List of top Questions asked in MHT CET- 2026

In thermodynamic process for free expansion, select the 'WRONG' statement out of the following options.

A piston of cross-sectional area \(2.5\times 10^{-2} \text{m}^2\) is used in a hydraulic lift to exert a force of \(250 \text{N}\) on water. The cross-sectional area of the other piston which supports a car of mass \(3000 \text{kg}\) is (\(g = 9.8 \text{m/s}^2\))

Two spherical black bodies of radii \(R_1\) and \(R_2\) having surface temperature \(T_1\) and \(T_2\) respectively, radiate the same power. The ratio of \(R_1\) to \(R_2\) will be

A solid cylinder and a solid sphere having the same mass and radius roll down on the same smooth inclined plane. The ratio of the acceleration of the cylinder \((a_c)\) to that of the sphere \((a_s)\) is

The pressure at half the depth of a lake is equal to two-third pressure at the bottom of the lake. So the depth 'h' of the lake is (\(ρ\) = density of water in the lake, \(g\) = acceleration due to gravity, \(P_0\) = atmospheric pressure).

The radius of gyration K of a hollow sphere of mass M and radius R about an axis XY is equal to R as shown in figure. The distance of that axis from the center of the sphere is h. The value of h is

The lengths of seconds pendulums on the surface of the earth and at an altitude '\(h\)' from the surface of the earth are \(l_s\) and \(l_h\) respectively. The radius of the earth is

Time period of a simple pendulum is \(T_1\) when on the earth's surface and \(T_2\) when taken to a height '2R' above the earth's surface, where 'R' is the radius of the earth. The ratio \(T_1:T_2\) is

A spherical object is falling under gravity through a viscous fluid. The sphere attains the terminal velocity when

A body moves along a circular path of diameter \(30 \text{cm}\). It starts from one end of diameter, moves along the circular path and reaches the other end of diameter in 3 second. The angular speed of the body in radian per second is

A block of mass M is lying on a horizontal frictionless surface. One end of the uniform rope of half the mass of the block is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. The tension in the middle of the rope will be

If two resistors of resistances have values \(R_1 = (350\pm 3) \Omega\) and \(R_2 = (140\pm 4) \Omega\). The percentage error for the sum and difference of \(R_1\) and \(R_2\) are respectively

The angle made by vector \(\overset{⃗}{A} = 2\hat{i}+3\hat{j}\) with x-axis and that with y-axis are respectively.

If the probabilities of a student succeeding in the entrance tests for institutes A, B and C are \(0.6\), \(0.5\) and \(0.4\) respectively, while the probability of succeeding in both A and B is \(0.3\), in both B and C is \(0.2\), in both A and C is \(0.2\), and in all three is \(0.1\), then the probability that the student succeeds in exactly one of these tests is......

The angular momentum of a rotating body is 'L'. When the frequency of rotating body is tripled and its kinetic energy is made one-third, the new angular momentum becomes

A fair coin is tossed 9 times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...

Let \(F(x)\) be the cumulative distribution function (c.d.f.) of a continuous random variable \(X\). If \(F(b) = 0.7\) and \(P(X > a) = 0.4\), then the value of \(P(a < X < b)\) is ...

If the plane \(\overset{̄}{r} = (λ+μ)\hat{i}+(2+μ)\hat{j}+(3λ+2μ)\hat{k}\), where \(λ\) and \(μ\) are parameters, intersects coordinate axes at points \((a,0,0)\), \((0,b,0)\) and \((0,0,c)\) then \(a+b+c =\)...

The maximum value of \(Z = 4x+5y\), subject to the constraints \(3x+y\leq 15,3x+4y\leq 24,x\geq 0,y\geq 0\) is

The coordinates of the point of intersection of the lines \(\frac{x-3}{1} = \frac{y-5}{2} = \frac{z-1}{-1}\) and \(\frac{x-4}{2} = \frac{y-2}{-1} = \frac{z-4}{2}\) are...

If the plane \(2x+3y+z = 6\) cuts coordinate axes at A, B and C, then the volume of tetrahedron OABC (where O is the origin) is ......cubic units.

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be three vectors of equal magnitude such that the angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is \(α\), \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is \(β\), \(\overset{̄}{c}\) and \(\overset{̄}{a}\) is \(γ\).
Then the minimum value of \(cosα+cosβ+cosγ\) is ...

The line \(\ell\) passes through the point \((2,1,1)\) and is parallel to the plane \(x+y+2z = 18\). If line \(\ell\) intersects the line \(\frac{x+2}{3} = \frac{y+1}{-1} = \frac{z-2}{1}\), then equation of the line \(\ell\) is...

If \(\overset{̄}{a} = \hat{i}-\hat{k}\), \(\overset{̄}{b} = x\hat{i}+\hat{j}+(1-x)\hat{k}\) and \(\overset{̄}{c} = y\hat{i}+x\hat{j}+(1+x-y)\hat{k}\) then \([\overset{̄}{a} \overset{̄}{b} \overset{̄}{c}]\) depends on

Let \(\overset{̄}{u},\overset{̄}{v},\overset{̄}{w}\) be three vectors such that \(|\overset{̄}{u}| = 1,|\overset{̄}{v}| = 2,|\overset{̄}{w}| = 3\). If the projection of \(\overset{̄}{v}\) along \(\overset{̄}{u}\) is equal to the projection of \(\overset{̄}{w}\) along \(\overset{̄}{u}\) and \(\overset{̄}{v},\overset{̄}{w}\) are perpendicular to each other, then \(|\overset{̄}{u}-\overset{̄}{v}+\overset{̄}{w}| =\)...