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Day 94: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked 2 times: 2021 Paper 5*, 28 Jun 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    158
    Let f:R→Rf:R \rightarrow R be continuous function satisfying f(x)+f(x+k)=nf(x) + f(x + k) = n, for all x∈Rx \in R where k>0k > 0 and nn is a positive integer. If I1=∫04nkf(x)dxI_{1}=\int_{0}^{4nk} f(x)dx and I2=∫−k3kf(x)dxI_{2}=\int_{- k}^{3k} f(x)dx, then

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  2. Question 2

    Three Dimensional Geometry. Asked 2 times: 2021 Paper 10*, 27 Jun 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    90
    Let the mirror image of the point (a,b,c)(a,b,c) with respect to the plane 3x−4y+12z+19=03x - 4y + 12z + 19 = 0 be (a- 6,β,γ)6,\beta,\gamma). If a+b+c=5a + b + c = 5, then 7β−9γ7\beta - 9\gamma is equal to

  3. Question 3

    Conic Sections. Asked 2 times: 2021 Paper 23*, 26 Jun 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    162
    The locus of the mid -point of the line segment joining the point (4,3)(4,3) and the points on the ellipse x2+2y2=4x^{2}+ 2y^{2}= 4 is an ellipse with eccentricity:

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  4. Question 4

    Limits and Continuity. Asked 2 times: 2021 Paper 7*, 26 Jun 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    154
    lim⁡x→0cos⁡(sin⁡x)−cos⁡xx4\lim_{x \rightarrow 0} \frac{\cos(\sin x) - \cos x}{x^{4}} is equal to:

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  5. Question 5

    Quadratic Equations. Asked 2 times: 2021 Paper 1*, 26 Jun 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    172
    Let pp and qq be two real numbers such that p+q=p + q = 3 and p4+q4=369p^{4}+q^{4}= 369. Then (1p+1q)−2\left( \frac{1}{p}+\frac{1}{q} \right)^{- 2} is equal to