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Day 515: JEE Mains Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 2021 Paper 8

    66
    The number of solutions of the equation sin⁡−1[x2+13]+cos⁡−1[x2−23]=x2\sin^{- 1}\left\lbrack x^{2}+\frac{1}{3} \right\rbrack+\cos^{- 1}\left\lbrack x^{2}-\frac{2}{3} \right\rbrack=x^{2}, for x∈[−1,1]x \in \lbrack - 1,1\rbrack, and [x]\lbrack x\rbrack denotes the greatest integer less than or equal to xx, is:

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  2. Question 2

    Limits and Continuity. Asked once: 6 Apr 2023

    153
     Limn→∞{(212−213)(212−215)……..(212−212n+1)}\ Lim_{n \rightarrow \infty}\left\{ \left( 2^{\frac{1}{2}}-2^{\frac{1}{3}} \right)\left( 2^{\frac{1}{2}}-2^{\frac{1}{5}} \right)\ldots\ldots..\left( 2^{\frac{1}{2}}-2^{\frac{1}{2n + 1}} \right) \right\}is equal to

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  3. Question 3

    Matrices. Asked once: 1 Feb 2024

    172
    Let A=I2−MMTA =I_{2}-MM^{T}, where MM is real matrix of order 2×12 \times 1 such that the relation MTM=I1M^{T}M =I_{1} holds. If λ\lambda is a real number such that the relation AX=λXAX = \lambda X holds for some non-zero real matrix XX of order 2×12 \times 1, then the sum of squares of all possible values of λ\lambda is equal to:

  4. Question 4

    Permutations and Combinations. Asked once: 27 Jan 2024

    169
    Let α=(4!)!(4!)3!\alpha =\frac{(4!)!}{(4!)^{3!}} and β=(5!)!(5!)4!\beta =\frac{(5!)!}{(5!)^{4!}}. Then:

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  5. Question 5

    Probability. Asked once: 15 Apr 2023

    77
    A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

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