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Day 281: JEE Mains Maths

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

  1. Question 1

    Sequences and Series. Asked once: 2021 Paper 18 (same type asked 3 times) See all 3 of this type

    77
    If the sum of an infinite GP a,ar,ar2,ar3,…a,ar,ar^{2},ar^{3},\ldots is 15 and the sum of the squares of its each term is 150 , then the sum of ar2,ar4,ar6,…ar^{2},ar^{4},ar^{6},\ldots is:

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  2. Question 2

    Straight Lines. Asked once: 31 Jan 2024 (same type asked 3 times) See all 3 of this type

    154
    Let a variable line passing through the centre of the circle x2+y2−16x−4y=0x^{2}+y^{2}- 16x - 4y = 0, meet the positive co-ordinate axes at the point AA and BB. Then the minimum value of OA+OBOA + OB, where OO is the origin, is equal to

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  3. Question 3

    Application of Derivatives. Asked once: 12 Apr 2023 (same type asked 3 times) See all 3 of this type

    67
    If the local maximum value of the function f(x)=(3e2sin⁡x)sin⁡2x, x∈(0,π2)f(x) =\left( \frac{\sqrt{3e}}{2\sin x} \right)^{\sin^{2}x},\ x \in\left( 0,\frac{\pi}{2} \right), is ke\frac{k}{e}, then (ke)8+k8e5+k8\left( \frac{k}{e} \right)^{8}+\frac{k^{8}}{e^{5}}+k^{8} is equal to

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  4. Question 4

    Relations and Functions. Asked once: 2021 Paper 24 (same type asked 3 times) See all 3 of this type

    77
    The range of the function, f(x)=log⁡5(3+cos⁡(3π4+x)+cos⁡(π4+x)+cos⁡(π4−x)−cos⁡(3π4−x))f(x) =\log_{\sqrt{5}}\left( 3 + \cos\left( \frac{3\pi}{4}+x \right)+ \cos\left( \frac{\pi}{4}+x \right)+ \cos\left( \frac{\pi}{4}-x \right)- \cos\left( \frac{3\pi}{4}-x \right) \right) is:

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  5. Question 5

    Differentiation. Asked once: 25 Jun 2022 (same type asked 3 times) See all 3 of this type

    66
    Let f:R→Rf:R \rightarrow R be defined as f(x)=x3+x−5f(x) =x^{3}+ x - 5. If g(x)g(x) is a function such that f(g(x))=xf(g(x)) = x, ∀x∈R\forall x \in R, then gg ' (63) is equal to

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