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Day 444: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 5 Apr 2026 S2

    67
    Let f(x)=lim⁡y→0(1−cos⁡(xy))tan⁡(xy)y3f(x) =\lim_{y\rightarrow 0} \frac{(1 - \cos(xy))\tan(xy)}{y^{3}}. Then the number of solutions of the equation f(x)=sin⁡xf(x) = \sin x, x∈Rx \in R is :

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  2. Question 2

    Matrices. Asked once: 6 Apr 2026 S1

    71
    Let A=[−11−1101001]A = \begin{bmatrix} - 1 & 1 & - 1 \\ 1 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix} satisfy A2+α(adj(adj(A)))+β(adj(A)(adj(adj(A))))=[2−22−20−100−1]A^{2} + \alpha(adj(adj(A))) + \beta(adj(A)(adj(adj(A)))) = \begin{bmatrix} 2 & - 2 & 2 \\ - 2 & 0 & - 1 \\ 0 & 0 & - 1 \end{bmatrix} for Some α,β∈R\alpha,\beta \in R. Then (α−β)2(\alpha - \beta)^{2} is equal to ____\_\_\_\_

  3. Question 3

    Permutations and Combinations. Asked once: 22 Jan 2026 S2

    75
    Let S be the set of the first 11 natural numbers. Then the number of elements in A={B⊆S:n(B)≥2A = \{ B \subseteq S:n(B) \geq 2 and the product of all elements of B is even }\} is____\_\_\_\_.

  4. Question 4

    Probability. Asked once: 5 Apr 2026 S2

    58
    The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If A is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team wins the tournament is 0.7 Then the probability, that the team wins the tournament, is:

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  5. Question 5

    Quadratic Equations. Asked once: 5 Apr 2026 S2

    51
    Let α,β\alpha,\beta be the roots of the equation x2−x+p=0x^{2}- x + p = 0 and γ,δ\gamma,\delta be the roots the equation x2−4x+q=0x^{2}- 4x + q = 0; p,q∈Zp,q \in Z. If α,β,γ,δ\alpha,\beta,\gamma,\delta are in G.P., then ∣p+q∣|p + q| equals:

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