Maharashtra Board Class 12 Mathematics & Statistics 2026 Question Paper with Solution PDF

Write the dual of the statement \( p \land [\neg q \lor (p \land q) \lor \neg r] \).

Find the area of a triangle with vertices \( A(1,2,3), B(2,3,4), \) and \( C(3,4,5) \).

Differentiate \( \cos^{-1} \left( \frac{1 - x^2}{1 + x^2} \right) \) with respect to \( x \).

Find the principal value of \( \sin^{-1}\left(-\frac{1}{2}\right) \).

Write the converse, inverse, and contrapositive of: "If voltage increases, then current decreases".

Evaluate \( \displaystyle \int \frac{x+2}{2x^2 + 6x + 5} \, dx \) using the substitution or partial fraction method.

A die is tossed twice. If a “success” is getting a number greater than 4, find the probability distribution of the number of successes.

The population of a town grows at a rate proportional to its size. If it grows from 40,000 to 60,000 in 40 years, what will it be in another 20 years?

Prove that \( \displaystyle \int \sqrt{a^2 - x^2} \, dx = \frac{x}{2}\sqrt{a^2 - x^2} + \frac{a^2}{2}\sin^{-1}\left(\frac{x}{a}\right) + C \).

Prove the Section Formula for internal division in vectors.