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Day 22: JEE Mains Maths

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

  1. Question 1

    Definite Integration. This type asked 6 times: 2021 Paper 6, 2021 Paper 8, 2021 Paper 11, 2021 Paper 13, 2021 Paper 19, 2021 Paper 25. This one: 2021 Paper 25 See all 6 of this type

    63
    The value of ∑n=1100∫n−1nex−[x]dx\sum_{n= 1}^{100} \int_{n- 1}^{n} e^{x- \lbrack x\rbrack}dx, where [x]\lbrack x\rbrack is the greatest integer ≤x\leq x, is:

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  2. Question 2

    Binomial Theorem. Asked 5 times: 2021 Paper 16*, 29 Jan 2023*, 30 Jan 2023*, 6 Apr 2023*, 10 Apr 2023 (* = numbers or wording changed that year) See all 5 times it was asked

    75
    If the coefficient of x7x^{7} in (ax−1bx2)13\left( ax -\frac{1}{bx^{2}} \right)^{13} and the coefficient of x−5x^{- 5} in (ax+1bx2)13\left( ax +\frac{1}{bx^{2}} \right)^{13} are equal, then a4b4a^{4}b^{4} is equal to:

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  3. Question 3

    Application of Integrals. This type asked 5 times: 2021 Paper 17, 2021 Paper 18, 7 Apr 2025, 21 Jan 2026 S2, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 5 of this type

    69
    The area of the region {(x,y):x2−8x≤y≤−x}\left\{ (x,y):x^{2}- 8x \leq y \leq - x \right\} is:

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  4. Question 4

    Limits and Continuity. This type asked 5 times: 2021 Paper 6, 25 Jun 2022, 28 Jun 2022, 26 Jul 2022, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 5 of this type

    75
    Let f(x)={x3+8x<0x2−4x≥0f(x) = \left\{ \begin{matrix} x^{3} + 8 & x < 0 \\ x^{2} - 4 & x \geq 0 \end{matrix} \right. and g(x)={(x−8)1/3;x<0(x+4)1/2;x≥0g(x) = \left\{ \begin{matrix} (x - 8)^{1/3}; & x < 0 \\ (x + 4)^{1/2}; & x \geq 0 \end{matrix} \right. Then the number of points, where the function gof is discontinuous, is ____\_\_\_\_ .

  5. Question 5

    Relations and Functions. This type asked 5 times: 29 Jan 2023, 6 Apr 2024, 24 Jan 2025, 28 Jan 2026 S2, 6 Apr 2026 S2. This one: 6 Apr 2026 S2 See all 5 of this type

    51
    Let f:R→Rf:R \rightarrow R be defined as f(x)=2x2−3x+23x2+x+3f(x) =\frac{2x^{2}- 3x + 2}{3x^{2}+ x + 3}. Then ff is :

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