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Day 338: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 3 Apr 2025 (same type asked 8 times) See all 8 of this type

    62
    Let gg be a differentiable function such that ∫0xg(t)dt=x−∫0xtg(t)dt,x≥0\int_{0}^{x} g(t)dt = x -\int_{0}^{x} tg(t)dt,x \geq 0 and let y=y(x)y = y(x) satisfy the differential equation dydx−ytanx=\frac{dy}{dx}-ytanx= 2(x+1)secxg(x),x∈[0,π2)2(x+ 1)secxg(x),x\in\left\lbrack 0,\frac{\pi}{2} \right). If y(0)=0y(0) = 0, then y(π3)y\left( \frac{\pi}{3} \right) is equal to.

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  2. Question 2

    Vector Algebra. Asked once: 27 Jun 2022 (same type asked 8 times) See all 8 of this type

    165
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be the vectors along the diagonal of a parallelogram having area 222\sqrt{2}. Let the angle between a→\overrightarrow{a} and b→\overrightarrow{b} be acute. ∣a→∣=1|\overrightarrow{a}| = 1 and ∣a→.b→∣=∣a→×b→∣|\overrightarrow{a}.\overrightarrow{b}| = |\overrightarrow{a}\times\overrightarrow{b}|. If c→=22(a→×b→)−2b→\overrightarrow{c}= 2\sqrt{2}(\overrightarrow{a}\times\overrightarrow{b}) - 2\overrightarrow{b}, then an angle between b→\overrightarrow{b} and c→\overrightarrow{c} is:

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  3. Question 3

    Statistics. Asked once: 10 Apr 2023 (same type asked 8 times) See all 8 of this type

    170
    Let μ\mu be the mean and σ\sigma be the standard deviation of the distribution
    xix_{i}012345
    fif_{i}k+2k + 22k2kk2−1k^{2}- 1k2−1k^{2}- 1k2+1k^{2}+ 1k−3k - 3
    where ∑fi=62\sum f_{i}= 62. If [x]\lbrack x\rbrack denotes the greatest integer ≤x\leq x, then [μ2+σ2]\left\lbrack \mu^{2}+\sigma^{2} \right\rbrack is equal to

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  4. Question 4

    Three Dimensional Geometry. Asked once: 29 Jan 2023 (same type asked 8 times) See all 8 of this type

    164
    If the lines x−11=y−22=z+31\frac{x - 1}{1}=\frac{y - 2}{2}=\frac{z + 3}{1} and x−a2=y+23=z−31\frac{x - a}{2}=\frac{y + 2}{3}=\frac{z - 3}{1} intersect at the point PP, then the distance of the point PP from the plane z=az = a is :

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  5. Question 5

    Permutations and Combinations. Asked once: 6 Apr 2023 (same type asked 8 times) See all 8 of this type

    161
    All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is

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