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Day 56: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. This type asked 3 times: 29 Jul 2022, 29 Jan 2023, 5 Apr 2026 S1. This one: 5 Apr 2026 S1 See all 3 of this type

    55
    ∑n=110(528n(n+1)(n+2))\sum_{n = 1}^{10} \left( \frac{528}{n(n + 1)(n + 2)} \right) is equal to :

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  2. Question 2

    Quadratic Equations. This type asked 3 times: 2 Apr 2025, 7 Apr 2025, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 3 of this type

    55
    If the quadratic equation (λ+2)x2−3λx+4λ=0(\lambda+ 2)x^{2}- 3\lambda x+ 4\lambda= 0, λ≠−2\lambda\neq - 2, has two positive roots, then the number of possible integral values of λ\lambda is :

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  3. Question 3

    Relations and Functions. This type asked 3 times: 29 Jun 2022, 28 Jan 2025, 4 Apr 2026 S2. This one: 4 Apr 2026 S2 See all 3 of this type

    66
    Let for some α∈R,f:R→R\alpha\in R,f:R\rightarrow R be a function satisfying f(x+y)=f(x)+2y2+y+αxyf(x + y) =f(x) + 2y^{2}+ y +\alpha xy for all x,y∈Rx,y \in R. If f(0)=−1f(0) = - 1 and f(1)=2f(1) = 2, then the value of ∑n=15(α+f(n))\sum_{n = 1}^{5} (\alpha+f(n)) is :

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  4. Question 4

    Matrices. This type asked 3 times: 2021 Paper 23, 26 Jul 2022, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 3 of this type

    55
    Let S={A=[abcd]:a,b,c,d∈{0,1,2,3,4}S =\left\{ A =\begin{bmatrix} a & b \\ c & d \end{bmatrix}\mathbf{:a,b,c,d \in \{ 0,1,2,3,4\}} \right. and  A2−4 A+3I=0}\left. \ A^{2}- 4\text{ }A + 3I = 0 \right\} be a set of 2×22 \times 2 matrices. Then the number of matrices in S, for which the sum of the diagonal elements is equal to 4 , is:

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  5. Question 5

    Straight Lines. This type asked 3 times: 30 Jan 2024, 24 Jan 2026 S1, 4 Apr 2026 S1. This one: 4 Apr 2026 S1 See all 3 of this type

    61
    Let the line L1:x+3=0L_{1}:x + 3 = 0 intersect the lines L2:x−y=0L_{2}:x - y = 0 and L3:3x+y=0L_{3}:3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L2L_{2} and L3L_{3} intersect the line L1L_{1} at the point C . Then BC2:AC2BC^{2}:AC^{2} is equal to :

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