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

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 ∧ ~r) ∧ (~q ∨ s)

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

~ p ∧ (q ∨ ~ r)

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)` 

If f(x) is odd and differentiable, then f′(x) is

If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)` 

If y = `tan^-1[sqrt((1 + cos x)/(1 - cos x))]`, find `("d"y)/("d"x)`

Differentiate sin² (sin⁻¹(x²)) w.r. to x