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Day 297: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 4 Apr 2025 (same type asked 8 times) See all 8 of this type

    58
    Let f:[0,∞]→Rf:\left\lbrack 0,\infty \right\rbrack\rightarrow\mathbb{R} be differentiable function such that f(x)=1−2x+f\left( x \right)= 1 - 2x + ∫0xex−tf(t)dt\int_{0}^{x} e^{x-t}f(t)dt for all x∈[0,∞)x \in \lbrack 0,\infty).Then the area of the region bounded by y=f(x)y =f(x) and the coordinate axes is

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  2. Question 2

    Vector Algebra. Asked once: 29 Jul 2022 (same type asked 8 times) See all 8 of this type

    74
    Let aa and bb be two- unit vectors such that the angle between them is π4\frac{\pi}{4}. If θ\theta is the angle between the vectors (a^+b^)(\widehat{a}+\widehat{b}) and (a^+2b^+2(a^×b^))(\widehat{a}+ 2\widehat{b}+ 2(\widehat{a}\times\widehat{b})) then the value of 164cos⁡2θ164\cos^{2}\theta is equal to :

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  3. Question 3

    Statistics. Asked once: 13 Apr 2023 (same type asked 8 times) See all 8 of this type

    90
    Let the mean of the data
    xx13579
    Frequency (f)(f)42428α\alpha8
    be 5. If mm and σ2\sigma^{2} are respectively the mean deviation about the mean and the variance of the data, then 3αm+σ2\frac{3\alpha}{m +\sigma^{2}} is equal to

  4. Question 4

    Three Dimensional Geometry. Asked once: 6 Apr 2023 (same type asked 8 times) See all 8 of this type

    173
    If the lines x−12=2−y−3=z−3α\frac{x - 1}{2}=\frac{2 - y}{- 3}=\frac{z - 3}{\alpha} and x−45=y−12=zβ\frac{x - 4}{5}=\frac{y - 1}{2}=\frac{z}{\beta} intersect, then the magnitude of the minimum value of 8αβ8\alpha\beta is

  5. Question 5

    Permutations and Combinations. Asked once: 11 Apr 2023 (same type asked 8 times) See all 8 of this type

    167
    If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is

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