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Day 180: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 29 Jan 2025 (same type asked 3 times) See all 3 of this type

    141
    Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains nn white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is 29/4529/45, then n is equal to:

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  2. Question 2

    Trigonometric Identities. Asked once: 9 Apr 2024 (same type asked 3 times) See all 3 of this type

    158
    Let the range of the function f(x)=12+sin⁡3x+cos⁡3x,x∈Rf(x) =\frac{1}{2 + \sin3x + \cos3x},x \in R be [a,b]\lbrack a,b\rbrack. If α\alpha and β\beta are respectively the A.M. and the G.M. of aa and bb, then αβ\frac{\alpha}{\beta} is equal to:

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  3. Question 3

    Application of Integrals. Asked once: 8 Apr 2024 (same type asked 3 times) See all 3 of this type

    89
    Let the area of the region enclosed by the curve y=min⁡{sin⁡x,cos⁡x}y = \min\{ \sin x,\cos x\} and the xx-axis between x=−πx = -\pi to x=πx=\pi be AA. Then A2A^{2} is equal to

  4. Question 4

    Indefinite Integration. Asked once: 22 Jan 2025 (same type asked 3 times) See all 3 of this type

    136
    If ∫ex(xsin⁡−1x1−x2+sin⁡−1x(1−x2)3/2+x1−x2)dx=g(x)+C\int e^{x}\left(\frac{x\sin^{-1}x}{\sqrt{1-x^{2}}}+\frac{\sin^{-1}x}{\left(1-x^{2}\right)^{3/2}}+\frac{x}{1-x^{2}}\right)dx = g(x)+C, where CC is the constant of integration, then g(12)g\left(\frac{1}{2}\right) equals:

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  5. Question 5

    Probability. Asked once: 30 Jan 2024 (same type asked 3 times) See all 3 of this type

    71
    Two integers xx and yy are chosen with replacement from the set {0,1,2,3,….,10}\mathbf{\{ 0,1,2,3,\ldots.,10\}}. Then the probability that ∣x−y∣>5|x - y| > 5 is:

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