Let A, B and C be three events, which are pair-wise independent and $\overrightarrow E $ denotes the completement of an event E. If $P\left( {A \cap B \cap C} \right) = 0$ and $P\left( C \right) > 0,$ then $P\left[ {\left( {\overline A \cap \overline B } \right)\left| C \right.} \right]$ is equal to :
Previous 10 Questions — JEE Main 2018 (16 April Morning Shift)
Nearest first
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The mean and the standard deviation (s.d.) of five observations are $9$ and $0$, respectively. If one of the observatio…
Topic: JEE Main 2018 (16 April Morning Shift)
If an angle $A$ of $\triangle ABC$ satisfies $5\cos A + 3 = 0$, then the roots of the quadratic equation $9x^{2} + 27x …
Topic: JEE Main 2018 (16 April Morning Shift)
Two different families $A$ and $B$ are blessed with equal number of children. There are $3$ tickets to be distributed a…
Topic: JEE Main 2018 (16 April Morning Shift)
Let $\mathbb{N}$ denote the set of all natural numbers. Define two binary relations on $\mathbb{N}$ as
$R_1 = {(x,y) \i…
Topic: JEE Main 2018 (16 April Morning Shift)
The least positive integer $n$ for which
$\left(\dfrac{1 + i\sqrt{3}}{1 - i\sqrt{3}}\right)^{n} = 1$ is:
Topic: JEE Main 2018 (16 April Morning Shift)
Let $p, q$ and $r$ be real numbers $(p \ne q,, r \ne 0)$, such that the roots of the equation
$\dfrac{1}{x+p} + \dfrac{…
Topic: JEE Main 2018 (16 April Morning Shift)
If the function $f$ defined as $f(x)=\dfrac{1}{x}-\dfrac{kx-1}{e^{2x}-1},\ x\ne0$, is continuous at $x=0$, then the ord…
Topic: JEE Main 2018 (16 April Morning Shift)
Let $M$ and $m$ be respectively the absolute maximum and the absolute minimum values of the function $f(x)=2x^{3}-9x^{2…
Topic: JEE Main 2018 (16 April Morning Shift)
If $\displaystyle \int \frac{\tan x}{1+\tan x+\tan^2 x},dx = x - \frac{K}{\sqrt{A}}\tan^{-1}!\left(\frac{K\tan x + 1}{\…
Topic: JEE Main 2018 (16 April Morning Shift)
The number of numbers between $2000$ and $5000$ that can be formed with the digits $0,1,2,3,4$ (repetition of digits is…
Topic: JEE Main 2018 (16 April Morning Shift)
Next 10 Questions — JEE Main 2018 (16 April Morning Shift)
Ascending by ID
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Let
$\vec{a} = \hat{i} + \hat{j} + \hat{k}$,
$\vec{c} = \hat{j} - \hat{k}$,
and a vector $\vec{b}$ be such that
$\vec{a…
Topic: JEE Main 2018 (16 April Morning Shift)
If the angle between the lines $\dfrac{x}{2}=\dfrac{y}{2}=\dfrac{z}{1}$ and $\dfrac{5-x}{-2}=\dfrac{7y-14}{p}=\dfrac{z-…
Topic: JEE Main 2018 (16 April Morning Shift)
If the length of the latus rectum of an ellipse is $4$ units and the distance between a focus an its nearest vertex on …
Topic: JEE Main 2018 (16 April Morning Shift)
The locus of the point of intersection of the lines $ \sqrt{2}x - y + 4\sqrt{2}k = 0$ and $\sqrt{2}kx + ky - 4\sqrt{2} …
Topic: JEE Main 2018 (16 April Morning Shift)
If a circle $C$, whose radius is $3$, touches externally the circle $x^{2}+y^{2}+2x-4y-4=0$ at the point $(2,2)$, then …
Topic: JEE Main 2018 (16 April Morning Shift)
