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Day 185: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 29 Jul 2022 (same type asked 3 times) See all 3 of this type

    156
    Let {an}n=0∞\left\{ a_{n} \right\}_{n = 0}^{\infty} be a sequence such that a0=a1=0a_{0}=a_{1}= 0 and an+2=3an+1−2an+1,∀n≥0a_{n + 2}= 3a_{n + 1}- 2a_{n}+ 1,\forall n \geq 0. Then a25a23−2a25a22−2a23a24+4a22a24a_{25}a_{23}- 2a_{25}a_{22}- 2a_{23}a_{24}+ 4a_{22}a_{24} is equal to:

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  2. Question 2

    Application of Derivatives. Asked once: 8 Apr 2024 (same type asked 3 times) See all 3 of this type

    171
    Let AA be the region enclosed by the parabola y2=2xy^{2}= 2x and the line x=24x= 24. Then the maximum area of the rectangle inscribed in the region AA is.

  3. Question 3

    Definite Integration. Asked once: 5 Apr 2024 (same type asked 3 times) See all 3 of this type

    167
    Let β(m,n)=∫01xm−1(1−x)n−1dx,m,n>0\beta(m,n) =\int_{0}^{1} x^{m - 1}(1 - x)^{n - 1}dx,m,n > 0. If ∫01(1−x10)20dx=a×β(b,c)\int_{0}^{1} \left( 1 -x^{10} \right)^{20}dx = a \times \beta(b,c), then 100(a+b+c)100(a + b + c) equals

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  4. Question 4

    Probability. Asked once: 11 Apr 2023 (same type asked 3 times) See all 3 of this type

    70
    Let S={M=[aij],aij∈{0,1,2},1≤i,j≤2}S =\left\{ M =\left\lbrack a_{ij} \right\rbrack,a_{ij}\mathbf{\in \{ 0,1,2\},1 \leq i,j \leq 2} \right\} be aa sample space and A={M∈S:M\mathbf{A = \{ M \in S:M} is invertible }\} be an event. Then P(A)P(A) is equal to

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  5. Question 5

    Complex Numbers. Asked once: 1 Feb 2023 (same type asked 3 times) See all 3 of this type

    78
    If the center and radius of the circle ∣z−2z−3∣=2\left| \frac{z - 2}{z - 3} \right|= 2 are respectively (α,β)(\alpha,\beta) and γ\gamma. then 3(α+β+γ)3(\alpha + \beta + \gamma) is equal to

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