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

Which of the following statement is true

The combined equation of the lines through origin and perpendicular to the pair of lines 3x² + 4xy − 5y² = 0 is ______

If p is any statement then ( p ˅ ∼ p) is a

Show that the combined equation of pair of lines passing through the origin is a homogeneous equation of degree 2 in x and y. Hence find the combined equation of the lines 2x + 3y = 0 and x − 2y = 0

State the truth value of `sqrt(3)` is not an irrational number

State the truth Value of x² = 25

State the truth value of (p ˅ ∼p)

State the truth value of (p ˄ ∼p) 

If statements p, q are true and r, s are false, determine the truth values of the following.

~ p ∧ (q ∨ ~ r)

If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)

The principal solutions of `sqrt(3)` sec x − 2 = 0 are ______

Find the principal solutions of cosec x = 2

Find the principal solutions of sin x − 1 = 0

Find the principal solutions of cos 2𝑥 = 1

Find the principal solutions of sin x = `-1/2`

Find the principal solutions of tan x = `-sqrt(3)`

If cos^–1x + cos^–1y – cos^–1z = 0, then show that x² + y² + z² – 2xyz = 1

Differentiate y = `sqrt(x^2 + 5)` w.r. to x

Differentiate y = e^tanx w.r. to x

If y = sin⁻¹ (2^x), find `("d"y)/(""d"x)`