HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

`int xcos^3x  "d"x`

`int (sin2x)/(3sin^4x - 4sin^2x + 1)  "d"x`

`int (3"e"^(2x) + 5)/(4"e"^(2x) - 5)  "d"x`

`int  ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1])  "d"x`

Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings drawn.

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

For X ~ B(n, p), if V(X) = 2.4 and p = 0.4, then n = ______.

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 ______.