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Day 145: JEE Mains Maths

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

  1. Question 1

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

    65
    Let x=x(y)x = x(y) be the solution of the differential equation 2(y+2)log⁡e(y+2)dx+(x+4−2log⁡e(y+2))dy=02(y + 2)\log_{e}(y + 2)dx +\left( x + 4 - 2\log_{e}(y + 2) \right)dy = 0, y>−1y > - 1 with x(e4−2)=1x\left( e^{4}- 2 \right)= 1. Then x(e9−2)x\left( e^{9}- 2 \right) is equal to

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  2. Question 2

    Definite Integration. Asked once: 30 Jan 2024 (same type asked 6 times) See all 6 of this type

    66
    The value of lim⁡n→∞∑k=1nn3(n2+k2)(n2+3k2)\lim_{n \rightarrow \infty} \sum_{k = 1}^{n} \frac{n^{3}}{\left( n^{2}+k^{2} \right)\left( n^{2}+ 3k^{2} \right)} is:

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  3. Question 3

    Differential Equations. Asked once: 25 Jan 2023 (same type asked 6 times) See all 6 of this type

    165
    Let y=y(t)y = y(t) be a solution of the differential equation dydt+αy=γe−βt\frac{dy}{dt}+ \alpha y = \gamma e^{- \beta t} where, α>0,β>0\alpha > 0,\beta > 0 and γ>0\gamma > 0. Then lim⁡t→∞y(t)\lim_{t \rightarrow \infty} y(t)

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  4. Question 4

    Vector Algebra. Asked once: 6 Apr 2024 (same type asked 6 times) See all 6 of this type

    62
    If A(3,1,−1),B(53,73,13),C(2,2,1)A(3,1, - 1),B\left( \frac{5}{3},\frac{7}{3},\frac{1}{3} \right),C(2,2,1) and D(103,23,−13)D\left( \frac{10}{3},\frac{2}{3},\frac{- 1}{3} \right) are the vertices of a quadrilateral ABCDABCD, then its area is

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  5. Question 5

    Limits and Continuity. Asked once: 30 Jan 2024 (same type asked 6 times) See all 6 of this type

    80
    Let f:[−π2,π2]→Rf:\left\lbrack -\frac{\pi}{2},\frac{\pi}{2} \right\rbrack\rightarrow R be a differentiable function such that f(0)=12f(0) =\frac{1}{2}, If the lim⁡x→0x∫0xf(t)dtex2−1=α\lim_{x \rightarrow 0} \frac{x\int_{0}^{x} f(t)dt}{e^{x^{2}}- 1}= \alpha, then 8α28\alpha^{2} is equal to :

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