The half-life of a radioactive substance is 10 days. After 30 days, the fraction remaining undecayed is: MCQ with Answer and Explanation

The half-life of a radioactive substance is 10 days. After 30 days, the fraction remaining undecayed is:
A. 1/3
B. 1/2
C. 1/8
D. 1/16
Answer: Option C
Solution (By JKSSB Mock Tests)
Number of half-lives n = total time / half-life = 30 days / 10 days = 3. Fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8. This exponential decay law is fundamental in radioactivity. Memory tip: 'After n half-lives, fraction = 1/2ⁿ'. Competitive exams frequently test such calculations with varying time intervals. Always compute number of half-lives first. Note: Activity (decays per second) also reduces by same fraction. This problem assesses understanding of half-life concept beyond rote memorization.

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A body starts from rest and moves with uniform acceleration. The ratio of distances covered in 1st, 2nd, and 3rd seconds is
A. 1:3:5
B. 1:4:9
C. 1:1:1
D. 1:2:3

Correct Answer: Option A


Explanation:
s_nth = u + a/2 (2n-1). u=0, so distances proportional to (2n-1): 1,3,5.

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In a transistor, the current gain β is defined as:
A. I_E / I_C
B. I_C / I_B
C. I_C / I_E
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Correct Answer: Option B


Explanation:
For a bipolar junction transistor (BJT) in common-emitter configuration, DC current gain β = I_C / I_B, where I_C is collector current, I_B base current. Typical β values range 20-200. Option D is α (common-base gain). Memory tip: 'β = collector current / base current; large β means small base current controls large collector current'. This definition-based question tests electronics fundamentals, frequently examined in competitive exams. Always distinguish β (CE configuration) from α (CB configuration) and their relationship: β = α/(1-α).

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The time of flight of a projectile is maximum when angle of projection is
A. 60°
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Correct Answer: Option B


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