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Day 621: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 29 Jul 2022

    66
    The integral ∫0π213+2sin⁡x+cos⁡xdx\int_{0}^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x}dx is equal to:

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  2. Question 2

    Sequences and Series. Asked once: 25 Jul 2022

    84
    Let a,ba,b be two non-zero real numbers. If pp and rr are the roots of the equation x2−8ax+2a=0x^{2}- 8ax + 2a = 0 and qq and ss are the roots of the equation x2+12bx+6bx^{2}+ 12bx + 6b =0= 0, such that 1p,1q,1r,1 s\frac{1}{p},\frac{1}{q},\frac{1}{r},\frac{1}{\text{ }s} are in A.P., then a−1−b−1a^{- 1}-b^{- 1} is equal to

  3. Question 3

    Conic Sections. Asked once: 4 Apr 2024

    153
    Let CC be a circle with radius 10\sqrt{10} units and centre at the origin. Let the line x+y=2x + y = 2 intersects the circle CC at the points PP and QQ. Let MNMN be a chord of CC of length 2 unit and slope -1 . Then, a distance (in units) between the chord PQ and the chord MN is

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  4. Question 4

    Definite Integration. Asked once: 28 Jul 2022

    159
    Let In(x)=∫0x1(t2+5)ndt,n=1,2,3,…I_{n}(x) =\int_{0}^{x} \frac{1}{\left( t^{2}+ 5 \right)^{n}}dt,n = 1,2,3,\ldots. Then

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  5. Question 5

    Sequences and Series. Asked once: 25 Jul 2022

    85
    Let a1=b1=1,an=an−1+2a_{1}=b_{1}= 1,a_{n}=a_{n - 1}+ 2 and bn=an+bn−1b_{n}=a_{n}+b_{n - 1} for every natural number n≥2n \geq 2. Then ∑n=115an⋅bn\sum_{n = 1}^{15} a_{n}\cdot b_{n} is equal to