HSC Arts (Marathi Medium) 12th Board Exam [इयत्ता १२ वि] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Differentiate the following w.r.t.x:

(x³ – 2x – 1)⁵

Without using truth table show that

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)

Find the differential equation of the family of all the parabolas with latus rectum 4a and whose axes are parallel to the x-axis

Without using truth table show that

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)

What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?

Prove that `tan^-1x + tan^-1  (2x)/(1 - x^2) = tan^-1  (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`