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Day 37: JEE Mains Maths

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

  1. Question 1

    Differential Equations. This type asked 4 times: 29 Jun 2022, 29 Jan 2024, 8 Apr 2024, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 4 of this type

    70
    Let y=y(x)y=y(x) be the solution of the differential equation dydx=(1+x+x2)(1−y+y2),y(0)=12\frac{dy}{dx}=\left( 1 + x +x^{2} \right)\left( 1 - y +y^{2} \right),y(0) =\frac{1}{2}. Then ( 2y(1)−12y(1) - 1 ) is equal to

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  2. Question 2

    Differentiation. This type asked 4 times: 2021 Paper 7, 2021 Paper 21, 14 Jun 2022, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 4 of this type

    66
    If y=tan⁡−1(3cos⁡x−4sin⁡x4cos⁡x+3sin⁡x)+2tan⁡−1(x1+1−x2)y=\tan^{- 1}\left( \frac{3\cos x- 4\sin x}{4\cos x+ 3\sin x} \right)+ 2\tan^{- 1}\left( \frac{x}{1 +\sqrt{1 -x^{2}}} \right), then dydx\frac{dy}{dx} at x=32x =\frac{\sqrt{3}}{2} is equal to :

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  3. Question 3

    Permutations and Combinations. This type asked 4 times: 8 Apr 2023, 22 Jan 2025, 23 Jan 2025, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 4 of this type

    58
    The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

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  4. Question 4

    Relations and Functions. This type asked 4 times: 6 Apr 2023, 8 Apr 2023, 23 Jan 2026 S2, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 4 of this type

    54
    The number of functions f:{1,2,3,4}→{a,b,c}\mathbf{f:\{ 1,2,3,4\} \rightarrow \{ a,b,c\}}, which are not onto, is :

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  5. Question 5

    Statistics. 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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