21.

A parents has two children. If one of them is boy, then the probability that other is, also a boy, is

• 1/2

• 1/4

• 1/3

• None of these

For the LPP Min z = x₁ + x₂ such that inequalities 5x₁ + 10x₂ $\ge$ 0, x₁ + x₂ $\le$ 1, x₂ $\le$ 4 and x₁, x₂ > 0

• There is a bounded solution

• There is no solution

• There are infinite solutions

• None of these

The equation of the plane containing the line $\frac{\mathrm{x} + 1}{- 3} = \frac{\mathrm{y} - 3}{2} = \frac{\mathrm{z} + 2}{1}$ and the point (0, 7, - 7) is

• x + y + z = 1

• x + y + z = 2

• x + y + z = 0

• None of these

Angle of intersection of the curve r = $\sin \left(\mathrm{\theta }\right) + \cos \left(\mathrm{\theta }\right)$ and r = 2$\sin \left(\mathrm{\theta }\right)$ is equal to

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• None of these

The volume of solid generated by revolving about the y-axis the figure bounded by the parabola y = x and x = y² is

• $\frac{21}{5}\mathrm{\pi }$

• $\frac{24}{5}\mathrm{\pi }$

• $\frac{2}{15}\mathrm{\pi }$

• $\frac{5}{24}\mathrm{\pi }$

The solution of the differential equation (3.xy + y²)dx + (x² + xy)dy = 0 is

• x²(2xy + y²) = c²

• x²(2xy - y²) = c²

• x²(y² - 2xy) = c²

• None of these

The order and degree of the differential equation $\sqrt{\frac{\mathrm{dy}}{\mathrm{dx}}} - 4\frac{\mathrm{dy}}{\mathrm{dx}}$ - 7x = 0 are

• 1 and 1/2

• 2 ana 1

• 1 and 1

• 1 and 2

If the vectors $\hat{\mathrm{i}} - 3\hat{\mathrm{j}} + 2\hat{\mathrm{k}}$, $- \hat{\mathrm{i}} + 2\hat{\mathrm{j}}$ represents the diagonals of a parallelogram, then its area will be

• $\sqrt{21}$

• $\frac{\sqrt{21}}{2}$

• $2\sqrt{21}$

• $\frac{\sqrt{21}}{4}$

The position vector of the points A, B, C are $\left(2\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}\right)$, $\left(3\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + \hat{\mathrm{k}}\right)$ and $\left(\hat{\mathrm{i}} + 4\hat{\mathrm{j}} - 3\hat{\mathrm{k}}\right)$ respectively. These points

• form an isosceles triangle

• form a right angled triangle

• are collinear

• form a scalene triangle

A random variable X has the probability distribution

For the events E = {x is prime number} and F = {x < 4} the probability of P(E ∪ F) is

• 0.50

• 0.77

• 0.35

• 0.87