If the area of an equilateral triangle inscribed in the circle $x^{2}+y^{2}+10x+12y+c=0$ is $27\sqrt{3}$ sq units, then $c$ is equal to :

1

If $\displaystyle \int x^{5}\,e^{-4x^{3}}\,dx=\dfrac{1}{48}\,e^{-4x^{3}}\,f(x)+C$, where $C$ is a constant of integrati…

Topic: JEE Main 2019 (10 January Evening Shift)

2

A helicopter is flying along the curve given by $y - x^{3/2} = 7,\ (x \ge 0)$. A soldier positioned at the point $\left…

Topic: JEE Main 2019 (10 January Evening Shift)

3

Two sides of a parallelogram are along the lines, $x+y=3$ and $x-y+3=0$. If its diagonals intersect at $(2,4)$, then on…

Topic: JEE Main 2019 (10 January Evening Shift)

4

The value of $\cot\!\left(\displaystyle\sum_{n=1}^{19}\cot^{-1}\!\left(1+\sum_{p=1}^{n}2p\right)\right)$ is :

Topic: JEE Main 2019 (10 January Evening Shift)

5

If mean and standard deviation of 5 observations $x_1,x_2,x_3,x_4,x_5$ are $10$ and $3$ respectively, then the variance…

Topic: JEE Main 2019 (10 January Evening Shift)

6

The value of $\cos \dfrac{\pi}{22}\cdot \cos \dfrac{\pi}{23}\cdot \ldots \cdot \cos \dfrac{\pi}{210}\cdot \sin \dfrac{\…

Topic: JEE Main 2019 (10 January Evening Shift)

7

If $\displaystyle \sum_{r=0}^{25} \left\{ {^{50}C_{r}} \cdot {^{\,50-r}C_{\,25-r}} \right\} = K \binom{50}{25}$, then $…

Topic: JEE Main 2019 (10 January Evening Shift)

8

Let $a_1,a_2,\dots,a_{10}$ be in G.P. with $a_i>0$ for $i=1,2,\dots,10$ and $S$ be the set of pairs $(r,k)$, $r,k\in\ma…

Topic: JEE Main 2019 (10 January Evening Shift)

9

Two vertices of a triangle are $(0,2)$ and $(4,3)$. If its orthocenter is at the origin, then its third vertex lies in …

Topic: JEE Main 2019 (10 January Evening Shift)

10

The value of $\displaystyle \int_{-\pi/2}^{\pi/2} \dfrac{dx}{[x] + [\sin x] + 4}$, where $[t]$ denotes the greatest i…

Topic: JEE Main 2019 (10 January Evening Shift)

1

The length of the chord of the parabola $x^2=4y$ having equation $x-\sqrt{2}\,y+4\sqrt{2}=0$ is –

Topic: JEE Main 2019 (10 January Evening Shift)

2

Let $\mathbb{N}$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f,g:\mathbb{N}\to\mathbb{N}…

Topic: JEE Main 2019 (10 January Evening Shift)