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

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 = _______________

Which value of x is in the solution set of inequality − 2X + Y ≥ 17

`int x^2/sqrt(1 - x^6)` dx = ________________

`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________

Negation of p → (p ˅ ∼ q) is ______

`int sqrt(x^2 + 2x + 5)` dx = ______________

A biconditional statement is the conjunction of two ______ statements.

If p → q is an implication, then the implication ∼ q → ∼ p is called its

The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.

`int 2/(sqrtx - sqrt(x + 3))` dx = ________________

`int cos sqrtx` dx = _____________

`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________

Find the negation of 10 + 20 = 30

`int (log x)/(log ex)^2` dx = _________

Show that the homogeneous equation of degree 2 in x and y represents a pair of lines passing through the origin if h² − ab ≥ 0.

Write the following compound statements symbolically.

Triangle is equilateral or isosceles