If $f(x)$ is a non-zero polynomial of degree $4$, having local extreme points at $x=-1,0,1$, then the set $S={x\in\mathbb{R}: f(x)=f(0)}$ contains exactly:

1

Let $f(x)=15-|x-10|,\ x\in\mathbb{R}$. Then the set of all values of $x$ at which the function $g(x)=f(f(x))$ is not di…

Topic: JEE Main 2019 (9 April Morning Shift)

2

Let $p,q\in\mathbb{R}$. If $2-\sqrt{3}$ is a root of the quadratic equation $x^{2}+px+q=0$, then:

Topic: JEE Main 2019 (9 April Morning Shift)

3

If the standard deviation of the numbers $-1,0,1,k$ is $\sqrt{5}$ where $k>0$, then $k$ is equal to:

Topic: JEE Main 2019 (9 April Morning Shift)

1

The value of $\displaystyle \int_{0}^{\pi/2}\frac{\sin^{3}x}{\sin x+\cos x},dx$ is:

Topic: JEE Main 2019 (9 April Morning Shift)

2

Let $\vec{\alpha}=3\hat{i}+\hat{j}$ and $\vec{\beta}=2\hat{i}-\hat{j}+3\hat{k}$. If $\vec{\beta}=\vec{\beta}{1}-\vec{\b…

Topic: JEE Main 2019 (9 April Morning Shift)

3

All the points in the set $S = \left\{ {{{\alpha + i} \over {\alpha - i}}:\alpha \in R} \right\}(i = \sqrt { - 1} )$…

Topic: JEE Main 2019 (9 April Morning Shift)

4

If $\begin{bmatrix}1 & 1 \\ 0 & 1\end{bmatrix} \begin{bmatrix}1 & 2 \\ 0 & 1\end{bmatrix} \begin{bmatrix}1 & 3 \\ 0 & …

Topic: JEE Main 2019 (9 April Morning Shift)

5

If one end of a focal chord of the parabola $y^{2}=16x$ is at $(1,4)$, then the length of this focal chord is:

Topic: JEE Main 2019 (9 April Morning Shift)

6

The value of $\cos^2 10^\circ - \cos 10^\circ \cos 50^\circ + \cos^2 50^\circ$ is

Topic: JEE Main 2019 (9 April Morning Shift)

7

If the function $f$ defined on $\left(\dfrac{\pi}{6}, \dfrac{\pi}{3}\right)$ by $f(x) = \begin{cases} \dfrac{\sqrt{2}\c…

Topic: JEE Main 2019 (9 April Morning Shift)

8

If the function $f : \mathbb{R} - {1, -1} \to A$ defined by $f(x) = \dfrac{x^2}{1 - x^2}$ is surjective, then $A$ is eq…

Topic: JEE Main 2019 (9 April Morning Shift)

9

Let $\displaystyle \sum_{k=1}^{10} f(a+k) = 16(2^{10} - 1)$ where the function $f$ satisfies $f(x+y) = f(x)f(y)$ for al…

Topic: JEE Main 2019 (9 April Morning Shift)

10

Let $\alpha $ and $\beta $ be the roots of the equation x2 + x + 1 = 0. Then for y $ \ne $ 0 in R, $\left| {\matrix{ …

Topic: JEE Main 2019 (9 April Morning Shift)