Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P(E_1)=\dfrac{2+3p}{6}$, $P(E_2)=\dfrac{2-p}{8}$ and $P(E_3)=\dfrac{1-p}{2}$. If the maximum and minimum values of $p$ are $p_1$ and $p_2$, then $(p_1+p_2)$ is equal to:

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Let $\vec{a} = \alpha \hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \alpha \hat{k}$, $\alpha > 0$. …

Topic: JEE Main 2022 (26 July Morning Shift)

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The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the lin…

Topic: JEE Main 2022 (26 July Morning Shift)

3

A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$. Let $f(x,…

Topic: JEE Main 2022 (26 July Morning Shift)

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If $\dfrac{dy}{dx} + 2y\tan x = \sin x,\ 0 < x < \tfrac{\pi}{2}$ and $y\!\left(\tfrac{\pi}{3}\right)=0$, then the maxim…

Topic: JEE Main 2022 (26 July Morning Shift)

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Let $f(x)= \begin{cases} x^{3}-x^{2}+10x-7, & x\le 1,\\ -2x+\log_{2}(b^{2}-4), & x>1. \end{cases}$ Then the set of all…

Topic: JEE Main 2022 (26 July Morning Shift)

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If $f(x)= \begin{cases} x+a, & x\le 0\\ |x-4|, & x>0 \end{cases} \quad\text{and}\quad g(x)= \begin{cases} x+1, & x

Topic: JEE Main 2022 (26 July Morning Shift)

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If the function $f(x) = \begin{cases} \dfrac{\log_e(1 - x + x^{2}) + \log_e(1 + x + x^{2})}{\sec x - \cos x}, & x \in …

Topic: JEE Main 2022 (26 July Morning Shift)

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Consider two G.P.s: $2, 2^{2}, 2^{3}, \ldots$ (of $60$ terms) and $4, 4^{2}, 4^{3}, \ldots$ (of $n$ terms). If the ge…

Topic: JEE Main 2022 (26 July Morning Shift)

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The odd natural number $a$, such that the area of the region bounded by $y=1$, $y=3$, $x=0$, $x=y^{a}$ is $\dfrac{364}{…

Topic: JEE Main 2022 (26 July Morning Shift)

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If the system of linear equations $8x + y + 4z = -2$ $x + y + z = 0$ $\lambda x - 3y = \mu$ has infinitely many sol…

Topic: JEE Main 2022 (26 July Morning Shift)

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$\tan\!\left(2\tan^{-1}\!\tfrac{1}{5}+\sec^{-1}\!\tfrac{\sqrt{5}}{2}+2\tan^{-1}\!\tfrac{1}{8}\right)$ is equal to:

Topic: JEE Main 2022 (26 July Morning Shift)