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Day 66: JEE Mains Maths

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

  1. Question 1

    Relations and Functions. This type asked 3 times: 2021 Paper 26, 27 Jan 2024, 23 Jan 2025. This one: 23 Jan 2025 See all 3 of this type

    56
    Let f(x)=log⁡exf(x) =\log_{e}x and g(x)=x4−2x3+3x2−2x+22x2−2x+1g(x) =\frac{x^{4}- 2x^{3}+ 3x^{2}- 2x + 2}{2x^{2}- 2x + 1} Then the domain of fog is

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  2. Question 2

    Complex Numbers. This type asked 3 times: 4 Apr 2024, 5 Apr 2024, 22 Jan 2025. This one: 22 Jan 2025 See all 3 of this type

    144
    Let the curve z(1+i)+zˉ(1−i)=4,z∈Cz(1 + i) +\bar{z}(1 - i) = 4,z \in C, divide the region ∣z−3∣≤1|z - 3| \leq 1 into two parts of areas α\alpha and β\beta. Then ∣α−β∣|\alpha - \beta| equals :

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  3. Question 3

    Definite Integration. This type asked 3 times: 2021 Paper 4, 13 Apr 2023, 22 Jan 2025. This one: 22 Jan 2025 See all 3 of this type

    65
    Let for f(x)=7tan⁡8x+7tan⁡6x−3tan⁡4x−3tan⁡2xf(x) = 7\tan^{8}x + 7\tan^{6}x - 3\tan^{4}x - 3\tan^{2}x, I1=∫0π/4f(x)dxI_{1}=\int_{0}^{\pi/4} f(x)dx and I2=∫0π/4xf(x)dxI_{2}=\int_{0}^{\pi/4} xf(x)dx. Then 7I1+12I27I_{1}+ 12I_{2} is equal to :

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  4. Question 4

    Probability. This type asked 3 times: 25 Jun 2022, 28 Jul 2022, 22 Jan 2025. This one: 22 Jan 2025 See all 3 of this type

    142
    If AA and BB are two events such that P(A∩B)=0.1P(A \cap B) = 0.1, and P(A∣B)P(A \mid B) and P(B∣A)P(B \mid A) are the roots of the equation 12x2−7x+1=012x^{2}- 7x + 1 = 0, then the value of P(A‾∪B‾)P(A‾∩B‾)\frac{P(\overline{A}\cup\overline{B})}{P(\overline{A}\cap\overline{B})} is:

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  5. Question 5

    Limits and Continuity. This type asked 3 times: 2021 Paper 16, 25 Jan 2023, 9 Apr 2024. This one: 9 Apr 2024 See all 3 of this type

    86
    Let f:(0,π)→Rf:(0,\pi) \rightarrow R be a function given by
    f(x)={(87)tan⁡8xtan⁡7x,0<x<π2a−8,x=π2(1+∣cot⁡x∣)ba∣tan⁡x∣,π2<x<πf(x) =\left\{ \begin{matrix} \left( \frac{8}{7} \right)^{\frac{\tan8x}{\tan7x}}, & 0 <x<\frac{\pi}{2} \\ a- 8, & x=\frac{\pi}{2} \\ (1 + |\cot x|)^{\frac{b}{a}|\tan x|}, & \frac{\pi}{2}<x<\pi \end{matrix} \right.
    Where a,b∈Za,b \in Z. If ff is continuous at x=π2x =\frac{\pi}{2}, then a2+b2a^{2}+b^{2} is equal to