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Day 536: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 8 Apr 2023

    78
    Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A ×\times B each having at least 3 and at most 6 element is:

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  2. Question 2

    Probability. Asked once: 30 Jan 2023

    172
    A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is qq. If p:q=m:np:q = m:n, where mm and nn are coprime, then m+nm + n is equal to

  3. Question 3

    Quadratic Equations. Asked once: 10 Apr 2023

    90
    The number of elements in the set {n∈Z:∣n2−10n+19∣<6}\left\{ n\in Z:\left| n^{2}- 10n + 19 \right|< 6 \right\} is

  4. Question 4

    Relations and Functions. Asked once: 6 Apr 2023

    155
    Let the sets A and B denote the domain and range respectively of the function f(x)=1⌈x⌉−xf(x) =\frac{1}{\sqrt{\lceil x\rceil - x}}, where ⌈x⌉\lceil x\rceil denotes the smallest integer greater than or equal to xx. Then among the statements (S1) :A∩B=(1,∞)−N:A \cap B = (1,\infty) - N and (S2) :A∪B=(1,∞):A \cup B = (1,\infty)

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  5. Question 5

    Sequences and Series. Asked once: 22 Jan 2025

    60
    If ∑r=1nTr=(2n−1)(2n+1)(2n+3)(2n+5)64\sum_{r = 1}^{n} T_{r}=\frac{(2n - 1)(2n + 1)(2n + 3)(2n + 5)}{64}, then lim⁡n→∞∑r=1n(1 Tr)\lim_{n \rightarrow \infty} \sum_{r = 1}^{n} \left( \frac{1}{{\text{ }T}_{r}} \right) is equal to :

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