List of top Questions asked in MHT CET- 2025

In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius 'r' with speed 'v'. The magnetic moment associated with electron is

The pressure on a square plate is measured by measuring the force acting on the plate and length of the sides of the plate. The maximum error in the measurement of force and length are respectively 4% and 2%, the percentage error in the measurement of pressure is

If A and B are independent events such that \( P(A \cap B') = \frac{3}{25} \) and \( P(A' \cap B) = \frac{8}{25} \), then \( P(A) = \)}

In a triangle with one of the angles \( 120^\circ \), the lengths of the sides form an A.P. If the length of the greatest side is 7 m, then the area of the triangle is

If \( x = e^{\tan^{-1} \left( \frac{y-x^2}{x^2} \right)} \), then \( \frac{dy}{dx} \) at \( x = 1 \) is

If \( ^{15}C_4 + ^{15}C_5 + ^{16}C_6 + ^{17}C_7 + ^{18}C_8 = ^{19}C_r \), then the value of \( r \) is equal to}

The difference between the maximum value and minimum value of objective function \( z = 3x + 5y \) subject to \( x + 3y \le 60, x + y \ge 10, x - y \ge 0, x, y \ge 0 \) is

If \( \bar{a} = \frac{1}{\sqrt{10}}(3\hat{i} + \hat{k}) \) and \( \bar{b} = \frac{1}{7}(2\hat{i} + 3\hat{j} - 6\hat{k}) \), then the value of \( (2\bar{a} - \bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a} + 2\bar{b})) = \)}

If \( f(x) = 3x^3 + 2x^2 f'(1) + x f''(2) + f'''(3) \) then \( f(x) = ....... \)}

The sum of two nonzero numbers is 4. The minimum value of the sum of their reciprocals is

The rates of change of the perimeter and area of a rectangle respectively when length $x=5$ cm and breadth $y=2$ cm, if $dx/dt = -5$ cm/min and $dy/dt = 3$ cm/min, are

If \( x = \sin \theta, y = \sin^3 \theta \), then \( \frac{d^2y}{dx^2} \) at \( \theta = \frac{\pi}{6} \) is

The angle between the line \( x = \frac{y-1}{2} = \frac{z-3}{\lambda} \) and the plane \( x + 2y + 3z = 6 \) is \( \cos^{-1} \sqrt{\frac{5}{14}} \), then the value of \( \lambda \) is

The combined equation of the tangent and normal to the curve \( xy = 15 \) at the point (5, 3) is

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

If \( 0 \le \cos^{-1} x \le \pi \) and \( -\frac{\pi}{2} \le \sin^{-1} x \le \frac{\pi}{2} \), then at \( x = \frac{1}{5} \) the value of \( \cos(2 \cos^{-1} x + \sin^{-1} x) \) is

If the line \( ax + by + c = 0 \) is normal to the curve \( xy = 1 \), then}

\( \int \sqrt{x^2 + 3x} dx = \)}

Let the plane passing through point (2, 1, -1) containing line joining the points (1, 3, 2) and (1, 2, 1) makes intercepts \( p, q, r \) on co-ordinate axes, then \( p + q + r = \)}

In a triangle ABC with usual notations if \( b \sin C (b \cos C + c \cos B) = 42 \), then area of triangle ABC =}

The area bounded by the curve \( y = x^2 + 3, y = x, x = 3 \) and \( y \)-axis is

Number of switches in alternative equivalent simple circuit for the circuit is (are)

\( \int_{0}^{1} \log (\frac{1}{x} - 1) dx = \)}

\( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (x^2 + \log (\frac{\pi - x}{\pi + x}) \cdot \cos x) dx = \)}

If the foot of the perpendicular drawn from the origin to a plane is \( P(2, -1, 4) \), then the equation of the plane is