If $\theta$ denotes the acute angle between the curves $y=10-x^{2}$ and $y=2+x^{2}$ at a point of their intersection, then $|\tan\theta|$ is equal to:

1

The area (in sq. units) bounded by the parabola $y=x^{2}-1$, the tangent at the point $(2,3)$ to it, and the $y$–axis i…

Topic: JEE Main 2019 (9 January Morning Shift)

2

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can…

Topic: JEE Main 2019 (9 January Morning Shift)

3

Let $\alpha$ and $\beta$ be two roots of the equation $x^{2}+2x+2=0$. Then $\alpha^{15}+\beta^{15}$ is equal to:

Topic: JEE Main 2019 (9 January Morning Shift)

4

The value of $\displaystyle\int_{0}^{\pi}\!\lvert\cos x\rvert^{3}\,dx$ is:

Topic: JEE Main 2019 (9 January Morning Shift)

5

For x2 $ \ne $ n$\pi $ + 1, n $ \in $ N (the set of natural numbers), the integral $\int {x\sqrt {{{2\sin ({x^2} - 1) …

Topic: JEE Main 2019 (9 January Morning Shift)

6

Let f : R $ \to $ R be a function defined as $f(x) = \left\{ {\matrix{ 5 & ; & {x \le 1} \cr {a + bx} …

Topic: JEE Main 2019 (9 January Morning Shift)

7

Five students of a class have an average height $150\ \mathrm{cm}$ and variance $18\ \mathrm{cm}^2$. A new student, who…

Topic: JEE Main 2019 (9 January Morning Shift)

8

If the fractional part of the number $\left\{\dfrac{2^{403}}{15}\right\}$ is $\dfrac{k}{15}$, then $k$ is equal to:

Topic: JEE Main 2019 (9 January Morning Shift)

9

If $a,b,c$ be three distinct real numbers in G.P. and $a+b+c=xb$, then $x$ cannot be:

Topic: JEE Main 2019 (9 January Morning Shift)

10

$\displaystyle \lim_{y\to 0}\frac{\sqrt{\,1+\sqrt{1+y^{4}}\,}-\sqrt{2}}{y^{4}}$:

Topic: JEE Main 2019 (9 January Morning Shift)

1

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field.…

Topic: JEE Main 2019 (9 January Morning Shift)