JEE MAIN 2018 Previous Year Questions (PYQs) – Page 2 of 9

A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $B$ is :

The mean of set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$, their mean remains the same. Then $\lambda$ is equal to :

If $\overrightarrow a ,\,\,\overrightarrow b ,$ and $\overrightarrow C $ are unit vectors such that $\overrightarrow a + 2\overrightarrow b + 2\overrightarrow c = \overrightarrow 0 ,$ then $\left| {\overrightarrow a \times \overrightarrow c } \right|$ is equal to :

Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} + 2y = f\left( x \right),$

where $f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right.$

If y(0) = 0, then $y\left( {{3 \over 2}} \right)$ is :

The value of the integral $\displaystyle \int_{-\pi/4}^{\pi/4} \sin^{4}x \left(1 + \log\left(\dfrac{2 + \sin 2x}{2 - \sin 2x}\right)\right),dx$ is :

The area (in sq. units) of the region ${(x,y)\in \mathbb{R}^{2} : x \ge 0,\ y \ge 0,\ y \ge x-2 \text{ and } y \le \sqrt{x}}$ is :

If a right circular cone, having maximum volume, is inscribed in a sphere of radius $3\ \text{cm}$, then the curved surface area (in $\text{cm}^{2}$) of this cone is :

If $f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,$ (x $ \in $ R $-${1, $-$ 2}), then $\int f \left( x \right)dx$ is equal to :
(where C is a constant of integration)

Let $S={(\lambda,\mu)\in\mathbb{R}\times\mathbb{R}: f(t)=(\lvert\lambda\rvert e^{\lvert t\rvert}-\mu)\cdot\sin(2\lvert t\rvert),\ t\in\mathbb{R},\text{ is a differentiable function}}$. Then $S$ is a subset of :

If $x^{2} + y^{2} + \sin y = 4$, then the value of $\dfrac{d^{2}y}{dx^{2}}$ at the point $(-2,0)$ is :