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Day 101: JEE Mains Maths

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

  1. Question 1

    Definite Integration. This type asked 2 times: 26 Jul 2022, 2 Apr 2026 S2. This one: 2 Apr 2026 S2 See all 2 of this type

    67
    The value of ∫020π(sin⁡4x+cos⁡4x)dx\int_{0}^{20\pi} \left( \sin^{4}x +\cos^{4}x \right)dx is equal to:

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  2. Question 2

    Indefinite Integration. This type asked 2 times: 25 Jan 2023, 2 Apr 2026 S2. This one: 2 Apr 2026 S2 See all 2 of this type

    69
    Let f(x)=∫(16x+24x2+2x−15)dxf(x) = \int\left( \frac{16x+ 24}{x^{2}+ 2x- 15} \right)dx. If f(4)=14log⁡e(3)f(4) = 14\log_{e}(3) and f(7)=log⁡e(2α⋅3β),α,β∈Nf(7) =\log_{e}\left( 2^{\alpha}\cdot3^{\beta} \right),\alpha,\beta\in N, then α+β\alpha+\beta is equal to:

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  3. Question 3

    Binomial Theorem. This type asked 2 times: 27 Jan 2024, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 2 of this type

    57
    The number of elements in the set S={(r,k):k∈ZS=\left\{ (r,k):k\in Z \right. and   36Cr+1=6( 35Cr)(k2−3)}\left. \ \ ^{36}C_{r+ 1}=\frac{6\left( \ ^{35}C_{r} \right)}{\left( k^{2}- 3 \right)} \right\}, is

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  4. Question 4

    Matrices. This type asked 2 times: 21 Jan 2026 S1, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 2 of this type

    54
    Let A=[121α]A=\begin{bmatrix} 1 & 2 \\ 1 & \alpha \end{bmatrix} and B=[33β2]B=\begin{bmatrix} 3 & 3 \\ \beta & 2 \end{bmatrix}. If A2−4A+I=0A^{2}- 4A+I= 0 and B2−5B−6I=0B^{2}- 5B- 6I= 0, then among the two statements : (S1) : [(B−A)(B+A)]T=[1315710]\lbrack(B - A)(B + A)\rbrack^{T}=\begin{bmatrix} 13 & 15 \\ 7 & 10 \end{bmatrix} and (S2) : det(adj(A+B))=−5det(adj(A + B)) = - 5,

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  5. Question 5

    Straight Lines. This type asked 2 times: 2021 Paper 24, 2 Apr 2026 S1. This one: 2 Apr 2026 S1 See all 2 of this type

    59
    Let the mid points of the sides of a triangle ABCABC be (52,7),(52,3)\left( \frac{5}{2},7 \right),\left( \frac{5}{2},3 \right) and (4,5)(4,5). If its incentre is (h,k)(h,k), then 3 h+k3\text{ }h + k is equal to :

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