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Day 543: JEE Mains Maths

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

  1. Question 1

    Limits and Continuity. Asked once: 25 Jul 2022

    87
    If lim⁡n→∞(n+1)k−1nk+1[(nk+1)+(nk+2)+…+\lim_{n \rightarrow \infty} \frac{(n + 1)^{k - 1}}{n^{k + 1}}\lbrack(nk + 1) + (nk + 2) + \ldots + (nk+n)]=33.lim⁡n→∞1nk+1⋅[1k+2k+3k+…+nk](nk + n)\rbrack = 33.\lim_{n \rightarrow \infty} \frac{1}{n^{k + 1}}\cdot\left\lbrack 1^{k}+2^{k}+3^{k}+ \ldots +n^{k} \right\rbrack, then the integral value of kk is equal to

  2. Question 2

    Matrices. Asked once: 6 Apr 2023

    70
    Let A=[aij]2×2A =\left\lbrack a_{ij} \right\rbrack_{2 \times 2} where aij≠0a_{ij}\neq 0 for all i,ji,j and A2=IA^{2}= I. Let aa be the sum of all diagonal elements of AA and b=∣A∣b = |A|, then 3a2+4 b23a^{2}+ 4{\text{ }b}^{2} is equal to

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  3. Question 3

    Permutations and Combinations. Asked once: 29 Jul 2022

    89
    Let S={4,6,9}\mathbf{S = \{ 4,6,9\}} and T={9,10,11,…,1000}\mathbf{T = \{ 9,10,11,\ldots,1000\}}. If A={a1+a2+…+ak:k∈N,a1,a2,a3,…,ak∈S}A =\left\{ a_{1}+a_{2}+ \ldots +a_{k}:k \in N,a_{1},a_{2},a_{3},\ldots,a_{k}\in S \right\}, then the sum of all the elements in the set T - A is equal to

  4. Question 4

    Probability. Asked once: 27 Jul 2022

    167
    A six faced die is biased such that 3×P(a3 \times P(a prime number )=6×P() = 6 \times P( a composite number )=2×P(1)) = 2 \times P(1). Let XX be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of XX is:

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  5. Question 5

    Quadratic Equations. Asked once: 8 Apr 2023

    66
    Let α,β,γ\alpha,\beta,\gamma be the three roots of the equation x3+bx+c=0x^{3}+ bx + c = 0. If βγ=1=−α\beta\gamma = 1 = - \alpha, then b3+2c3−3α3−6β3−8γ3b^{3}+ 2c^{3}- 3\alpha^{3}- 6\beta^{3}- 8\gamma^{3} is equal to

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