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Day 627: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 25 Jul 2022

    176
    Let ff be a twice differentiable function on RR. If f′(0)=4f^{'}(0) = 4 and f(x)+∫0x(x−t)f′(t)dt=(e2x+e−2x)cos⁡2x+2axf(x) +\int_{0}^{x} (x - t)f^{'}(t)dt =\left( e^{2x}+e^{- 2x} \right)\cos2x +\frac{2}{a}x, then (2a+1)5a2(2a + 1)^{5}a^{2} is equal to

  2. Question 2

    Sequences and Series. Asked once: 14 Jun 2022

    175
    The remainder on dividing 1+3+32+33+…+320211 + 3 +3^{2}+3^{3}+ \ldots +3^{2021} by 50 is

  3. Question 3

    Conic Sections. Asked once: 12 Apr 2023

    65
    Let P(237,67),Q,RP\left( \frac{2\sqrt{3}}{\sqrt{7}},\frac{6}{\sqrt{7}} \right),Q,R and SS be four points on the ellipse 9x2+4y2=369x^{2}+ 4y^{2}= 36. Let PQPQ and RS be mutually perpendicular and pass through the origin. If 1(PQ)2+1(RS)2=pq\frac{1}{(PQ)^{2}}+\frac{1}{(RS)^{2}}=\frac{p}{q}, where pp and qq are coprime, then p+qp + q is equal to

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  4. Question 4

    Definite Integration. Asked once: 25 Jul 2022

    177
    Let an=∫−1n(1+x2+x23+x34+…….+xn−1n)dxa_{n}=\int_{- 1}^{n} \left( 1 +\frac{x}{2}+\frac{x^{2}}{3}+\frac{x^{3}}{4}+ \ldots\ldots. +\frac{x^{n - 1}}{n} \right)dx for n∈Nn \in N. Then the sum of all the elements of the set {n∈N:an∈(2,30)}\left\{ n \in N:a_{n}\in (2,30) \right\} is

  5. Question 5

    Sequences and Series. Asked once: 2021 Paper 26

    87
    If the arithmetic mean and geometric mean of the pth p^{\text{th~}} and qth q^{\text{th~}} terms of the sequence −16,8,−4,2- 16,8, - 4,2, satisfy the equation 4x2−9x+5=4x^{2}- 9x + 5 = 0 , then p+qp + q is equal to