PYQ Vault
EbooksTutor

Day 95: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked 2 times: 2021 Paper 16*, 14 Jun 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    156
    The value of the integral ∫−π/2π/2dx(1+ex)(sin⁡6x+cos⁡6x)\int_{-\pi/2}^{\pi/2} \frac{dx}{\left( 1 +e^{x} \right)\left( \sin^{6}x+\cos^{6}x \right)} is equal to

    Tap an option to check your answer.

  2. Question 2

    Probability. Asked 2 times: 2021 Paper 21*, 14 Jun 2022 (* = numbers or wording changed that year) See all 2 times it was asked

    162
    A random variable XX has the following probability distribution:
    XX01234
    P(X)P(X)kk2k2k4k4k6k6k8k8k
    The value of P(1<X<4∣X≤2)P(1 < X < 4 \mid X \leq 2) is equal to:

    Tap an option to check your answer.

  3. Question 3

    Complex Numbers. Asked 2 times: 2021 Paper 17*, 2021 Paper 26 (* = numbers or wording changed that year) See all 2 times it was asked

    89
    Let zz be those complex number which satisfy ∣z+5∣≤4|z + 5| \leq 4 and z(1+i)+zˉ(1−i)≥−10,i=−1z(1 + i) +\bar{z}(1 - i) \geq - 10,i =\sqrt{- 1}. If the maximum value of ∣z+1∣2|z + 1|^{2} is α+β2\alpha + \beta\sqrt{2}, then the value of (α+β)(\alpha + \beta) is

  4. Question 4

    Three Dimensional Geometry. Asked 2 times: 2021 Paper 23*, 2021 Paper 24 (* = numbers or wording changed that year) See all 2 times it was asked

    72
    The distance of line 3y−2z−1=0=3x−z+43y- 2z- 1 = 0 = 3x-z+ 4 from the point (2,−1,6)(2, - 1,6) is:

    Tap an option to check your answer.

  5. Question 5

    Vector Algebra. Asked 2 times: 2021 Paper 8*, 2021 Paper 24 (* = numbers or wording changed that year) See all 2 times it was asked

    88
    Let a→=2i^−j^+2k^\overrightarrow{a}= 2\widehat{i}-\widehat{j}+ 2\widehat{k} and b→=i^+2j^−k^\overrightarrow{b}=\widehat{i}+ 2\widehat{j}-\widehat{k}. Let a vector v→\overrightarrow{v} be in the plane containing a→\overrightarrow{a} and b→\overrightarrow{b}. If v→\overrightarrow{v} is perpendicular to the vector 3i^+2j^−k^3\widehat{i}+ 2\widehat{j}-\widehat{k} and its projection on a→\overrightarrow{a} is 19 units, then ∣2v→∣2|2\overrightarrow{v}|^{2} is equal to