$\displaystyle \int_{\pi/6}^{\pi/3}\sec^{\tfrac{2}{3}}x;\csc^{\tfrac{4}{3}}x,dx$ is equal to:

1

Suppose that $20$ pillars of the same height are erected along the boundary of a circular stadium. If the top of each p…

Topic: JEE Main 2019 (10 April Evening Shift)

2

Let $y=y(x)$ be the solution of the differential equation $\dfrac{dy}{dx}+y\tan x=2x+x^{2}\tan x,\ x\in\left(-\dfrac{\p…

Topic: JEE Main 2019 (10 April Evening Shift)

3

Lines are drawn parallel to the line $4x-3y+2=0$, at a distance $\dfrac{3}{5}$ from the origin. Then which one of the f…

Topic: JEE Main 2019 (10 April Evening Shift)

4

If both the mean and the standard deviation of $50$ observations $x_{1},x_{2},\ldots,x_{50}$ are equal to $16$, then th…

Topic: JEE Main 2019 (10 April Evening Shift)

5

If $\cos^{-1}x-\cos^{-1}\left(\dfrac{y}{2}\right)=\alpha$, where $-1\le x\le1,\ -2\le y\le2,\ x\le\dfrac{y}{2}$, then f…

Topic: JEE Main 2019 (10 April Evening Shift)

6

The distance of the point having position vector $-\hat{i}+2\hat{j}+6\hat{k}$ from the straight line passing through th…

Topic: JEE Main 2019 (10 April Evening Shift)

7

Let $a_1,a_2,a_3,\ldots$ be an A.P. with $a_6=2$. Then the common difference of this A.P., which maximises the product …

Topic: JEE Main 2019 (10 April Evening Shift)

8

If $\displaystyle \int x^{5}e^{-x^{2}},dx=g(x)e^{-x^{2}}+c$, where $c$ is a constant of integration, then $g(-1)$ is eq…

Topic: JEE Main 2019 (10 April Evening Shift)

9

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than $9…

Topic: JEE Main 2019 (10 April Evening Shift)

10

If $\displaystyle \lim_{x\to1}\frac{x^{2}-ax+b}{x-1}=5$, then $a+b$ is equal to:

Topic: JEE Main 2019 (10 April Evening Shift)

1

The area (in sq. units) of the region bounded by the curves $y=2^{x}$ and $y=|x+1|$, in the first quadrant, is:

Topic: JEE Main 2019 (10 April Evening Shift)

2

If $z$ and $w$ are two complex numbers such that $|zw|=1$ and $\arg(z)-\arg(w)=\dfrac{\pi}{2}$, then:

Topic: JEE Main 2019 (10 April Evening Shift)

3

If $5x+9=0$ is the directrix of the hyperbola $16x^{2}-9y^{2}=144$, then its corresponding focus is:

Topic: JEE Main 2019 (10 April Evening Shift)

4

The smallest natural number $n$ such that the coefficient of $x$ in the expansion of $\left(x^{2}+\dfrac{1}{x^{3}}\righ…

Topic: JEE Main 2019 (10 April Evening Shift)

5

The sum of the real roots of the equation $\left| {\matrix{ x & { - 6} & { - 1} \cr 2 & { - 3x} &am…

Topic: JEE Main 2019 (10 April Evening Shift)

6

Let $\lambda $ be a real number for which the system of linear equations x + y + z = 6, 4x + $\lambda $y – $\lambda $z …

Topic: JEE Main 2019 (10 April Evening Shift)