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Day 14: JEE Mains Maths

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

  1. Question 1

    Differential Equations. This type asked 7 times: 2021 Paper 2, 27 Jun 2022, 28 Jun 2022, 26 Jul 2022, 5 Apr 2024, 22 Jan 2025, 7 Apr 2025. This one: 7 Apr 2025 See all 7 of this type

    138
    Let y=y(x)y=y\left( x \right) be the solution of the differential equation (x2+1)y′−\left( x^{2}+ 1 \right)y^{'}- 2xy=(x4+2x2+1)cos⁡x2xy=\left( x^{4}+ 2x^{2}+ 1 \right)\cos x, y(0)=1y(0) = 1. Then ∫−33y(x)dx\int_{- 3}^{3} y(x)dx is :

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  2. Question 2

    Probability. This type asked 7 times: 28 Jul 2022, 29 Jan 2023, 5 Apr 2024, 6 Apr 2024, 8 Apr 2024, 28 Jan 2025, 4 Apr 2025. This one: 4 Apr 2025 See all 7 of this type

    69
    A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is.

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  3. Question 3

    Quadratic Equations. This type asked 7 times: 2021 Paper 1, 14 Jun 2022, 26 Jun 2022, 26 Jul 2022, 25 Jan 2023, 9 Apr 2024, 22 Jan 2025. This one: 22 Jan 2025 See all 7 of this type

    137
    Let αθ\alpha_{\theta} and βθ\beta_{\theta} be the distinct roots of 2x2+(cos⁡θ)x−1=0,θ∈(0,2π)2x^{2}+ (\cos\theta)x - 1 = 0,\theta \in (0,2\pi). If mm and MM are the minimum and the maximum values of αθ4+βθ4\alpha_{\theta}^{4}+\beta_{\theta}^{4}, then 16(M+m)16(M + m) equals :

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  4. Question 4

    Binomial Theorem. This type asked 7 times: 2021 Paper 2, 2021 Paper 8, 2021 Paper 19, 2021 Paper 20, 26 Jul 2022, 24 Jan 2023, 30 Jan 2024. This one: 30 Jan 2024 See all 7 of this type

    174
    Let α=∑k=0n(( nCk)2k+1)\alpha=\sum_{k = 0}^{n} \left( \frac{\left( \ ^{n}C_{k} \right)^{2}}{k + 1} \right) and β=∑k=0n−1( nCk nCk+1k+2)\beta=\sum_{k = 0}^{n - 1} \left( \frac{\ ^{n}C_{k}\ ^{n}C_{k + 1}}{k + 2} \right). If 5α=6β5\alpha= 6\beta, then nn equals

  5. Question 5

    Application of Derivatives. This type asked 7 times: 2021 Paper 20, 2021 Paper 22, 14 Jun 2022, 27 Jun 2022, 28 Jun 2022, 6 Apr 2023, 29 Jan 2024. This one: 29 Jan 2024 See all 7 of this type

    84
    Let f(x)=2x−x2,x∈Rf(x) =2^{x}-x^{2},x \in R. If mm and nn are respectively the number of points at which the curves y=f(x)y = f(x) and y=f′(x)y =f^{'}(x) intersects the xx-axis, then the value of m+nm + n is