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Day 510: JEE Mains Maths

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

  1. Question 1

    Differential Equations. Asked once: 2021 Paper 20

    72
    Let us consider a curve, y=f(x)y = f(x) passing through the point (−2,2)(-2,2) and the slope of the tangent to the curve at any point (x,f(x))(x,f(x)) is given by f(x)+x f′(x)=x2f(x) + x\,f'(x) = x^{2}. Then:

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  2. Question 2

    Differentiation. Asked once: 27 Jul 2022

    156
    Let f(x)=2+∣x∣−∣x−1∣+∣x+1∣,x∈Rf(x) = 2 + |x| - |x - 1| + |x + 1|,x \in R. Consider (S1): f′(−32)+f′(−12)+f′(12)+f′(32)=2f^{'}\left( -\frac{3}{2} \right)+f^{'}\left( -\frac{1}{2} \right)+f^{'}\left( \frac{1}{2} \right)+f^{'}\left( \frac{3}{2} \right)= 2 (S2): ∫−22f(x)dx=12\int_{- 2}^{2} f(x)dx = 12 Then,

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  3. Question 3

    Indefinite Integration. Asked once: 12 Apr 2023

    85
    Let I(x)=∫x+7xdxI(x) = \int\sqrt{\frac{x + 7}{x}}dx and I(9)=12+7log⁡e7I(9) = 12 + 7\log_{e}7. If I(1)=α+7log⁡e(1+22)I(1) = \alpha + 7\log_{e}(1 + 2\sqrt{2}), then α4\alpha^{4} is equal to

  4. Question 4

    Inverse Trigonometric Functions. Asked once: 14 Jun 2022

    151
    Let x∗y=x2+y3x*y =x^{2}+y^{3} and (x∗1)∗1=x∗(1∗1)(x*1)*1 = x*(1*1). Then a value of 2sin⁡−1(x4+x2−2x4+x2+2)2\sin^{- 1}\left( \frac{x^{4}+x^{2}- 2}{x^{4}+x^{2}+ 2} \right) is

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  5. Question 5

    Limits and Continuity. Asked once: 8 Apr 2023

    79
    lim⁡x→0((1−cos⁡2(3x)cos⁡3(4x))(sin⁡3(4x)(log⁡e(2x+1))5))\lim_{x \rightarrow 0} \left( \left( \frac{1 -\cos^{2}(3x)}{\cos^{3}(4x)} \right)\left( \frac{\sin^{3}(4x)}{\left( \log_{e}(2x + 1) \right)^{5}} \right) \right) is equal to

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