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Day 163: JEE Mains Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 31 Jan 2024 (same type asked 4 times) See all 4 of this type

    82
    Let S=(−1,∞)S = ( - 1,\infty) and f:S→Rf:S \rightarrow R be defined as f(x)=∫−1x(et−1)11(2t−1)5(t−2)7(t−3)12(2t−10)61dtf(x) =\int_{- 1}^{x} \left( e^{t}- 1 \right)^{11}(2t - 1)^{5}(t - 2)^{7}(t - 3)^{12}(2t - 10)^{61}dt. Let p=p = Sum of square of the values of xx, where f(x)f(x) attains local maxima on S. and q=q = Sum of the values of xx, where f(x)f(x) attains local minima on SS. Then, the value of p2+2qp^{2}+ 2q is

  2. Question 2

    Inverse Trigonometric Functions. Asked once: 29 Jan 2025 (same type asked 4 times) See all 4 of this type

    75
    Let S={x:cos⁡−1x=π+sin⁡−1x+sin⁡−1(2x+1)}S=\{x:\cos^{-1}x=\pi+\sin^{-1}x+\sin^{-1}(2x+1)\}. Then ∑x∈S(2x−1)2\sum_{x\in S}(2x-1)^{2} is equal to

  3. Question 3

    Relations and Functions. Asked once: 13 Apr 2023 (same type asked 4 times) See all 4 of this type

    74
    For x∈Rx\in R, two real valued functions f(x)f(x) and g(x)g(x) are such that, g(x)=x+1g(x) =\sqrt{x}+ 1 and f∘g(x)=x+3−xf \circ g(x) = x + 3 -\sqrt{x}. Then f(0)f(0) is equal to

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  4. Question 4

    Permutations and Combinations. Asked once: 21 Jan 2026 S2 (same type asked 4 times) See all 4 of this type

    70
    The largest n∈Nn \in N, for which 7n7^{n} divides 101!, is :

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  5. Question 5

    Relations and Functions. Asked once: 3 Apr 2025 (same type asked 4 times) See all 4 of this type

    135
    Let ff be a function such that f(x)+3f(24x)f(x) + 3f\left( \frac{24}{x} \right) =4x,x≠0= 4x,x\neq 0. Then f(3)+f(8)f(3) +f(8) is equal to.

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