List of top Questions asked in MHT CET- 2026

A vector \(\overset{̄}{r}\) of magnitude \(3\sqrt{2}\) units which makes angles of \(\frac{π}{4}\) and \(\frac{π}{2}\) respectively with Y and Z axes is

The plane \(\frac{x}{2}+\frac{y}{3}+\frac{z}{4} = 1\) cuts the co-ordinate axes at the points A, B, C respectively. Then the area of triangle ABC is

The point having position vector \(4\hat{i}-11\hat{j}+2\hat{k}\) lies on the line

In L.P.P., the corner points of the feasible region for the constraints \(3x-y\geq 6,x\leq 3,y\leq 2,y\geq 0,x\geq 0\) are .....

The volume of a tetrahedron with vertices \(5\hat{i}-\hat{j}+\hat{k},7\hat{i}-4\hat{j}+p\hat{k},\hat{i}-6\hat{j}+10\hat{k}\) and \(-\hat{i}-3\hat{j}+7\hat{k}\) is 11 cubic units, then one of the values of p is

If a parallelogram is constructed on the vectors \(\overset{̄}{a} = 3\overset{̄}{p}-\overset{̄}{q},\overset{̄}{b} = \overset{̄}{p}+3\overset{̄}{q}\) and \(|\overset{̄}{p}| = 3,|\overset{̄}{q}| = 2\) and angle between \(\overset{̄}{p}\) and \(\overset{̄}{q}\) is \(\frac{π}{3}\), then the ratio of the lengths of adjacent sides \(\overset{̄}{a}\) and \(\overset{̄}{b}\) of the parallelogram is

A spherical balloon expands at a rate proportional to its surface area. Initially its radius is 2 cm and 5 minutes later it increases upto 7 cm, then surface area of spherical balloon after 12 minutes will be

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be unit vectors such that \(\overset{̄}{a}\) is perpendicular to the plane of \(\overset{̄}{b}\) and \(\overset{̄}{c}\). If the angle between \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is \(\frac{π}{3}\), then \(|\overset{̄}{a}+\overset{̄}{b}+\overset{̄}{c}| =\)

The value of the integral \(\int _{-\sqrt{3}}^{\sqrt{3}}\frac{(2x^9+3x^8-5x^7+9x^6+4x^3-x+3)}{x^2+3}\,dx\) is

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be three vectors having magnitudes 1, 1 and 2 respectively. If \(\overset{̄}{a}\times (\overset{̄}{a}\times \overset{̄}{c})+\overset{̄}{b} = \overset{̄}{0}\), then the acute angle between \(\overset{̄}{a}\) and \(\overset{̄}{c}\) is

A wire 40 metre in length is to be cut into two pieces. One piece is formed into a square and the other piece into a circle. The lengths of the two pieces so that the combined area of the square and the circle is minimum, are respectively

If a spherical balloon has a variable diameter \(3x+\frac{9}{2}\) units, then the rate of change of its volume with respect to \(x\) is

If \(\int \frac{sin2x}{sin^4x+cos^4x}\,dx = f(x)+c\) where c is constant of integration, then the value of \(tan(f(x))\) is

If \(\int _0^a\frac{dx}{1+4x^2} = \frac{π}{8}\), then \(a =\)

\(\int e^{2x}\frac{2(sin2xcos2x-1)}{2sin^22x}\,dx = A\,e^{2x}cot2x+c\)
(Where c is the constant of integration.), then \(A^3 =\)

\(\int \frac{30x^{14}+15^xlog225}{x^{15}+15^x}\,dx =\)

Let \(f(x) = x-5\).
If \(g(x) = [f(4h(x)+3)]^2\) and \(h(1) = 4,h^'(1) = -2\), then \(g^'(1) =\) .....

If \(y = tan^{-1}\{\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\}\), where \(|x| < 1\), then \(\frac{dy}{dx}\) is equal to

If \(f(x) = \left\{ \begin{array}{cc}\frac{(8-2x)^{\frac{1}{3}}-2}{3-(243+5x)^{\frac{1}{5}}}, & \text{if }x\neq 0 \\ k, & \text{if }x = 0\end{array} \right.\) is continuous at \(x = 0\), then \(k =\)

The equation of the normal to the curve \(xy+7 = 0\) is \(Ax+By+C = 0\), then

If \(y = x+e^x\), then \(\frac{d^2x}{dy^2}\) is equal to

The domain of the function \(f(x) = e^{\sqrt{5x-3-2x^2}}\) is

With usual notations, in \(△ABC\), if \(2a^2 = b^2+c^2\), then \(\frac{cos3A}{cosA}+2 =\)

In a triangle ABC, with usual notations if \(\frac{s-a}{11} = \frac{s-b}{12} = \frac{s-c}{13}\) and \(λtan^2\frac{A}{2} = 455\), then \(λ =\)

Consider the statement patterns
A. \((q\rightarrow p)∨(p\rightarrow q)\)
B. \((\sim p∨\sim q)\leftrightarrow \sim (p∧q)\)
C. \([(p∨q)∧\sim p]∧\sim q\)
D. \((p∧q)∧(\sim p∨\sim q)\)
then statement patterns