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Day 87: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked 2 times: 2021 Paper 9*, 30 Jan 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    89
    If the function f(x)={1∣x∣,∣x∣≥2ax2+2b,∣x∣<2f(x) =\left\{ \begin{matrix} \frac{1}{|x|} & ,|x| \geq 2 \\ ax^{2}+ 2b, & |x| < 2 \end{matrix} \right. is differentiable on RR, then 48(a+b)48(a + b) is equal to

  2. Question 2

    Statistics. Asked 2 times: 29 Jun 2022*, 29 Jan 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    154
    If the mean and variance of five observations are 245\frac{24}{5} and 19425\frac{194}{25} respectively and the mean of first four observations is 72\frac{7}{2}, then the variance of the first four observations is equal to

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  3. Question 3

    Vector Algebra. Asked 2 times: 27 Jan 2024*, 29 Jan 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    73
    Let OO be the origin and the position vector of AA and BB be 2i^+2j^+k^2\widehat{i}+ 2\widehat{j}+\widehat{k} and 2i^+4j^+4k^2\widehat{i}+ 4\widehat{j}+ 4\widehat{k} respectively. If the internal bisector of ∠AOB\angle AOB meets the line ABAB at CC, then the length of OCOC is

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  4. Question 4

    Application of Derivatives. Asked 2 times: 10 Apr 2023*, 27 Jan 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    158
    Let g(x)=3f(x3)+f(3−x)g(x) = 3f\left( \frac{x}{3} \right)+f(3 -x) and f′′(x)>0f^{''}(x) > 0 for all x∈(0,3)x\in (0,3). If gg is decreasing in (0,α)(0,\alpha) and increasing in (α,3)(\alpha,3), then 8α8\alpha is

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  5. Question 5

    Binomial Theorem. Asked 2 times: 2021 Paper 11*, 27 Jan 2024 (* = numbers or wording changed that year) See all 2 times it was asked

    175
    The coefficient of x2012x^{2012} in the expansion of (1−x)2008(1+x+x2)2007(1 - x)^{2008}\left( 1 + x +x^{2} \right)^{2007} is equal to