HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

A r.v. X ~ B(n, p). If the values of mean and variance of X are 18 and 12 respectively, then find total number of positive values of X.

Let the p.m.f. of r.v. X be P(x) = `""^4"C"_x (5/9)^x (4/9)^(4 - x)`, x = 0, 1, 2, 3, 4. Find E(X) and Var(X)

Choose the correct alternative:

`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?

Equation of line passing through the points (0, 0, 0) and (2, 1, –3) is ______.

If X ~ B (n, p) and E(X) = 6 and Var (X) = 4.2, then find n and p.

Evaluate: `int (dx)/(2 + cos x - sin x)`

Evaluate: `int (2x^2 - 3)/((x^2 - 5)(x^2 + 4))dx`

ΔOAB is formed by lines x² – 4xy + y² = 0 and the line x + y – 2 = 0. Find the equation of the median of the triangle drawn from O.

Minimize z = x + 2y,

Subject to x + 2y ≥ 50, 2x – y ≤ 0, 2x + y ≤ 100, x ≥ 0, y ≥ 0.

Find the coordinates of the point of intersection of the pair of lines 6x² + 5xy – 4y² + 7x + 13y – 3 = 0.

Find the point of intersection of the lines given by x² + 3xy + 2y² + x – y – 6 = 0

Find the values of p and q if the equation px² – 6xy + y² + 18x – qy + 8 = 0 represents a pair of parallel lines.

If Rolle's theorem holds for the function f(x) = x³ + bx² + ax + 5, x ∈ [1, 3] with c = `2 + 1/sqrt(3)`, find the values of a and b.

Draw the rough graph and shade the feasible region for the inequalities x + y ≥ 2, 2x + y ≤ 8, x ≥ 0, y ≥ 0.

If x – y ≥ 8, x ≥ 3, y ≥ 3, x ≥ 0, y ≥ 0 then find the coordinates of the corner points of the feasible region.

Evaluate:

`int x/((x + 2)(x - 1)^2)dx`

Find feasible solution for the following system of linear inequation graphically.

3x + 4y ≥ 12, 4x + 7y ≤ 28, x ≥ 0, y ≥ 0

A body is heated at 110°C and placed in air at 10°C. After 1 hour its temperature is 60°C. How much additional time is required for it to cool to 35°C?

Find the angle between the planes `bar r.(2bar i+barj-bark)=3 and bar r.(hati+2hatj+hatk)=1`

Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below: