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Day 25: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Statistics. 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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  2. Question 2

    Vector Algebra. This type asked 5 times: 2021 Paper 22, 4 Apr 2024, 22 Jan 2025, 7 Apr 2025, 28 Jan 2026 S1. This one: 28 Jan 2026 S1 See all 5 of this type

    69
    For three-unit vectors a→,b→,c→\overrightarrow{a},\overrightarrow{b},\overrightarrow{c} satisfying ∣a→−b→∣2+∣b→−c→∣2+∣c→−a→∣2=9 and |\overrightarrow{a}-\overrightarrow{b}|^{2}+ |\overrightarrow{b}-\overrightarrow{c}|^{2}+ |\overrightarrow{c}-\overrightarrow{a}|^{2}= 9\text{~and~} ∣2a→+kb→+kc→∣=3|2\overrightarrow{a}+k\overrightarrow{b}+k\overrightarrow{c}| = 3 the positive value of kk is :

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  3. Question 3

    Definite Integration. This type asked 5 times: 2021 Paper 24, 14 Jun 2022, 29 Jun 2022, 29 Jan 2023, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 5 of this type

    71
    If f(x)f(x) satisfies the relation f(x)=ex+∫01(y+xex)f(y)dyf(x) = e^{x} + \int_{0}^{1} \left( y + {xe}^{x} \right)f(y)dy, then e+f(0)e + f(0) is equal to ____\_\_\_\_ .

  4. Question 4

    Relations and Functions. This type asked 5 times: 14 Jun 2022, 29 Jul 2022, 9 Apr 2024, 21 Jan 2026 S1, 24 Jan 2026 S2. This one: 24 Jan 2026 S2 See all 5 of this type

    63
    If the domain of the function f(x)=sin⁡−1(1x2−2x−2)f(x) =\sin^{- 1}\left( \frac{1}{x^{2}- 2x - 2} \right), is (−∞,α]∪[β,γ]∪[δ,∞)( - \infty,\alpha\rbrack \cup \lbrack\beta,\gamma\rbrack \cup \lbrack\delta,\infty), then α+β+γ+δ\alpha + \beta + \gamma + \delta is equal to

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  5. Question 5

    Probability. This type asked 5 times: 2021 Paper 17, 6 Apr 2023, 31 Jan 2024, 4 Apr 2024, 24 Jan 2026 S1. This one: 24 Jan 2026 S1 See all 5 of this type

    67
    From a lot containing 10 defective and 90 nondefective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-

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