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Day 53: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked 3 times: 2021 Paper 24, 24 Jan 2023, 22 Jan 2025 See all 3 times it was asked

    62
    Let x=x(y)x = x(y) be the solution of the differential equation y2dx+(x−1y)dy=0y^{2}dx +\left( x -\frac{1}{y} \right)dy = 0. If x(1)=1x(1) = 1, then x(12)x\left( \frac{1}{2} \right) is :

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  2. Question 2

    Differential Equations. Asked 3 times: 27 Jun 2022*, 26 Jul 2022*, 22 Jan 2025 (* = numbers or wording changed that year) See all 3 times it was asked

    146
    Let y=f(x)y=f(x) be the solution of the differential equation dydx+xyx2−1=x6+4x1−x2, −1<x<1\frac{dy}{dx}+\frac{xy}{x^{2}-1}=\frac{x^{6}+4x}{\sqrt{1-x^{2}}},\ -1<x<1, such that f(0)=0f(0)=0. If 6∫−1/21/2f(x)dx=2π−α6\int_{-1/2}^{1/2} f(x)dx = 2\pi-\alpha, then α2\alpha^{2} is equal to

  3. Question 3

    Vector Algebra. Asked 3 times: 30 Jan 2023*, 30 Jan 2024*, 31 Jan 2024 (* = numbers or wording changed that year) See all 3 times it was asked

    88
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two vectors such that ∣a→∣=1,∣b→∣=4|\overrightarrow{a}| = 1,|\overrightarrow{b}| = 4 and a→⋅b→=2\overrightarrow{a}\cdot\overrightarrow{b}= 2. If c→=(2a→×b→)−3b→\overrightarrow{c}= (2\overrightarrow{a}\times\overrightarrow{b}) - 3\overrightarrow{b} and the angle between b→\overrightarrow{b} and c→\overrightarrow{c} is α\alpha, then 192sin⁡2α192\sin^{2}\alpha is equal to

  4. Question 4

    Conic Sections. Asked 3 times: 2021 Paper 26*, 26 Jun 2022*, 10 Apr 2023 (* = numbers or wording changed that year) See all 3 times it was asked

    160
    Let a circle of radius 4 be concentric to the ellipse 15x2+19y2=28515x^{2}+ 19y^{2}= 285. Then the common tangents are inclined to the minor axis of the ellipse at the angle.

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  5. Question 5

    Permutations and Combinations. Asked 3 times: 27 Jun 2022*, 29 Jul 2022*, 31 Jan 2023 (* = numbers or wording changed that year) See all 3 times it was asked

    171
    Let A=[aij],aij∈Z∩[0,4],1≤i,j≤2A =\left\lbrack a_{ij} \right\rbrack,a_{ij}\in Z \cap \lbrack 0,4\rbrack,1 \leq i,j \leq 2. The number of matrices AA such that the sum of all entries is a prime number p∈(2,13)p \in (2,13) is