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Day 3: JEE Mains Maths

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

  1. Question 1

    Statistics. 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

    Vector Algebra. This type asked 13 times: 2021 Paper 18, 25 Jun 2022, 28 Jun 2022, 29 Jun 2022, 25 Jul 2022, 24 Jan 2023, 25 Jan 2023, 27 Jan 2024, 31 Jan 2024, 6 Apr 2024, 2 Apr 2025, 21 Jan 2026 S1, 6 Apr 2026 S1. This one: 6 Apr 2026 S1 See all 13 of this type

    73
    If a→=i^+j^+k^,b→=j^−k^\overrightarrow{a} = \widehat{i} + \widehat{j} + \widehat{k},\overrightarrow{b} = \widehat{j} - \widehat{k} and c→\overrightarrow{c} be three vectors such that a→×c→=b→\overrightarrow{a} \times \overrightarrow{c} = \overrightarrow{b} and a→⋅c→=3\overrightarrow{a} \cdot \overrightarrow{c} = 3, then c→⋅(a→−2b→)\overrightarrow{c} \cdot (\overrightarrow{a} - 2\overrightarrow{b}) is equal to ____\_\_\_\_ .

  3. Question 3

    Differential Equations. This type asked 13 times: 2021 Paper 7, 2021 Paper 11, 2021 Paper 16, 2021 Paper 17, 29 Jan 2023, 27 Jan 2024, 30 Jan 2024, 4 Apr 2024, 6 Apr 2024, 9 Apr 2024, 23 Jan 2025, 22 Jan 2026 S2, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 13 of this type

    70
    Let y=y(x)y=y(x) be the solution curve of the differential equation (1+sin⁡x)dydx+(y+1)cos⁡x=0,y(0)=0(1 + \sin x)\frac{dy}{dx}+ (y+ 1)\cos x= 0,y(0) = 0. If the curve y=y(x)y = y(x) passes through the point (α,−12)\left( \alpha,\frac{- 1}{2} \right), then a value of α\alpha is :

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  4. Question 4

    Statistics. 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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  5. Question 5

    Relations and Functions. This type asked 13 times: 2021 Paper 17, 2021 Paper 22, 28 Jun 2022, 27 Jul 2022, 28 Jul 2022, 24 Jan 2023, 29 Jan 2023, 31 Jan 2023, 1 Feb 2023, 8 Apr 2023, 28 Jan 2025, 29 Jan 2025, 23 Jan 2026 S2. This one: 23 Jan 2026 S2 See all 13 of this type

    66
    Let A={0,1,2,….9)\mathbf{A = \{ 0,1,2,\ldots.9)}. Let R be a relation on A defined by (x,y)∈R(x,y) \in R if and only if ∣x−y∣|x - y| is a multiple of 3. Given below are two statements: Statement I: n(R)=36n(R) = 36 Statement II: RR is an equivalence relation. In the light of the above statements, choose the correct answer from the options given below

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