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Day 217: JEE Mains Maths

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

  1. Question 1

    Probability. Asked once: 25 Jan 2023 (same type asked 2 times) See all 2 of this type

    162
    Let NN be the sum of the numbers appeared when two fair dice are rolled and let the probability that N−2,3 N, N+2N - 2,\sqrt{3\text{ }N},\text{ }N + 2 are in geometric progression be k48\frac{k}{48}. Then the value of kk is

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  2. Question 2

    Binomial Theorem. Asked once: 6 Apr 2023 (same type asked 2 times) See all 2 of this type

    152
    Among the statements: (S1): 20232022−199920222023^{2022}-1999^{2022} is divisible by 8. (S2): 13(13)n−11n−1313(13)^{n}- 11n - 13 is divisible by 144 for infinitely many n∈Nn \in N.

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  3. Question 3

    Determinants. Asked once: 1 Feb 2023 (same type asked 2 times) See all 2 of this type

    65
    Let SS denote the set of all real values of λ\lambda such that the system of equations
    λx+y+z=1\lambda x + y + z = 1
    x+λy+z=1x + \lambda y + z = 1
    x+y+λz=1x + y + \lambda z = 1
    is inconsistent, then ∑λ∈S(∣λ∣2+∣λ∣)\sum_{\lambda \in S} \left( |\lambda|^{2}+ |\lambda| \right) is equal to

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  4. Question 4

    Differentiation. Asked once: 27 Jun 2022 (same type asked 2 times) See all 2 of this type

    176
    If y(x)=(xx)x, x>0y(x)=\left(x^{x}\right)^{x},\ x>0, then d2xdy2+20\dfrac{d^{2}x}{dy^{2}}+20 at x=1x=1 is equal to:

  5. Question 5

    Inverse Trigonometric Functions. Asked once: 25 Jan 2023 (same type asked 2 times) See all 2 of this type

    85
    If the sum of all the solutions of tan⁡−1(2x1−x2)+cot⁡−1(1−x22x)=π3,−1<x<1,x≠0\tan^{- 1}\left( \frac{2x}{1 -x^{2}} \right)+\cot^{- 1}\left( \frac{1 -x^{2}}{2x} \right)=\frac{\pi}{3}, - 1 < x < 1,x \neq 0, is α−43\alpha -\frac{4}{\sqrt{3}}, then α\alpha is equal to