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Day 304: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 8 Apr 2023 (same type asked 6 times) See all 6 of this type

    82
    Let [t] denotes the greatest integer ≤t\leq t. If the constant term in the expansion of (3x2−12x5)7\left( 3x^{2}-\frac{1}{2x^{5}} \right)^{7} is α\alpha, then [α]\lbrack\alpha\rbrack is equal to

  2. Question 2

    Differentiation. Asked once: 29 Jul 2022 (same type asked 6 times) See all 6 of this type

    78
    The number of points, where the function f:R→R,f(x)=∣x−1∣cos⁡∣x−2∣sin⁡∣x−1∣+f:R \rightarrow R,f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x−3)∣x2−5x+4∣(x - 3)\left| x^{2}- 5x + 4 \right|, is NOT differentiable, is :

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  3. Question 3

    Differentiation. Asked once: 15 Apr 2023 (same type asked 6 times) See all 6 of this type

    66
    Let [x]\lbrack x\rbrack denote the greatest integer function and f(x)=max⁡{1+x+[x],2+x,x+2[x]},0≤x≤2f(x) = \max\{ 1 + x + \lbrack x\rbrack,2 + x,x + 2\lbrack x\rbrack\},0 \leq x \leq 2. Let mm be the number of points in [0,2], where ff is not continuous and nn be the number of points in (0,2)(0,2), where ff is not differentiable. Then (m+n)2+2(m + n)^{2}+ 2 is equal to:

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  4. Question 4

    Application of Derivatives. Asked once: 2021 Paper 23 (same type asked 6 times) See all 6 of this type

    90
    Let f(x)f(x) be a cubic polynomial with f(1)=−10f(1) = - 10, f(−1)=6f( - 1) = 6, and has a local minima at x=1x = 1, and f′(x)f^{'}(x) has a local minima at x=−1x = - 1. Then f(3)f(3) is equal to

  5. Question 5

    Statistics. Asked once: 2021 Paper 23 (same type asked 6 times) See all 6 of this type

    80
    The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is:

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