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Day 635: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 2

    89
    The sum of first four terms of a geometric progression (G.P.) is 6512\frac{65}{12} and the sum of their respective reciprocals is 6518\frac{65}{18}. If the product of first three terms of the G.P. is 1 , and the third term is α\alpha, then 2α2\alpha is

  2. Question 2

    Conic Sections. Asked once: 31 Jan 2023

    61
    If the maximum distance of normal to the ellipse x24+y2b2=1,b<2\frac{x^{2}}{4}+\frac{y^{2}}{b^{2}}= 1,b < 2, from the origin is 1 , then the eccentricity of the ellipse is:

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  3. Question 3

    Definite Integration. Asked once: 2021 Paper 21

    79
    The value of the integral ∫01xdx(1+x)(1+3x)(3+x)\int_{0}^{1} \frac{\sqrt{x}dx}{(1 +x)(1 + 3x)(3 +x)} is:

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  4. Question 4

    Sequences and Series. Asked once: 2021 Paper 1

    79
    If e(cos⁡2x+cos⁡4x+cos⁡6x+…∞)log⁡e2e^{\left( \cos^{2}x+\cos^{4}x+\cos^{6}x+ \ldots\infty \right)\log_{e}2} satisfies the equation t2−9t+8=0t^{2}- 9t+ 8 = 0, then the value of 2sin⁡xsin⁡x+3cos⁡x(0<x<π2)\frac{2\sin x}{\sin x+\sqrt{3}\cos x}\left( 0 <x<\frac{\pi}{2} \right) is :

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  5. Question 5

    Conic Sections. Asked once: 31 Jan 2023

    66
    Let a circle C1C_{1} be obtained on rolling the circle x2+y2−4x−6y+11=0x^{2}+y^{2}- 4x - 6y + 11 = 0 upwards 4 units on the tangent TT to it at the point (3,2)(3,2). Let C2C_{2} be the image of C1C_{1} in TT. Let AA and BB be the centers of circles C1C_{1} and C2C_{2} respectively, and MM and NN be respectively the feet of perpendiculars drawn from AA and BB on the xx-axis. Then the area of the trapezium AMNB is:

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