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Day 279: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 26 (same type asked 3 times) See all 3 of this type

    84
    In Im,n=∫01xm−1(1−x)n−1dxI_{m,n}=\int_{0}^{1} x^{m - 1}(1 - x)^{n - 1}dx, for m,n≥1m,n \geq 1 and ∫01xm−1+xn−1(1+x)m+ndx=αIm,n\int_{0}^{1} \frac{x^{m - 1}+x^{n - 1}}{(1 + x)^{m + n}}dx = \alpha I_{m,n}, α∈R\alpha \in R, then α\alpha equals

  2. Question 2

    Probability. Asked once: 29 Jun 2022 (same type asked 3 times) See all 3 of this type

    61
    The probability that a randomly chosen 2×22 \times 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to:

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  3. Question 3

    Complex Numbers. Asked once: 25 Jan 2023 (same type asked 3 times) See all 3 of this type

    166
    Let zz be a complex number such that ∣z−2iz+i∣=2,z≠−i\left| \frac{z - 2i}{z + i} \right|= 2,z \neq - i. Then zz lies on the circle of radius 2 and centre

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  4. Question 4

    Indefinite Integration. Asked once: 2021 Paper 22 (same type asked 3 times) See all 3 of this type

    70
    The integral ∫1(x−1)3(x+2)54dx\int\frac{1}{\sqrt[4]{(x- 1)^{3}(x+ 2)^{5}}}dx is equal to : (where CC is a constant of integration)

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  5. Question 5

    Relations and Functions. Asked once: 2021 Paper 26 (same type asked 3 times) See all 3 of this type

    77
    Let f(x)=sin⁡−1xf(x) =\sin^{- 1}x and g(x)=x2−x−22x2−x−6g(x) =\frac{x^{2}-x- 2}{2x^{2}-x- 6}. If g(2)=lim⁡x→2g(x)g(2) =\lim_{x\rightarrow 2} g(x), then the domain of the function fog is:

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