31.

The equation to the plane through the points (2, 3, 1) and ( 4, - 5 3) paralled to x - axis is

• x + y + 4z = 7

• x + 4z = 7

• y - 4z = 7

• y + 4z = 7

The angle between r = (1 + 2µ)i +(2 + µ)j + (2µ - 1)k and the plane 3x - 2y + 6z = 0 (whereµ is a scalar) is

• ${\sin }^{-1}\left(\frac{15}{21}\right)$

• ${\cos }^{-1}\left(\frac{16}{21}\right)$

• ${\sin }^{-1}\left(\frac{16}{21}\right)$

• $\frac{\mathrm{\pi }}{2}$

The length of the shortest distance between the two lines r = (- 3i + 6j) + s (- 4i + 3j + 2k) and r = (- 2i + 7k) + t(- 4i + j + k) is

• 7 unit

• 13 unit

• 8 unit

• 9 unit

The perpendicular distance of the point (6, 5, 8) from y-axis is

• 5 unit

• 6 unit

• 8 unit

• 10 unit

The equation of the plane passing through the origin and containing the line

$\frac{\mathrm{x} - 1}{5} = \frac{\mathrm{y} - 2}{4} = \frac{\mathrm{z} - 3}{5}$ is

• x + 5y - 3z = 0

• x - 5y + 3z = 0

• x - 5y - 3z = 0

• 3x - 10y + 5z = 0

A random variable X takes values 0, 1, 2, 3, ... with probability P(X = x) = k(x + 1)${\left(\frac{1}{5}\right)}^{\mathrm{x}}$, where k is constant, then P(X = 0) is

• 7/25

• 18/25

• 13/25

• 16/25

Out of 15 persons 10 can speak Hindi and 8 can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

• 3/5

• 7/12

• 1/5

• 2/5

A random variable X has the following probability distribution

X = x1	1	2	3	4
P(X = x1)	0.1	.02	0.3	0.4

The mean and the standard deviation are respectively

• 3 and 2

• 3 and 1

• $3 \mathrm{and} \sqrt{3}$

• 2 and 1

If g(x) = ${\int }_0^{\mathrm{x}}{\cos }^4\left(\mathrm{t}\right)d\mathrm{t}$, then $\mathrm{g}\left(\mathrm{x} + \mathrm{\pi }\right)$ is equsl to

• g(x) + g($\mathrm{\pi }$)

• g(x) - g()

• g(x) . g($\mathrm{\pi }$)

• $\frac{\mathrm{g}\left(\mathrm{x}\right)}{\mathrm{g}\left(\mathrm{\pi }\right)}$

If the distances covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

• a constant

• $\propto {\mathrm{s}}^3$

• $\propto \frac{1}{{\mathrm{s}}^3}$

• $\propto {\mathrm{s}}^5$