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Day 636: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 18

    74
    The value of ∫−1/21/2((x+1x−1)2+(x−1x+1)2−2)1/2dx\int_{- 1/\sqrt{2}}^{1/\sqrt{2}} \left( \left( \frac{x+ 1}{x- 1} \right)^{2}+\left( \frac{x- 1}{x+ 1} \right)^{2}- 2 \right)^{1/2}dx is:

    Tap an option to check your answer.

  2. Question 2

    Sequences and Series. Asked once: 2021 Paper 1

    88
    Let A={n∈N:nA\mathbf{= \{}n\in N:n is a 3-digit number }\}
    B={9k+2:k∈N}B\mathbf{= \{ 9}k+ 2:k\in N\}
    and
    C:{9k+l:k∈N} for some l(0<l<9)C\mathbf{:\{ 9k +}\mathcal{l}:k \in N\}\text{~for some~}\mathcal{l}(0 <\mathcal{l}< 9)
    If the sum of all the elements of the set A∩(B∪C)A\cap (B\cup C) is 274×400274 \times 400, then l\mathcal{l} is equal to

  3. Question 3

    Conic Sections. Asked once: 31 Jan 2023

    174
    Let SS be the set of all a∈Na \in N such that the area of the triangle formed by the tangent at the point P(bP(b, c), b,c∈Nb,c \in N, on the parabola y2=2axy^{2}= 2ax and the lines x=b,y=0x = b,y = 0 is 16unit216unit^{2}, then ∑a∈sa\sum_{a \in s} a is equal to

  4. Question 4

    Definite Integration. Asked once: 2021 Paper 17

    85
    If ∫0π(sin⁡3x)e−sin⁡2xdx=α−βe∫01tetdt\int_{0}^{\pi} \left( \sin^{3}x \right)e^{-\sin^{2}x}dx=\alpha-\frac{\beta}{e}\int_{0}^{1} \sqrt{t}e^{t}dt, then α+β\alpha+\beta is equal to

  5. Question 5

    Conic Sections. Asked once: 30 Jan 2023

    173
    Let P(a1, b1)P\left( a_{1},{\text{ }b}_{1} \right) and Q(a2, b2)Q\left( a_{2},{\text{ }b}_{2} \right) be two distinct points on a circle with center C(2,3)C(\sqrt{2},\sqrt{3}). Let OO be the origin and OCOC be perpendicular to both CPCP and CQCQ. If the area of the triangle OCP is 352\frac{\sqrt{35}}{2}, then a12+a22+b12+b22a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2} is equal to