The integral $\int\limits_1^e {\left\{ {{{\left( {{x \over e}} \right)}^{2x}} - {{\left( {{e \over x}} \right)}^x}} \right\}} \,$ log_e x dx is equal to :

1

$.$ In a game, a man wins Rs. $100$ if he gets $5$ or $6$ on a throw of a fair die and loses Rs. $50$ for getting any o…

Topic: JEE Main 2019 (12 January Evening Shift)

2

If a curve passes through the point $(1, -2)$ and has slope of the tangent at any point $(x, y)$ on it as $\dfrac{x^2 -…

Topic: JEE Main 2019 (12 January Evening Shift)

3

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other …

Topic: JEE Main 2019 (12 January Evening Shift)

4

$\displaystyle \lim_{x\to1^-}\frac{\sqrt{x}-\sqrt{2\sin^{-1}x}}{\sqrt{1-x}}$ is equal to:

Topic: JEE Main 2019 (12 January Evening Shift)

5

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B$, then the loc…

Topic: JEE Main 2019 (12 January Evening Shift)

6

If   nC4, nC5 and nC6 are in A.P., then n can be :

Topic: JEE Main 2019 (12 January Evening Shift)

7

The total number of irrational terms in the binomial expansion of $(7^{1/5}-3^{1/10})^{60}$ is:

Topic: JEE Main 2019 (12 January Evening Shift)

8

The number of integral values of $m$ for which the quadratic expression $(1+2m)x^2-2(1+3m)x+4(1+m)$, $x\in\mathbb{R}$, …

Topic: JEE Main 2019 (12 January Evening Shift)

9

The set of all values of $\lambda$ for which the system of linear equations$x-2y-2z=\lambda x$$x+2y+z=\lambda y$$-x-y=\…

Topic: JEE Main 2019 (12 January Evening Shift)

10

The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of the observations are $3, 4…

Topic: JEE Main 2019 (12 January Evening Shift)