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Binomial Distribution

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 14 times: May 2022 S1, 3 May 2023 S1, 4 May 2023 S2, 16 May 2023 S2, 12 May 2024 S1, 14 May 2024 S1, 14 May 2024 S2, 21 Apr 2025 S2, 22 Apr 2025 S1, 13 Apr 2026 S1, 16 Apr 2026 S2, 17 Apr 2026 S2, 15 May 2026 S1, 19 May 2026 S2. This one: 19 May 2026 S2 See all 14 of this type

    98
    If XX follows a Binomial distribution with parameters n=8n = 8 and p=12p = \dfrac{1}{2} then P(∣X−4∣≤2)P(|X - 4| \le 2)

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  2. Question 2

    This type asked 12 times: 2 May 2023 S2, 10 May 2023 S1, 11 May 2023 S2, 9 May 2024 S1, 10 May 2024 S1, 11 May 2024 S1, 12 May 2024 S2, 19 Apr 2025 S1, 20 Apr 2025 S1, 21 Apr 2025 S1, 19 Apr 2026 S1, 20 Apr 2026 S1. This one: 20 Apr 2026 S1 See all 12 of this type

    98
    A random variable X∼B(n,p)X \sim B(n, p) follows a binomial distribution with n=6n = 6. If 9P(X=4)=P(X=2)9P(X = 4) = P(X = 2), then the probability of success pp is..

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  3. Question 3

    This type asked 10 times: May 2021 S1, 11 May 2023 S1, 22 Apr 2025 S2, 25 Apr 2025 S1, 25 Apr 2025 S2, 26 Apr 2025 S1, 15 Apr 2026 S1, 20 Apr 2026 S2, 13 May 2026 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 10 of this type

    98
    It is known that 10%10\% of certain articles manufactured are defective. What is the probability that in a random sample of 1212 such articles, 99 are defective?

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  4. Question 4

    This type asked 9 times: May 2022 S1, 3 May 2023 S2, 11 May 2023 S1, 16 May 2023 S1, 9 May 2024 S1, 9 May 2024 S2, 11 May 2024 S2, 21 Apr 2025 S2, 15 Apr 2026 S1. This one: 15 Apr 2026 S1 See all 9 of this type

    99
    The Variance of the following probability distribution of X is
    X00112233
    P(X)q3q^33q2p3q^2p3qp23qp^2p3p^3
    where 0<p<1,q=1−p0 < p < 1, q = 1 - p

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  5. Question 5

    This type asked 8 times: 2 May 2023 S1, 3 May 2023 S1, 3 May 2023 S2, 15 Apr 2026 S2, 16 Apr 2026 S1, 18 Apr 2026 S2, 19 Apr 2026 S2, 14 May 2026 S1. This one: 14 May 2026 S1 See all 8 of this type

    98
    The probability that a person hits a target is 0.60.6. If he fires 55 shots at the target, then the probability that he hits the target at least once is

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  6. Question 6

    This type asked 7 times: 3 May 2023 S2, 9 May 2023 S1, 9 May 2023 S2, 11 May 2024 S2, 11 Apr 2026 S1, 17 Apr 2026 S1, 19 May 2026 S1. This one: 19 May 2026 S1 See all 7 of this type

    99
    The sum and product of mean and variance of a binomial distribution are 3 and 2 respectively. Then, P(X>0)=…P(X > 0) = \ldots

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  7. Question 7

    Asked 4 times: May 2022 S1, 3 May 2023 S2, 9 May 2024 S2, 11 May 2024 S2 See all 4 times it was asked

    142
    Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of tens is

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  8. Question 8

    This type asked 4 times: 10 May 2024 S2, 13 May 2024 S2, 12 May 2026 S1, 13 May 2026 S1. This one: 13 May 2026 S1 See all 4 of this type

    98
    If the mean of a binomial distribution is twice its variance and n=18n = 18, then the probability of success is...

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  9. Question 9

    This type asked 4 times: 11 May 2023 S1, 23 Apr 2025 S1, 11 Apr 2026 S2, 18 Apr 2026 S1. This one: 18 Apr 2026 S1 See all 4 of this type

    98
    A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...

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  10. Question 10

    Asked 3 times: 9 May 2023 S1*, 9 May 2023 S2*, 11 Apr 2026 S1 (* = numbers or wording changed that year) See all 3 times it was asked

    98
    Let X∼B(n,p)X \sim B(n, p). If E(X)=2E(X) = 2 and Var(X)=1\mathrm{Var}(X) = 1, then the probability of getting at most one success is .....

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