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Day 274: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 14 Jun 2022 (same type asked 3 times) See all 3 of this type

    180
    Let P1P_{1} be a parabola with vertex (3,2)\left( 3,2 \right) and focus (4,4)\left( 4,4 \right) and P2P_{2} be its mirror image with respect to the line x+2y=6x+ 2y= 6. Then the directrix of P2P_{2} is x+2y=x+ 2y=

  2. Question 2

    Definite Integration. Asked once: 27 Jul 2022 (same type asked 3 times) See all 3 of this type

    178
    Let ff be aa differentiable function satisfying f(x)=23∫03f(λ2x3)dλ,x>0f(x) =\frac{2}{\sqrt{3}}\int_{0}^{\sqrt{3}} f\left( \frac{\lambda^{2}x}{3} \right)d\lambda,x > 0 and f(1)=3f(1) =\sqrt{3}. If y=f(x)y = f(x) passes through the point (α,6)(\alpha,6), then α\alpha is equal to

  3. Question 3

    Probability. Asked once: 29 Jul 2022 (same type asked 3 times) See all 3 of this type

    166
    Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:

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  4. Question 4

    Trigonometric Identities. Asked once: 2021 Paper 17 (same type asked 3 times) See all 3 of this type

    73
    Let α=max⁡x∈R{82sin⁡3x⋅44cos⁡3x}\alpha=\max_{x\in R} \left\{ 8^{2\sin3x}\cdot4^{4\cos3x} \right\} and β=min⁡x∈R{82sin⁡3x⋅44cos⁡3x}\beta=\min_{x\in R} \left\{ 8^{2\sin3x}\cdot4^{4\cos3x} \right\}. If 8x2+bx+c=08x^{2}+bx+c= 0 is a quadratic equation whose roots are α1/5\alpha^{1/5} and β1/5\beta^{1/5}, then the value of c−bc-b is equal to:

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  5. Question 5

    Indefinite Integration. Asked once: 27 Jun 2022 (same type asked 3 times) See all 3 of this type

    69
    ∫(x2+1)ex(x+1)2dx=f(x)ex+C\int\frac{\left( x^{2}+ 1 \right)e^{x}}{(x + 1)^{2}}dx = f(x)e^{x}+ C, Where CC is a constant, then d3fdx3\frac{d^{3}f}{dx^{3}} at x=1x = 1 is equal to:

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