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

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → r

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ p ∨ q

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p→(q ∨ r)

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → q

The following is the c.d.f. of r.v. X:

P (X ≤ 3/ X > 0)

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ (p ∨ q) ∧ r

Write the negation of the following.

An angle is a right angle if and only if it is of measure 90°.

Evaluate the following.

`int 1/("a"^2 - "b"^2 "x"^2)` dx

Evaluate the following.

`int 1/(sqrt(3"x"^2 + 8))` dx

The probability distribution of discrete r.v. X is as follows :

(i) Determine the value of k.

(ii) Find P(X≤4), P(2<X< 4), P(X≥3).

Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f

f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise.

Calculate: P(x≤1)

Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f

f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise.

Calculate: P(0.5 ≤ x ≤ 1.5)

Let X be amount of time for which a book is taken out of library by randomly selected student and suppose X has p.d.f

f (x) = 0.5x, for 0 ≤ x ≤ 2 and = 0 otherwise. Calculate: P(x ≥ 1.5)

Objective function of LPP is ______.

Solve the following problem :

Let the p. m. f. of the r. v. X be

`"P"(x) = {((3 - x)/(10)", ","for"  x = -1", "0", "1", "2.),(0,"otherwise".):}`
Calculate E(X) and Var(X).

The feasible region is the set of point which satisfy.

`int 1/sqrt((x - 3)(x + 2))` dx = ______.

The point of which the maximum value of z = x + y subject to constraints x + 2y ≤ 70, 2x + y ≤ 90, x ≥ 0, y ≥ 0 is obtained at

`int 1/(cos x - sin x)` dx = _______________