List of top Questions asked in MHT CET- 2026

In a capillary tube of radius 'R', a straight thin metal wire of radius 'r' is inserted symmetrically and one end of the combination is dipped vertically in water such that lower end of the capillary and thin wire are at same level. If 'T' is the surface tension of water and '\(ρ\)' is the density of water then the rise of water in the capillary is

Due to surface tension, the excess pressure inside a smaller drop is \(9\) units. If \(27\) smaller drops combine then excess pressure inside the bigger drop is

If events A and B are such that \(P(A) = \frac{1}{4}\), \(P(A\cap B) = \frac{1}{10}\) and \(P(A/B) = 2P(B/A)\) then \(P(B) =\)...........

A mass M moving with velocity V along X-axis collides and sticks to another mass 2M which is moving along Y-axis with velocity 3V. The velocity of the combination, after the collision is

The vectors \((\overset{⃗}{A}+\overset{⃗}{B})\) and \((\overset{⃗}{A}-\overset{⃗}{B})\) are perpendicular to each other. This is possible under the condition

The angular speed of the minute hand of a clock in degrees per second is

In non uniform circular motion, the ratio of radial acceleration to tangential acceleration is (V is the velocity, r is the radius and \(α\) is the angular acceleration)

A quantity P is related as \(X^{-2}Y^{-3/2}Z^{2/5}\) where X,Y,Z are independent parameters which have fractional errors of \(0.1,0.2\) and \(0.5\) respectively in measurement. The maximum fractional error in P is

If the centroid of a tetrahedron \(OABC\) is \((1,2,-1)\), where O is the origin, \(A(a,2,3),B(1,b,2),C(2,1,c)\) are the other vertices, then the distance of the point \(P(a,b,c)\) from the origin is...

If \(X\sim B(n,p)\), then the value of \(\frac{P(X = k)}{P(X = k-1)}\) is

A player tosses two fair coins, he wins Rs. \(5\) if two heads appear, Rs. \(3\) if one head appears and Rs. \(2\) if no head appears, then the variance of the winning amount is

The probability mass function of a random variable X is given by
\(P(X = x) = \frac{^5C_x}{2^5}\), for \(x = 0,1,2,3,4,5\) and \(= 0\), otherwise.
Then which of the following is correct?

If the lines \(\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}\) and \(\frac{x-3}{1} = \frac{y-c}{2} = \frac{z}{1}\) intersect, then the radius of circle \(x^2+y^2-4x+10y+c = 0\) is

The corner points of the feasible region determined by a system of linear constraints are \((0,3),(1,1)\) and \((3,0)\). If the objective function is \(z = px+qy\), where \(p,q > 0\), then the condition on p and q such that the minimum of z occurs at both \((3,0)\) and \((1,1)\) is _____

If \(|\overset{̄}{a}| = 4,|\overset{̄}{b}| = 3\) and \(\overset{̄}{a}\cdot \overset{̄}{b} = 8\) then \([\overset{̄}{a} \overset{̄}{a}+\overset{̄}{b} \overset{̄}{a}\times \overset{̄}{b}] =\)

The vector equation of the plane passing through the point \(A(-2,7,5)\) and parallel to the vectors \(4\hat{i}-\hat{j}+3\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\) is ...

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be the unit vectors such that \(\overset{̄}{a}\) is perpendicular to \(\overset{̄}{b}\) and the angle between \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is \(120^{\circ}\). If \(\overset{̄}{a}+\overset{̄}{c}\) is perpendicular to \(\overset{̄}{b}+\overset{̄}{c}\) then

Let \(x_0\) be the point of local maxima of \(f(x) = \overset{̄}{a}\cdot (\overset{̄}{b}\times \overset{̄}{c})\) where \(\overset{̄}{a} = x\hat{i}-2\hat{j}+3\hat{k},\overset{̄}{b} = -2\hat{i}+x\hat{j}-\hat{k}\) and \(\overset{̄}{c} = 7\hat{i}-2\hat{j}+x\hat{k}\) then the value of \(\overset{̄}{a}\cdot \overset{̄}{c}\) at \(x = x_0\) is

The parallelopiped is determined by vectors \(\overset{̄}{a} = -2\hat{i}+5\hat{j}+3\hat{k}\), \(\overset{̄}{b} = \hat{i}+3\hat{j}-2\hat{k}\), \(\overset{̄}{c} = -3\hat{i}+\hat{j}+4\hat{k}\). The altitude of parallelopiped on the parallelogram base determined by vectors \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is

The point of intersection of the two lines \(\frac{x-3}{3} = \frac{y-3}{-1},z-1 = 0\) and \(\frac{x-6}{2} = \frac{z-1}{3},y-2 = 0\) is....

If \(\overset{̄}{a} = \hat{i}+\hat{j}+\hat{k},\overset{̄}{b} = \hat{i}-\hat{j}+2\hat{k}\) and \(\overset{̄}{c} = x\hat{i}+(x-2)\hat{j}-\hat{k}\) are three vectors in which \(\overset{̄}{c}\) lies in the plane of \(\overset{̄}{a}\) and \(\overset{̄}{b}\), then \(x = \cdots\)

If the area enclosed between the curves \(y^2 = 4kx\) and \(y = kx,k > 0\) is \(\frac{2k}{3}\) sq. units then \(k =\)

The solution of the differential equation \(2x\frac{dy}{dx}-y = 3\) represents a family of

The area bounded by the curve \(y = xsin(\frac{x}{2})\) and the X-axis between the lines \(x = 0\) and \(x = 4π\) (in square units), is....

The solution of the differential equation \(x\frac{dy}{dx}+y = x^3y^6\), is...