Let f : R $ \to $ R be a function defined as
$f(x) = \left\{ {\matrix{ 5 & ; & {x \le 1} \cr {a + bx} & ; & {1 < x < 3} \cr {b + 5x} & ; & {3 \le x < 5} \cr {30} & ; & {x \ge 5} \cr } } \right.$ Then, f is

1

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)

2

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)

3

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)

4

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

Topic: JEE Main 2019 (9 January Morning Shift)

5

Axis of a parabola lies along the x–axis. If its vertex and focus are at distances $2$ and $4$ respectively from the or…

Topic: JEE Main 2019 (9 January Morning Shift)

6

For $x \in \mathbb{R} - \{0,1\}$, let $f_1(x)=\dfrac{1}{x}$, $f_2(x)=1-x$, and $f_3(x)=\dfrac{1}{1-x}$ be three given f…

Topic: JEE Main 2019 (9 January Morning Shift)

7

If $A=\begin{bmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{bmatrix}$, then the matrix $A^{-50}$ when …

Topic: JEE Main 2019 (9 January Morning Shift)

8

If $y=y(x)$ is the solution of the differential equation $x\dfrac{dy}{dx}+2y=x^{2}$, satisfying $y(1)=1$, then $y\!\lef…

Topic: JEE Main 2019 (9 January Morning Shift)

9

Let $0

Topic: JEE Main 2019 (9 January Morning Shift)

10

If $\cos^{-1}\!\left(\dfrac{2}{3x}\right)+\cos^{-1}\!\left(\dfrac{3}{4x}\right)=\dfrac{\pi}{2}\ \ (x>\dfrac{3}{4})$, th…

Topic: JEE Main 2019 (9 January Morning Shift)

1

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)

2

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

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

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)

5

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)

6

If $\theta$ denotes the acute angle between the curves $y=10-x^{2}$ and $y=2+x^{2}$ at a point of their intersection, t…

Topic: JEE Main 2019 (9 January Morning Shift)

7

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)