Let the sum of the first $n$ terms of a non-constant A.P., $a_1, a_2, a_3, \dots$ be $50n + \dfrac{n(n - 7)}{2}A$, where $A$ is a constant. If $d$ is the common difference of this A.P., then the ordered pair $(d, a_{50})$ is equal to

1

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)

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

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)

4

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)

5

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)

6

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)

7

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)

8

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)

9

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)

10

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)

1

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)

2

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)

3

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)

4

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)