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

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

`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

Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.

Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra

Write the following statements in symbolic form

Even though it is not cloudy, it is still raining