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Day 139: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 1 Feb 2024 (same type asked 7 times) See all 7 of this type

    83
    If the Coefficient of x30x^{30} in the expansion of (1+1x)6(1+x2)7(1−x3)8;x≠0\left( 1 +\frac{1}{x} \right)^{6}\left( 1 +x^{2} \right)^{7}\left( 1 -x^{3} \right)^{8};x \neq 0 is α\alpha, then ∣α∣|\alpha| equals

  2. Question 2

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

    134
    The integral ∫0π8xdx4cos⁡2x+sin⁡2x\int_{0}^{\pi} \frac{8xdx}{4\cos^{2}x+\sin^{2}x} is equal to.

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  3. Question 3

    Differential Equations. Asked once: 5 Apr 2024 (same type asked 7 times) See all 7 of this type

    172
    Let y=y(x)y = y(x) be the solution of the differential equation dydx+2x(1+x2)2y=xe1(1+x2);y(0)=0\frac{dy}{dx}+\frac{2x}{\left( 1 +x^{2} \right)^{2}}y = xe^{\frac{1}{\left( 1 +x^{2} \right)}};y(0) = 0. Then the area enclosed by the curve f(x)=y(x)e−1(1+x2)f(x) = y(x)e^{-\frac{1}{\left( 1 +x^{2} \right)}} and the line y−x=4y - x = 4 is

  4. Question 4

    Probability. Asked once: 8 Apr 2024 (same type asked 7 times) See all 7 of this type

    83
    Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables XX and YY respectively denote the number of blue and Yellow balls. If Xˉ\bar{X} and Yˉ\bar{Y} are the means of XX and YY respectively, then 7Xˉ+4Yˉ7\bar{X}+ 4\bar{Y} is equal to

  5. Question 5

    Quadratic Equations. Asked once: 9 Apr 2024 (same type asked 7 times) See all 7 of this type

    79
    Let α,β\alpha,\beta be the roots of the equation x2+22x−1=0x^{2}+ 2\sqrt{2}x- 1 = 0. The quadratic equation, whose roots are α4+β4\alpha^{4}+\beta^{4} and 110(α6+β6)\frac{1}{10}\left( \alpha^{6}+\beta^{6} \right), is:

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