List of top Questions asked in MHT CET- 2026

A plane is formed by the axes whose centroid is \(\left(2, -\frac{2}{3}, \frac{1}{2}\right)\). Find the distance of the plane from the origin.

Evaluate: \(\int_0^3 \sqrt{9 - x^2} \, dx\).

If \(\tan^{-1}(-1) + \tan^{-1}(5) + \tan^{-1}(3) + \tan^{-1}\left(\frac{1}{4}\right) = \pi + \tan^{-1}\left(\frac{\alpha}{2}\right)\), find \(\alpha\).

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

Determine the shortest distance between the lines \( \dfrac{x-1}{2} = \dfrac{y-2}{3} = \dfrac{z-3}{4} \) and \( \dfrac{x-2}{3} = \dfrac{y-4}{4} = \dfrac{z-5}{5} \).

Evaluate the integral: \[ \int_{3}^{5} |x-4|\,dx \]