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

Given that X ~ B(n = 10, p), E(X) = 8, then value of p = ______

A die is thrown. If X denotes the number of positive divisors of the outcomes, then find the range of random variable X

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 `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.

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

Find the vector equation of the plane passing through the point A(–1, 2, –5) and parallel to the vectors `4hati - hatj + 3hatk` and `hati + hatj - hatk`.

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

The solution of the differential equation `dx/dt = (xlogx)/t` is ______.

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

If the foot of the perpendicular drawn from the origin to the plane is (4, –2, 5), then the equation of the plane is ______.

If sec x + tan x is the integrating factor of `dy/dx + Py` = Q, then value of P is ______.

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 equation of the plane containing the lines `(x - 1)/2 = (y + 1)/-1 = z/3` and `x/2 = (y - 2)/-1 = (z + 1)/3`.

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.