List of top Questions asked in MHT CET- 2026

The equation of the curve passing through the point (0, 1) and having a slope of the tangent at point \(P(x,y)\) is equal to \(\frac{y}{x+y}\), is

For the differential equation \(\frac{d^3y}{dx^3}+cos(\frac{d^2y}{dx^2}) = 0\), which of the following is true ?

If \(f(x)\) is a polynomial such that \(f(x) = [f^'(x)]^2\) and \(f(2) = 0\), then \(f(-2) = \ldots\)

The equation of a line in cartesian form passing through (0, 0, 0) and (4, 3, c) and parallel to \(\overset{⃗}{a}\times \overset{⃗}{b}\) where \(\overset{⃗}{a} = 2\hat{i}+\hat{j}+2\hat{k}\), \(\overset{⃗}{b} = 3\hat{i}-4\hat{j}\) is

The value of integral \(\int _0^1cot^{-1}(1+x^2-x)\,dx\) is...

The area of the region common to the parabolas \(4y^2 = 9x\) and \(3x^2 = 16y\) is...

\(\int \frac{x^4+1}{x^6+1}dx =\)

The value of \(\int _{-π}^π\frac{2x(1+sinx)}{1+cos^2x}dx\) is...

If \(a > 0,b > 0\) and \(\int \frac{1}{ax^2+b}dx = \frac{1}{\sqrt{6}}tan^{-1}(\frac{\sqrt{2}x}{\sqrt{3}})+c\), then \(\int \frac{1}{bx^2+a}dx = \ldots\)

The area of the region enclosed by the lines \(y = 2x,2y = x\) and \(x = 2\) (in sq.units) is...

A cylindrical tank without a top lid is being manufactured to hold a fixed volume of \(125π\) cubic cm. The minimum surface area required to construct this tank is ............square cm

A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

The equation of tangent to the curves \(x = 1-3t^2\) and \(y = t-3t^3\) at the point \((-2,2)\) is...

If \(y = cos^{-1}(\frac{1-4^x}{1+4^x})\), then \(\frac{dy}{dx}\) at \(x = 1\) is

If \(f(x) = cosx\), then the value of \(\int \frac{e^{f(x)}(xsin^3x+f(x))}{1-(f(x))^2}dx =\)

If \((tan^{-1}x)^2+(cot^{-1}x)^2 = \frac{5π^2}{8}\), then the value of \(x\) is equal to...

If \(cot[f(x)] = \frac{3x-x^3}{1-3x^2}\) and \(sin[g(x)] = \frac{1-x^2}{1+x^2}\), then \(\underset{x\rightarrow t}{lim}\frac{f(x)-f(t)}{g(x)-g(t)} = \ldots\)

Let f(x) be a twice differentiable function such that \(f^{''}(x) = -f(x)\), \(f^'(x) = g(x)\) and \(h(x) = \{f(x)\}^2+\{g(x)\}^2\). If \(h(5) = 11\), then \(h(10)\) is equal to ...

If \(e^x+e^{f(x)} = e\), then the domain of \(f(x)\) is

If the function f is continuous at \(x = π\), where \(f(x) = \frac{1-cos[7(x-π)]}{5(x-π)^2}\), for \(x\neq π\), then \(f(π) =\)

If \(f(\frac{x-1}{x+1}) = x+1\), then \(\int f(x)\,dx = \cdots\)

If \(A = [\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}]\), \(B^{-1} = \left[ \begin{array}{cc}\frac{1}{5} & \frac{2}{5} \\ \frac{2}{5} & -\frac{1}{5}\end{array} \right]\), then \((AB)^{-1} =\)

The value of \(cot^{-1}[\frac{\sqrt{1-sinx}+\sqrt{1+sinx}}{\sqrt{1-sinx}-\sqrt{1+sinx}}]\), where \(x\in (0,\frac{π}{2})\) is...

If \(A = [a_{ij}]_{3\times 3}\) is a matrix such that \(a_{ij} = |2i-5j|\), where \(|.|\) denotes the modulus function, then the element in the \(2^{\text{nd}}\) row and \(3^{\text{rd}}\) column of \(A^{-1}\) is ...

In triangle ABC, with usual notations, if \(a = 4,b = 5\) and \(c = 6\), then angle C is equal to...