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JEE Mains Maths. Try each one first, then open its answer.

Top 10 JEE Mains 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 13 times: 2021 Paper 11, 2021 Paper 12, 2021 Paper 16, 2021 Paper 19, 27 Jun 2022, 1 Feb 2023, 8 Apr 2023, 29 Jan 2024, 31 Jan 2024, 2 Apr 2025, 3 Apr 2025, 23 Jan 2026 S1, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 13 of this type

    58
    Let the mean and the variance of seven observations 2,4,α,8,β,12,14,α<β2,4,\alpha,8,\beta,12,14,\alpha<\beta, be 8 and 16 respectively. Then the quadratic equation whose roots are 3α+23\alpha+ 2 and 2β+12\beta+ 1 is :

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  2. Question 2

    This type asked 13 times: 2021 Paper 18, 26 Jun 2022, 28 Jun 2022, 27 Jul 2022, 25 Jan 2023, 8 Apr 2023, 13 Apr 2023, 15 Apr 2023, 27 Jan 2024, 6 Apr 2024, 24 Jan 2025, 7 Apr 2025, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 13 of this type

    68
    The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation α\alpha in this data is replaced by β\beta, then the mean and variance become 10.1 and 1.99, respectively. Then α+β\alpha + \beta equals.

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  3. Question 3

    This type asked 8 times: 2021 Paper 6, 2021 Paper 8, 2021 Paper 21, 29 Jan 2023, 31 Jan 2023, 6 Apr 2023, 11 Apr 2023, 8 Apr 2026 S2. This one: 8 Apr 2026 S2 See all 8 of this type

    57
    A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

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  4. Question 4

    This type asked 8 times: 2021 Paper 17, 31 Jan 2023, 6 Apr 2023, 10 Apr 2023, 13 Apr 2023, 9 Apr 2024, 23 Jan 2026 S2, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 8 of this type

    58
    If the mean of the data
    ClassFrequency
    5-102
    10-15kk
    15-2028
    20-2554
    25-30k+1k + 1
    30-355
    is 21, then kk is one of the roots of the equation :

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  5. Question 5

    This type asked 8 times: 2021 Paper 20, 25 Jun 2022, 24 Jan 2023, 30 Jan 2023, 1 Feb 2023, 23 Jan 2025, 22 Jan 2026 S2, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 8 of this type

    64
    Let X={x∈N:1≤x≤19}X = \{ x \in N:1 \leq x \leq 19\} and for some a,b∈Ra,b \in R, Y={ax+b:x∈X}Y = \{ ax + b:x \in X\}. If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of bb is

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  6. Question 6

    This type asked 6 times: 2021 Paper 26, 29 Jul 2022, 1 Feb 2024, 29 Jan 2025, 4 Apr 2026 S2, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 6 of this type

    59
    A data consists of 20 observations x1,x2,…..,x20x_{1},x_{2},\ldots..,x_{20}. If ∑i=120(xi+5)2=2500\sum_{i= 1}^{20} \left( x_{i}+ 5 \right)^{2}= 2500 and ∑i=120(xi−5)2=100\sum_{i= 1}^{20} \left( x_{i}- 5 \right)^{2}= 100, then the ratio of mean to standard deviation of this data is :

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  7. Question 7

    This type asked 6 times: 2021 Paper 23, 29 Jun 2022, 26 Jul 2022, 30 Jan 2023, 29 Jan 2024, 2 Apr 2026 S2. This one: 2 Apr 2026 S2 See all 6 of this type

    59
    The mean and variance of nn observations are 8 and 16, respectively. If the sum of the first ( n−1n- 1 ) observations is 48 and the sum of squares of the first ( n−1n - 1 ) observations is 496 , then the value of n is :

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  8. Question 8

    This type asked 5 times: 26 Jun 2022, 11 Apr 2023, 4 Apr 2024, 4 Apr 2025, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 5 of this type

    65
    The mean and variance of 10 observations are 9 and 34.2 , respectively. If 8 of these observations are 2,3,5,10,11,13,15,212,3,5,10,11,13,15,21, then the mean deviation about the median of all the 10 observations is

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  9. Question 9

    This type asked 4 times: 25 Jul 2022, 1 Feb 2024, 9 Apr 2024, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 4 of this type

    60
    Suppose that the mean and median of the nonnegative numbers 21, 8, 17, a, 51,103,b,13,6751,103,b,13,67, (a>b)(a > b), are 40 and 21, respectively. If the mean deviation about the median is 26 , then 2a2a is equal to :

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  10. Question 10

    Asked 2 times: 2021 Paper 26*, 1 Feb 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    168
    Consider 10 observation x1,x2,…,x10x_{1},x_{2},\ldots,x_{10} such that ∑i=110(xi−α)=2\sum_{i = 1}^{10} \left( x_{i}- \alpha \right)= 2 and ∑i=110(xi−β)2=40\sum_{i = 1}^{10} \left( x_{i}- \beta \right)^{2}= 40, where α,β\alpha,\beta are positive integers. Let the mean and the variance of the observations be 65\frac{6}{5} and 8425\frac{84}{25} respectively. Then βα\frac{\beta}{\alpha} is equal to:

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