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Day 177: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 29 Jan 2024 (same type asked 3 times) See all 3 of this type

    162
    If sin⁡(yx)=log⁡e∣x∣+α2\sin\left( \frac{y}{x} \right)=\log_{e}|x| +\frac{\alpha}{2} is the solution of the differential equation xcos(yx)dydx=ycos(yx)+xxcos\left( \frac{y}{x} \right)\frac{dy}{dx}= ycos\left( \frac{y}{x} \right)+ x and y(1)=π3y(1) =\frac{\pi}{3}, then α2\alpha^{2} is equal to

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  2. Question 2

    Limits and Continuity. Asked once: 28 Jan 2026 S1 (same type asked 3 times) See all 3 of this type

    64
    The value of lim⁡x→0log⁡e(sec(ex)⋅sec(e2x)⋅…⋅sec(e10x))e2−e2cos⁡x\underset{x\rightarrow 0}{\lim} \frac{\log_{e}\left( sec(ex) \cdot sec\left( e^{2}x \right)\cdot \ldots \cdot sec\left( e^{10}x \right) \right)}{e^{2}-e^{2\cos x}} is equal to

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  3. Question 3

    Sequences and Series. Asked once: 29 Jan 2023 (same type asked 3 times) See all 3 of this type

    83
    Suppose ff is a function satisfying f(x+y)=f(x)+f(y)f(x + y) = f(x) + f(y) for all x,y∈Nx,y \in N and f(1)=15f(1) =\frac{1}{5}. If ∑n=1mf(n)n(n+1)(n+2)=112\sum_{n = 1}^{m} \frac{f(n)}{n(n + 1)(n + 2)}=\frac{1}{12}, then mm is equal to

  4. Question 4

    Quadratic Equations. Asked once: 7 Apr 2025 (same type asked 3 times) See all 3 of this type

    64
    Let the set of all values of p∈Rp\in\mathbb{R}, for which both the roots of the equation x2−(p+2)x+(2p+9)=x^{2}- (p+ 2)x+ (2p+ 9) = 0 are negative real numbers, be the interval (α,β](\alpha,\beta\rbrack. Then β−2α\beta- 2\alpha is equal to.

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  5. Question 5

    Matrices. Asked once: 26 Jul 2022 (same type asked 3 times) See all 3 of this type

    180
    The number of matrices A=[abcd]A =\begin{bmatrix} a & b \\ c & d \end{bmatrix}, where a, b,c,d ∈{−1,0,1,2,3,……,10}\mathbf{\in \{ - 1,0,1,2,3,\ldots\ldots,10\}}, such that A=A−1A =A^{- 1}, is