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

Solve the following :

Find the area of the region bounded by the following curve, the X-axis and the given lines : 0 ≤ x ≤ 5, 0 ≤ y ≤ 2

If a r.v. X has p.d.f., 

f (x) = `c /x` , for 1 < x < 3, c > 0, Find c, E(X) and Var (X).

Choose the correct option from the given alternative:

P.d.f. of a.c.r.v X is f (x) = 6x (1 − x), for 0 ≤ x ≤ 1 and = 0, otherwise (elsewhere)

If P (X < a) = P (X > a), then a = .....

Choose the correct option from the given alternative:

If the p.d.f of a.c.r.v. X is f (x) = 3 (1 − 2x2 ), for 0 < x < 1 and = 0, otherwise (elsewhere) then the c.d.f of X is F(x) =

If the p.d.f. of c.r.v. X is f(x) = `x^2/18`, for -3 < x < 3 and = 0, otherwise, then P(|X| < 1) = ______. 

Solve the following :

Find the area of the region in first quadrant bounded by the circle x² + y² = 4 and the X-axis and the line x = `ysqrt(3)`.

Solve the following :

Find the area of the region bounded by the parabola y² = x and the line y = x in the first quadrant.

Choose the correct option from the given alternative:

If a d.r.v. X takes values 0, 1, 2, 3, . . . which probability P (X = x) = k (x + 1)·5 ^−x , where k is a constant, then P (X = 0) =

Solve the following :

Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π

Solve the following :

Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = `pi/(3)`

Solve the following:

Find the area of the region lying between the parabolas: 4y² = 9x and 3x² = 16y

Solve the following :

Find the area of the region lying between the parabolas : y² = x and x² = y.

Choose the correct option from the given alternative:

If p.m.f. of a d.r.v. X is P (X = x) = `((c_(x)^5 ))/2^5` , for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise If a = P (X ≤ 2) and b = P (X ≥ 3), then E (X ) =

Choose the correct option from the given alternative:

If p.m.f. of a d.r.v. X is P (X = x) = `x^2 /(n (n + 1))`, for x = 1, 2, 3, . . ., n and = 0, otherwise then E (X ) =

Choose the correct option from the given alternative :

If p.m.f. of a d.r.v. X is P (x) = `c/ x^3` , for x = 1, 2, 3 and = 0, otherwise (elsewhere) then E (X ) =

Solve the following:

Find the area enclosed between the circle x² + y² = 1 and the line x + y = 1, lying in the first quadrant.

Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

If Sunday is not holiday then Ram studies on holiday.

Choose the correct option from the given alternative:

If the a d.r.v. X has the following probability distribution :

then P (X = −1) =

Choose the correct option from the given alternative:

If the a d.r.v. X has the following probability distribution :

then P (X = −1) =

Choose the correct option from the given alternative:

Find expected value of and variance of X for the following p.m.f.