HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Choose the correct option from the given alternatives :

The area bounded by the ellipse `x^2/a^2  y^2/b^2` = 1 and the line `x/a + y/b` = 1 is

Choose the correct option from the given alternatives :

The area bounded by the parabola y = x² and the line y = x is

Choose the correct option from the given alternatives :

The area enclosed between the two parabolas y² = 4x and y = x is

The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is ______.

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The area of the region bounded by x² = 16y, y = 1, y = 4 and x = 0 in the first quadrant, is

Choose the correct option from the given alternatives :

The area of the region included between the parabolas y² = 4ax and x² = 4ay, (a > 0) is given by

Choose the correct option from the given alternatives :

The area of the region included between the line x + y = 1 and the circle x² + y² = 1 is

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 ) =