41.

$\int \frac{\mathrm{x} + 1}{{\mathrm{x}}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\mathrm{dx} =$

• - x^3/2 + x^1/2 + C

• x^1/2

• x^3/2 + 2x^1/2 + C

• $\frac{2{\mathrm{x}}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}{3} + 2{\mathrm{x}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} + \mathrm{C}$

In a flight 50 people speak Hindi, 20 speak English and 10 speak both English and Hindi. The number of people who speak atleast one of the two languages is

• 40

• 50

• 20

• 60

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

• 3/4

• 1/4

• 1/2

• 2/3

$\int \frac{\mathrm{dx}}{{\mathrm{e}}^{\mathrm{x}} + {\mathrm{e}}^{- \mathrm{x}} + 2}$ is equal to

• $\frac{1}{{\mathrm{e}}^{\mathrm{x}} + 1} + \mathrm{C}$

• $\frac{- 1}{{\mathrm{e}}^{\mathrm{x}} + 1} + \mathrm{C}$

• $\frac{1}{1 + {\mathrm{e}}^{- \mathrm{x}}} + \mathrm{C}$

• $\frac{1}{{\mathrm{e}}^{- \mathrm{x}} - 1} + \mathrm{C}$

${\int }_{- 1}^0\frac{\mathrm{dx}}{{\mathrm{x}}^2 + \mathrm{x} + 2}$ is equal to

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

• $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• $\mathrm{\pi }$

• $\frac{4}{\sqrt{7}}{\tan }^{-1}\left(\frac{1}{\sqrt{7}}\right)$