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Day 449: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 4 Apr 2026 S1

    56
    Let A=[112−201135]A =\begin{bmatrix} 1 & 1 & 2 \\ - 2 & 0 & 1 \\ 1 & 3 & 5 \end{bmatrix}. Then the sum of all elements of the matrix adj(adj(2(adj A)−1))adj\left( adj\left( 2(adj\text{ }A)^{- 1} \right) \right) is equal to :

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  2. Question 2

    Permutations and Combinations. Asked once: 21 Jan 2026 S1

    59
    The number of strictly increasing functions f from the set {1,2,3,4,5,6}\mathbf{\{ 1,2,3,4,5,6\}} to the set (1,2,3,…,9)(1,2,3,\ldots,9) such that f(i)≠if(i) \neq i for 1≤i≤61 \leq i \leq 6, is equal to :

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  3. Question 3

    Probability. Asked once: 4 Apr 2026 S1

    71
    A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p , then 96p is equal to ____\_\_\_\_ .

  4. Question 4

    Quadratic Equations. Asked once: 4 Apr 2026 S1

    52
    If the set of all solutions of ∣x2+x−9∣=∣x∣+∣x2−9∣\left| x^{2}+x- 9 \right|= |x| +\left| x^{2}- 9 \right| is [α,β]∪[γ,∞)\lbrack\alpha,\beta\rbrack \cup \lbrack\gamma,\infty), then (α2+β2+γ2)\left( \alpha^{2}+\beta^{2}+\gamma^{2} \right) is equal to :

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  5. Question 5

    Relations and Functions. Asked once: 4 Apr 2026 S2

    51
    For the function f:[1,∞)→[1,∞)f:\lbrack 1,\infty) \rightarrow \lbrack 1,\infty) defined by f(x)=(x−1)4+1f(x) = (x - 1)^{4}+ 1, among the two statements : (I) The set S={x∈[1,∞):f(x)=f−1(x)}S = \left\{ x \in \lbrack 1,\infty):f(x) = f^{-1}(x) \right\} contains exactly two elements, and (II) The set S={x∈[1,∞):f(x)=f−1(x+1)}S = \left\{ x \in \lbrack 1,\infty):f(x) = f^{-1}(x + 1) \right\} is an empty set,

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