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 all natural numbers $x, y$ and $f(1) = 2$. Then the natural number $a$ is

1

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)

2

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)

3

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)

4

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)

5

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)

6

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)

7

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)

8

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)

9

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\math…

Topic: JEE Main 2019 (9 April Morning Shift)

10

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)

1

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)

2

The area (in sq. units) of the region $A = {(x, y) : x^2 \le y \le x + 2}$ is

Topic: JEE Main 2019 (9 April Morning Shift)

3

The integral $\displaystyle \int \sec^{2/3}x , \csc^{4/3}x , dx$ is equal to (Hence $C$ is a constant of integration)

Topic: JEE Main 2019 (9 April Morning Shift)

4

Let the sum of the first $n$ terms of a non-constant A.P., $a_1, a_2, a_3, \dots$ be $50n + \dfrac{n(n - 7)}{2}A$, wher…

Topic: JEE Main 2019 (9 April Morning Shift)

5

The solution of the differential equation $x\dfrac{dy}{dx} + 2y = x^2 \ (x \ne 0)$ with $y(1) = 1$, is:

Topic: JEE Main 2019 (9 April Morning Shift)

6

A committee of $11$ members is to be formed from $8$ males and $5$ females. If $m$ is the number of ways the committee …

Topic: JEE Main 2019 (9 April Morning Shift)

7

If the fourth term in the binomial expansion of $\left(\dfrac{2}{x}+x^{\log_8 x}\right)^6$ $(x>0)$ is $20\times 8^7$, t…

Topic: JEE Main 2019 (9 April Morning Shift)

8

Slope of a line passing through $P(2, 3)$ and intersecting the line $x + y = 7$ at a distance of $4$ units from $P$, is:

Topic: JEE Main 2019 (9 April Morning Shift)