31.

Probability that a person will develop immunity after vaccinations is 0.8. If 8 people are given the vaccine, then probability that all develop immunity is =

• (0.2)⁸

• (0.8)⁸

• 1

• ${}^8\mathrm{C}_6{\left(0.2\right)}^6{\left(0.8\right)}^2$

If distance of points $2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + \mathrm{\lambda }\hat{\mathrm{k}}$ from the plane $\mathrm{r} . \left(3\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 6\hat{\mathrm{k}}\right)$= 13 is 5 units, then $\mathrm{\lambda }$ = n

• $6, - \frac{17}{3}$

• $6, \frac{17}{3}$

• $- 6, - \frac{17}{3}$

• $- 6, \frac{17}{3}$

The particular solution of the differential equation xdy + 2ydx = 0, when x = 2, y = 1 is

• xy = 4

• x²y = 4

• xy² = 4

• x²y² = 4

$∆$ABC has vertices at A = (2, 3, 5), B = (-1, 3, 2) and C = $\left(\mathrm{\lambda }, 5, \mathrm{\mu }\right)$. If the median through A is equally inclined to the axes, then the values of $\mathrm{\lambda } \mathrm{and} \mathrm{\mu }$ respectively are

• 10, 7

• 9, 10

• 7, 9

• 7, 10

For the following distribution function F(x) of a rv.X.

$\mathrm{P}\left(3 < \mathrm{x} \le 5\right)$ =

• 0.48

• 0.37

• 0.27

• 1.47

$\int \frac{{\sec }^8\left(\mathrm{x}\right)}{\csc \left(\mathrm{x}\right)}\mathrm{dx}$ =

• $\frac{{\sec }^8\left(\mathrm{x}\right)}{8} + \mathrm{c}$

• $\frac{{\sec }^7\left(\mathrm{x}\right)}{7} + \mathrm{c}$

• $\frac{{\sec }^6\left(\mathrm{x}\right)}{6} + \mathrm{c}$

• $\frac{{\sec }^9\left(\mathrm{x}\right)}{9} + \mathrm{c}$