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Day 567: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 14 Jun 2022

    82
    In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is

  2. Question 2

    Probability. Asked once: 27 Jun 2022

    180
    Let S={E1,E2…E8}S =\left\{ E_{1},E_{2}\ldots E_{8} \right\} be a sample space of random experiment such that P(En)=n36P\left( E_{n} \right)=\frac{n}{36} for every n=1,2…8n = 1,2\ldots 8. Then the number of elements in the set {A⊂S:P(A)≥45}\left\{ A \subset S:P(A) \geq\frac{4}{5} \right\} is

  3. Question 3

    Quadratic Equations. Asked once: 28 Jul 2022

    90
    The sum of all real values of xx for which 3x2−9x+17x2+3x+10=5x2−7x+193x2+5x+12\frac{3x^{2}- 9x + 17}{x^{2}+ 3x + 10}=\frac{5x^{2}- 7x + 19}{3x^{2}+ 5x + 12} is equal to

  4. Question 4

    Relations and Functions. Asked once: 28 Jul 2022

    78
    Let α,β\alpha,\beta and γ\gamma be three positive real numbers. Let f(x)=αx5+βx3+γx,x∈Rf(x) = \alpha x^{5}+ \beta x^{3}+ \gamma x,x \in R and g:R→Rg:R \rightarrow R be such that g(f(x))=xg(f(x)) = x for all x∈Rx \in R. If a1,a2,a3,…,ana_{1},a_{2},a_{3},\ldots,a_{n} be in arithmetic progression with mean zero, then the value of f(g(1n∑i=1nf(ai)))f\left( g\left( \frac{1}{n}\sum_{i = 1}^{n} f\left( a_{i} \right) \right) \right) is equal to:

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  5. Question 5

    Sequences and Series. Asked once: 4 Apr 2024

    157
    The value of 1×22+2×32+…+100×(101)212×2+22×3+…+1002×101\frac{1 \times2^{2}+ 2 \times3^{2}+ \ldots + 100 \times (101)^{2}}{1^{2}\times 2 +2^{2}\times 3 + \ldots +100^{2}\times 101} is

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