A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :
Previous 10 Questions — JEE Main 2018 (Offline)
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Let $a_1, a_2, a_3, \ldots, a_{49}$ be in A.P. such that
$\displaystyle \sum_{k=0}^{12} a_{4k+1} = 416$ and $a_9 + a_{4…
Topic: JEE Main 2018 (Offline)
If $\left|\begin{bmatrix}
x-4 & 2x & 2x \\
2x & x-4 & 2x \\
2x & 2x & x-4
\end{bmatrix}\right| = (A+Bx)(x-A)^{2}$ then …
Topic: JEE Main 2018 (Offline)
Two sets $A$ and $B$ are as under :
$A = {(a,b) \in \mathbb{R} \times \mathbb{R} : |a-5| < 1 \text{ and } |b-5| < 1}$
…
Topic: JEE Main 2018 (Offline)
If the system of linear equations$x + ky + 3z = 0$$3x + ky - 2z = 0$$2x + 4y - 3z = 0$has a non-zero solution $(x, y, z…
Topic: JEE Main 2018 (Offline)
If $\alpha, \beta \in \mathbb{C}$ are the distinct roots of the equation $x^{2} - x + 1 = 0$, then $\alpha^{101} + \bet…
Topic: JEE Main 2018 (Offline)
Let $S = {x \in \mathbb{R} : x \ge 0 \text{ and } 2\lvert\sqrt{x}-3\rvert + \sqrt{x}(\sqrt{x}-6)+6=0}$. Then $S$ :
Topic: JEE Main 2018 (Offline)
From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged…
Topic: JEE Main 2018 (Offline)
Next 10 Questions — JEE Main 2018 (Offline)
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If $\displaystyle \sum_{i=1}^{9}(x_i-5)=9$ and $\displaystyle \sum_{i=1}^{9}(x_i-5)^{2}=45$, then the standard deviatio…
Topic: JEE Main 2018 (Offline)
Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a}=2\hat{i}+3\hat{j}-\hat{k}$ and $\vec{b}=\hat{j}+\hat{k}$. …
Topic: JEE Main 2018 (Offline)
A straight line through a fixed point $(2,3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is …
Topic: JEE Main 2018 (Offline)
Let $y = y(x)$ be the solution of the differential equation
$\sin x \dfrac{dy}{dx} + y \cos x = 4x,\ x \in (0,\pi).$
If…
Topic: JEE Main 2018 (Offline)
The integral
$\displaystyle \int \frac{\sin^{2}x \cos^{2}x}{\left(\sin^{5}x + \cos^{3}x \sin^{2}x + \sin^{3}x \cos^{2}x…
Topic: JEE Main 2018 (Offline)
The value of $\displaystyle \int_{-\pi/2}^{\pi/2} \frac{\sin^{2}x}{1+2^{x}},dx$ is :
Topic: JEE Main 2018 (Offline)
Let $g(x)=\cos x^{2}$, $f(x)=\sqrt{x}$ and $\alpha,\beta\ (\alpha
Topic: JEE Main 2018 (Offline)
Let $S={t\in\mathbb{R}: f(x)=|x-\pi|,(e^{|x|}-1)\sin|x|\ \text{is not differentiable at }t}$. Then the set $S$ is equal…
Topic: JEE Main 2018 (Offline)
Let $f(x) = x^{2} + \dfrac{1}{x^{2}}$ and $g(x) = x - \dfrac{1}{x}$, $x \in \mathbb{R} - {-1,0,1}$.
If $h(x) = \dfrac{f…
Topic: JEE Main 2018 (Offline)
For each $t \in \mathbb{R}$, let $[t]$ be the greatest integer less than or equal to $t$.
Then $\displaystyle \lim_{x \…
Topic: JEE Main 2018 (Offline)
