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Day 240: JEE Mains Maths

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

  1. Question 1

    Binomial Theorem. Asked once: 5 Apr 2024 (same type asked 6 times) See all 6 of this type

    160
    If the constant term in the expansion of (35x+2x53)12,x≠0\left( \frac{\sqrt[5]{3}}{x}+\frac{2x}{\sqrt[3]{5}} \right)^{12},x \neq 0, is α×28×35\alpha \times2^{8}\times\sqrt[5]{3}, then 25α25\alpha is equal to :

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  2. Question 2

    Differentiation. Asked once: 31 Jan 2024 (same type asked 6 times) See all 6 of this type

    164
    Consider the function f:(0,∞)→Rf:(0,\infty) \rightarrow R defined by f(x)=e−∣log⁡ex∣f(x) =e^{-\left| \log_{e}x \right|}. If mm and nn be respectively the number of points at which ff is not continuous and ff is not differentiable, then m+nm + n is

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  3. Question 3

    Differentiation. Asked once: 28 Jan 2025 (same type asked 6 times) See all 6 of this type

    74
    Let
    f(x)={3x,x<0min⁡{1+x+[x],x+2[x]},0≤x≤25,x>2f(x) =\left\{ \begin{matrix} 3x, & x < 0 \\ \min\{ 1 + x + \lbrack x\rbrack,x + 2\lbrack x\rbrack\}, & 0 \leq x \leq 2 \\ 5, & x > 2 \end{matrix} \right.
    where [.] denotes greatest integer function. If α\alpha and β\beta are the number of points, where f is not continuous and is not differentiable, respectively, then α+β\alpha+\beta equals. ………\ldots\ldots\ldots

  4. Question 4

    Application of Derivatives. Asked once: 25 Jul 2022 (same type asked 6 times) See all 6 of this type

    67
    The curve y(x)=ax3+bx2+cx+5y(x) = ax^{3}+ bx^{2}+ cx + 5 touches the xx-axis at the point P(−2,0)P( - 2,0) and cuts the yy-axis at the point QQ, where y′y^{'} is equal to 3 . Then the local maximum value of y(x)y(x) is:

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  5. Question 5

    Statistics. Asked once: 26 Jul 2022 (same type asked 6 times) See all 6 of this type

    176
    The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ\sigma is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ238\sigma^{2} is equal to