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Day 492: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 31 Jan 2024

    160
    Let f:R→(0,∞)f:R \rightarrow (0,\infty) be strictly increasing function such that lim⁡x→∞f(7x)f(x)=1\lim_{x \rightarrow \infty} \frac{f(7x)}{f(x)}= 1. Then, the value of lim⁡x→∞[f(5x)f(x)−1]\lim_{x \rightarrow \infty} \left\lbrack \frac{f(5x)}{f(x)}- 1 \right\rbrack is equal to

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  2. Question 2

    Matrices. Asked once: 9 Apr 2024

    163
    Let B=[1315]B=\begin{bmatrix} 1 & 3 \\ 1 & 5 \end{bmatrix} and AA be a 2×22 \times 2 matrix such that AB−1=A−1AB^{- 1}=A^{- 1}. If BCB−1=ABCB^{- 1}= A and C4+αC2+βI=OC^{4}+\alpha C^{2}+\beta I = O, then 2β−α2\beta-\alpha is equal to:

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  3. Question 3

    Permutations and Combinations. Asked once: 5 Apr 2024

    163
    Let the set S={2,4,8,16,…..,512}\mathbf{S = \{ 2,4,8,16,\ldots..,512\}} be partitioned into 3 sets A,B,CA,B,C with equal number of elements such that A∪B∪C=SA \cup B \cup C = S and A∩B=B∩C=A∩C=ϕA \cap B = B \cap C = A \cap C = \phi. The maximum number of such possible partitions of SS is equal to:

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  4. Question 4

    Probability. Asked once: 9 Apr 2024

    167
    If an unbiased dice is rolled thrice, then the probability of getting a greater number in the ith i^{\text{th~}} roll than the number obtained in the (i−1)th (i - 1)^{\text{th~}} roll, i=2,3i = 2,3, is equal to :

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  5. Question 5

    Quadratic Equations. Asked once: 29 Jan 2025

    59
    The number of solutions of the equation (9x−9x+2)(2x−7x+3)=0\left( \frac{9}{x}-\frac{9}{\sqrt{x}}+ 2 \right)\left( \frac{2}{x}-\frac{7}{\sqrt{x}}+ 3 \right)= 0 is :

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