Two different families $A$ and $B$ are blessed with equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family $B$ is $\dfrac{1}{12}$, then the number of children in each family is:
Previous 10 Questions — JEE Main 2018 (16 April Morning Shift)
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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)
$\displaystyle\lim_{x\to0} \dfrac{(27+x)^{1/3}-3}{9-(27+x)^{2/3}}$ equals :
Topic: JEE Main 2018 (16 April Morning Shift)
Let $\dfrac{1}{x_1},\dfrac{1}{x_2},\ldots,\dfrac{1}{x_n}$ $(x_i\ne0\text{ for }i=1,2,\ldots,n)$ be in A.P. such that $x…
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} - 9…
Topic: JEE Main 2018 (16 April Morning Shift)
Next 10 Questions — JEE Main 2018 (16 April Morning Shift)
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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)
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)
Let A, B and C be three events, which are pair-wise independent and $\overrightarrow E $ denotes the completement of an…
Topic: JEE Main 2018 (16 April Morning Shift)
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)
