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Day 264: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 23 Jan 2025 (same type asked 4 times) See all 4 of this type

    72
    The sum of all rational terms in the expansion of (1+21/3+31/2)6\left( 1 +2^{1/3}+3^{1/2} \right)^{6} is equal to ____\_\_\_\_

  2. Question 2

    Conic Sections. Asked once: 30 Jan 2023 (same type asked 4 times) See all 4 of this type

    66
    If P(h,k)P(h,k) be a point on the parabola x=4y2x = 4y^{2}, which is nearest to the point Q(0,33)Q(0,33), then the distance of PP from the directrix of the parabola y2=4(x+y)y^{2}= 4(x + y) is equal to:

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  3. Question 3

    Determinants. Asked once: 30 Jan 2024 (same type asked 4 times) See all 4 of this type

    77
    If f(x)=∣2cos⁡4x2sin⁡4x3+sin⁡22x3+2cos⁡4x2sin⁡4xsin⁡22x2cos⁡4x3+2sin⁡4xsin⁡22x∣f(x) =\left| \begin{matrix} 2\cos^{4}x & 2\sin^{4}x & 3 +\sin^{2}2x \\ 3 + 2\cos^{4}x & 2\sin^{4}x & \sin^{2}2x \\ 2\cos^{4}x & 3 + 2\sin^{4}x & \sin^{2}2x \end{matrix} \right| then 15f′(0)\frac{1}{5}f^{'}(0) is equal to

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  4. Question 4

    Definite Integration. Asked once: 24 Jan 2025 (same type asked 4 times) See all 4 of this type

    71
    Let f be a differentiable function such that (x+2)2f(x)−3(x+2)2=10∫0x(t+2)f(t)dt(x + 2)^{2}f(x) - 3(x + 2)^{2}= 10\int_{0}^{x} (t + 2)f(t)dt x≥0x \geq 0. Then f(2)f(2) is equal to _____\_\_\_\_\_ .

  5. Question 5

    Matrices. Asked once: 31 Jan 2023 (same type asked 4 times) See all 4 of this type

    77
    Let A=(10004−1012−3)A =\begin{pmatrix} 1 & 0 & 0 \\ 0 & 4 & - 1 \\ 0 & 12 & - 3 \end{pmatrix}. Then the sum of the diagonal elements of the matrix (A+I)11(A + I)^{11} is equal to

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