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Day 608: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 9 Apr 2024

    171
    Consider the circle C:x2+y2=4C:x^{2}+y^{2}= 4 and the parabola P:y2=8xP:y^{2}= 8x. If the set of all values of α\alpha, for which three chords of the circle CC on three distinct lines passing through the point (α,0)(\alpha,0) are bisected by the parabola PP is the interval (p,q)(p,q), then (2q−p)2(2q-p)^{2} is equal to

  2. Question 2

    Definite Integration. Asked once: 31 Jan 2023

    70
    The value of ∫π3π2(2+3sin⁡x)sin⁡x(1+cos⁡x)dx\int_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2 + 3\sin x)}{\sin x(1 + \cos x)}dx is equal to

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  3. Question 3

    Matrices. Asked once: 2021 Paper 6

    83
    Let A=[a1a2]A=\begin{bmatrix} a_{1} \\ a_{2} \end{bmatrix} and B=[b1b2]B=\begin{bmatrix} b_{1} \\ b_{2} \end{bmatrix} be two 2×12 \times 1 matrices with real entries such that A=XBA=XB, where X=13[1−11k]X=\frac{1}{\sqrt{3}}\begin{bmatrix} 1 & - 1 \\ 1 & k \end{bmatrix}, and k∈Rk\in R. If a12+a22=23(b12+b22)a_{1}^{2}+a_{2}^{2}=\frac{2}{3}\left( b_{1}^{2}+b_{2}^{2} \right) and (k2+1)b22≠−2b1b2\left( k^{2}+ 1 \right)b_{2}^{2}\neq - 2b_{1}b_{2}, then the value of kk is

  4. Question 4

    Relations and Functions. Asked once: 2021 Paper 6

    68
    Let A={2,3,4,5,…,30}\mathbf{A = \{ 2,3,4,5,\ldots,30\}} and ' ≃\simeq ' be an equivalence relation on A×AA \times A, defined by (a,b)≃(c,d)(a,b) \simeq (c,d), if and only if ad=bcad=bc. Then the number of ordered pairs which satisfy this equivalence relation with ordered pair (4,3)(4,3) is equal to:

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  5. Question 5

    Sequences and Series. Asked once: 30 Jan 2023

    168
    The parabolas: ax2+2bx+cy=0ax^{2}+ 2bx + cy = 0 and dx2+2ex+fy=0dx^{2}+ 2ex + fy = 0 intersect on the line y=1y = 1. If a,b,c,d,e,fa,b,c,d,e,f are positive real numbers and a,b,ca,b,c are in G.P., then

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