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Day 186: JEE Mains Maths

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

  1. Question 1

    Indefinite Integration. Asked once: 8 Apr 2024 (same type asked 3 times) See all 3 of this type

    180
    If ∫1(x−1)4(x+3)65dx=A(αx−1βx+3)B+C\int\frac{1}{\sqrt[5]{(x - 1)^{4}(x + 3)^{6}}}dx = A\left( \frac{\alpha x - 1}{\beta x + 3} \right)^{B}+ C, where CC is the constant of integration, then the value of α+β+20AB\alpha+\beta+ 20AB is

  2. Question 2

    Relations and Functions. Asked once: 27 Jan 2024 (same type asked 3 times) See all 3 of this type

    156
    Let f:R−{−12}→Rf:R -\left\{ \frac{- 1}{2} \right\}\rightarrow R and g:R−{−52}→Rg:R -\left\{ \frac{- 5}{2} \right\}\rightarrow R be defined as f(x)=2x+32x+1f(x) =\frac{2x+ 3}{2x+ 1} and g(x)=∣x∣+12x+5g(x) =\frac{|x| + 1}{2x+ 5}. Then the domain of the function fog is:

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  3. Question 3

    Complex Numbers. Asked once: 5 Apr 2024 (same type asked 3 times) See all 3 of this type

    153
    Let S1={z∈C:∣z∣≤5}S_{1}\mathbf{= \{ z \in C:|z| \leq 5\}}, S2={z∈C:Im(z+1−3i1−3i)≥0}S_{2}=\left\{ z \in C:Im\left( \frac{z + 1 -\sqrt{3}i}{1 -\sqrt{3}i} \right)\geq 0 \right\} and S3={z∈C:Re(z)≥0}S_{3}\mathbf{= \{ z \in C:Re(z) \geq 0\}}. Then the area of the region S1∩S2∩S3S_{1}\cap S_{2}\cap S_{3} is

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  4. Question 4

    Definite Integration. Asked once: 13 Apr 2023 (same type asked 3 times) See all 3 of this type

    170
    The value of e−π4+∫0π4e−xtan⁡50xdx∫0π4e−x(tan⁡49x+tan⁡51x)dx\frac{e^{-\frac{\pi}{4}}+\int_{0}^{\frac{\pi}{4}} e^{- x}\tan^{50}xdx}{\int_{0}^{\frac{\pi}{4}} e^{- x}\left( \tan^{49}x +\tan^{51}x \right)dx} is

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  5. Question 5

    Probability. Asked once: 28 Jul 2022 (same type asked 3 times) See all 3 of this type

    169
    Let AA and BB be two events such that P(B∣A)=25P(B \mid A) =\frac{2}{5}, P(A∣B)=17P(A \mid B) =\frac{1}{7} and P(A∩B)=19P(A \cap B) =\frac{1}{9}. Consider (S1)P(A′∪B)=56(S1)P\left( A^{'}\cup B \right)=\frac{5}{6}, (S2) P(A′∩B′)=118P\left( A^{'}\cap B^{'} \right)=\frac{1}{18}. Then

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