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Day 438: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 8 Apr 2026 S2

    72
    If ∫π/6π/4(cot⁡(x−π3)cot⁡(x+π3)+1)dx=αlog⁡e(3−1)\int_{\pi/6}^{\pi/4} \left( \cot\left( x - \frac{\pi}{3} \right)\cot\left( x + \frac{\pi}{3} \right) + 1 \right)dx = \alpha\log_{e}(\sqrt{3} - 1), then 9α29\alpha^{2} is equal to

  2. Question 2

    Determinants. Asked once: 4 Apr 2026 S2

    56
    Let A=[1274−2838−7]A =\begin{bmatrix} 1 & 2 & 7 \\ 4 & - 2 & 8 \\ 3 & 8 & - 7 \end{bmatrix} and det(A−αI)=0det(A -\alpha I) = 0, where α\alpha is a real number. If the largest possible value of α\alpha is pp, then the circle (x−p)2+(y−2p)2=(x-p)^{2}+ (y- 2p)^{2}= 320, intersects the co-ordinate axes at

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  3. Question 3

    Differential Equations. Asked once: 5 Apr 2026 S2

    70
    Let f(x)f(x) and g(x)g(x) be twice differentiable functions satisfying f′′(x)=g′′(x)f^{''}(x) =g^{''}(x) for all x∈Rx \in R, f′(1)=2 g′(1)=4f^{'}(1) = 2{\text{ }g}^{'}(1) = 4 and g(2)=3f(2)=9g(2) = 3f(2) = 9. Then f(25)−g(25)f(25) - g(25) is equal to :

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  4. Question 4

    Differentiation. Asked once: 8 Apr 2026 S2

    63
    For the function f(x)=e∣sin⁡x∣−∣x∣,x∈Rf(x) =e^{|\sin x|}- |x|,x \in R, consider the following statements: Statement I : f is differentiable for all x∈Rx \in R. Statement II : f is increasing in (−π,−π2)\left( - \pi, - \frac{\pi}{2} \right). In the light of the above statements, choose the correct answer from the options given below:

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  5. Question 5

    Indefinite Integration. Asked once: 28 Jan 2026 S1

    61
    If ∫ (1−5cos⁡2xsin⁡5xcos⁡2x)dx=f(x)+C\int_{}^{}\ \left( \frac{1 - 5\cos^{2}x}{\sin^{5}x\cos^{2}x} \right)dx=f(x) +C where CC is the constant of integration, then f(π6)−f(π4)f\left( \frac{\pi}{6} \right)- f\left( \frac{\pi}{4} \right) is equal to

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