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Day 641: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 1

    86
    If ∫−aa(∣x∣+∣x−2∣)dx=22,(a>2)\int_{-a}^{a} (|x| + |x- 2|)dx= 22,(a> 2) and [x]\lbrack x\rbrack denotes the greatest integer ≤x\leq x, then ∫a−a(x+[x])dx\int_{a}^{-a} (x+ \lbrack x\rbrack)dx is equal to

  2. Question 2

    Conic Sections. Asked once: 28 Jul 2022

    72
    Let CC be the centre of the circle x2+y2−x+2y=x^{2}+y^{2}- x + 2y = 114\frac{11}{4} and PP be a point on the circle. A line passes through the point CC, makes an angle of π4\frac{\pi}{4} with the line CPCP and intersects the circle at the points QQ and RR. Then the area of the triangle PQR (in unit  2\ ^{2} ) is:

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  3. Question 3

    Conic Sections. Asked once: 27 Jul 2022

    162
    AA circle C1C_{1} passes through the origin OO and has diameter 4 on the positive xx-axis. The line y=2xy = 2x gives a chord OA of a circle C1C_{1}. Let C2C_{2} be the circle with OAOA as a diameter. If the tangent to C2C_{2} at the point AA meets the xx-axis at PP and yy-axis at QQ, then QA: AP is equal to:

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  4. Question 4

    Conic Sections. Asked once: 27 Jul 2022

    79
    If the circle x2+y2−2gx+6y−19c=0,g,c∈Rx^{2}+y^{2}- 2gx + 6y - 19c = 0,g,c \in R passes through the point (6,1)(6,1) and its centre lies on the line x−2cy=8x - 2cy = 8, then the length of intercept made by the circle on xx-axis is

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  5. Question 5

    Conic Sections. Asked once: 27 Jul 2022

    71
    Let P(a, b)P(a,\text{ }b) be a point on the parabola y2=8xy^{2}= 8x such that the tangent at PP passes through the centre of the circle x2+y2−10x−14y+65=0x^{2}+y^{2}- 10x - 14y + 65 = 0. Let AA be the product of all possible values of aa and BB be the product of all possible values of bb. Then the value of A+BA + B is equal to:

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