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Day 638: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 25 Jan 2023

    177
    Points P(−3,2),Q(9,10)P( - 3,2),Q(9,10) and (a,4)(a,4) lie on a circle CC with PRPR as its diameter, The tangents to CC at the points QQ and RR intersect at the point SS. If SS lies on the line 2x−ky=12x - ky = 1, then kk is equal to

  2. Question 2

    Definite Integration. Asked once: 2021 Paper 10

    68
    Let g(x)=∫0xf(t)dtg(x) =\int_{0}^{x} f(t)dt, where ff is continuous function in [0,3]\lbrack 0,3\rbrack such that 13≤f(t)≤1\frac{1}{3}\leq f(t) \leq 1 for all t∈[0,1]t \in \lbrack 0,1\rbrack and 0≤f(t)≤120 \leq f(t) \leq\frac{1}{2} for all t∈(1,3]t \in (1,3\rbrack. The largest possible interval in which g(3)g(3) lies is:

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  3. Question 3

    Conic Sections. Asked once: 25 Jan 2023

    86
    The vertices of a hyperbola HH are (±6,0)( \pm 6,0) and its eccentricity is 52\frac{\sqrt{5}}{2}. Let NN be the normal to HH at a point in the first quadrant and parallel to the line 2x+y=22\sqrt{2}x + y = 2\sqrt{2}. If dd is the length of the line segment of NN between HH and the yy-axis then d2d^{2} is equal to

  4. Question 4

    Definite Integration. Asked once: 2021 Paper 9

    83
    Let f(x)f(x) and g(x)g(x) be two functions satisfying f(x2)+g(4−x)=4x3f\left(x^{2}\right)+g(4-x)=4x^{3} and g(4−x)+g(x)=0g(4-x)+g(x)=0. Then the value of ∫−44f(x) dx\int_{-4}^{4} f(x)\,dx is

  5. Question 5

    Conic Sections. Asked once: 25 Jan 2023

    154
    The equations of two sides of a variable triangle are x=0x = 0 and y=3y = 3, and its third side is a tangent to parabola y2=6xy^{2}= 6x. The locus of its circumcentre is:

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