 to a maximum at t = 1/λ (dashed vertical line), then falls to zero at large t; dashed horizontal line at 1]

Official answer

Option 2

NTA final key.

Chapter
Nuclei
Topic
Radioactive Decay
Idea tested
Successive Decay Chains

Same idea in other shifts

Asked 3× in all
  1. 4 Apr 2025, Shift 2 · Q42A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents…MediumDiagram basedHas a figure
  2. 31 Aug 2021, Shift 1 · Q3A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable…MediumDiagram basedHas a figure

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.