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Day 576: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 30 Jan 2024

    169
    Let f:R→Rf:R \rightarrow R be a function defined f(x)=x(1+x4)1/4f(x) =\frac{x}{\left( 1 +x^{4} \right)^{1/4}} and g(x)=f(f(f(f(x))))g(x) = f(f(f(f(x)))) then 18∫025x2g(x)dx18\int_{0}^{\sqrt{2\sqrt{5}}} x^{2}g(x)dx

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  2. Question 2

    Limits and Continuity. Asked once: 2021 Paper 15

    53
    Let P(x)P(x) be a polynomial with P′′(x)P^{''}(x) constant, and let f(x)=P(x)sin⁡(x−2)f(x) =\frac{P(x)}{\sin(x- 2)}, x≠2x\neq 2, be continuous at x=2x = 2 with f(2)=7f(2) = 7. If P(3)=9P(3) = 9, then P(5)P(5) is equal to

  3. Question 3

    Matrices. Asked once: 28 Jul 2022

    74
    Let the matrix A=[010001100]A =\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix} and the matrix B0=A49+2A98B_{0}=A^{49}+ 2A^{98}. If Bn=Adj(Bn−1)B_{n}= Adj\left( B_{n - 1} \right) for all n≥1n \geq 1, then det(B4)det\left( B_{4} \right) is equal to:

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  4. Question 4

    Permutations and Combinations. Asked once: 2021 Paper 19

    81
    The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit "1" and they all are multiple of 11, is

  5. Question 5

    Probability. Asked once: 2021 Paper 21

    64
    Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is:

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