List of top Questions asked in MHT CET

A conveyor belt is moving with constant velocity \( V \). Sand is being dropped on the belt at the rate of \( M \, \text{kg/s} \). The force necessary to keep the belt moving with a constant velocity \( V \, \text{m/s} \) will be

A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the \( n^{th} \) second of its motion to the total distance travelled in \( n \) seconds is

In air, a charged soap bubble of radius \( R \) breaks into 64 small soap bubbles of equal radius \( r \). The ratio of mechanical force per unit area of big soap bubble to that of a small bubble is

A ray of light travelling through rarer medium is incident at a very small angle \( \theta \) on a glass slab and after refraction its velocity is reduced by 20%. The angle of deviation is

A coil is wound on a core of rectangular cross section. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the self inductance increases by a factor

A body is rotating about its own axis. Its rotational kinetic energy is \( x \) and its angular momentum is \( y \). Hence its moment of inertia about its own axis is

When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are \( V_1 \) and \( V_2 \) respectively. The ratio \( V_1 : V_2 \) is

The radii of circular orbits of two satellites \( A \) and \( B \) of the earth are \( R \) and \( R' \) respectively, where \( R \) is the radius of the earth. If the speed of satellite \( B \) is 6 V, then the speed of satellite \( A \) will be

Using Bohr's quantization condition, the rotational kinetic energy in the third orbit for a diatomic molecule is \( \left( h = \text{Planck's constant}, I = \text{moment of inertia of diatomic molecule} \right) \)

The space within the current carrying toroid is filled with aluminium of susceptibility \( \chi \). The percentage increase in the magnetic field \( B \) will be

Error in the measurement of radius of the sphere is 2%. The error in the calculated value of its volume is

The two coherent sources produce interference with intensity ratio 'b'. In the interference pattern, the ratio \[ \frac{I_{\text{max}}}{I_{\text{min}}} \] will be

In a culture, the bacteria count is 1,00,000 initially. The number increases by 10% in the first 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

In the circuit shown in the figure, \( P \neq R \). The reading of the galvanometer remains the same with switch \( S \) open or closed. Then

The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is \( I \). It is rotating with angular velocity \( \omega \). Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis, then loss in kinetic energy is

A unit vector in the direction of resultant vector of \[ \mathbf{A} = -2\hat{i} + 3\hat{j} + \hat{k}, \quad \mathbf{B} = \hat{i} + 2\hat{j} - 4\hat{k} \] is

Evaluate the integral \[ \int \frac{x^3}{(x+1)^2} \, dx. \]

If \( y = ax^r - bx^{r-1} \), then \[ \frac{d^2y}{dx^2} = ? \]

The points \( (1, 3) \) and \( (5, 1) \) are two opposite vertices of a rectangle. The other two vertices lie on the line \[ y = 2x + c, \quad \text{where} \quad c \text{ is the constant}, \quad \text{then the co-ordinates of the other two vertices are} \]

Angle between the parabola \[ y^2 = 4(x - 1) \quad \text{and} \quad x^2 + 4(y - 3) = 0 \quad \text{at the common end of their latus rectum is} \]

A wire of length 8 units is cut into two parts which are bent respectively in the form of a square and a circle. The least value of the sum of the areas so formed is

The distance of the point \( P(3, 8, 2) \) from the line \[ \frac{x}{2} = \frac{y - 3}{4} = \frac{z - 3}{3}, \quad \text{measured parallel to the plane} \quad 3x + 2y - 2z + 15 = 0, \] is

The abscissae of the points of the curve \[ y = x^3 \quad \text{are in the interval} \quad [-2, 2], \] where the slope of the tangents can be obtained by the mean value theorem for the interval \( [-2, 2] \), are

The solution set for minimizing the function \( z = x + y \) with constraints \[ x + y \geq 2, \quad x + 2y \leq 8, \quad x \leq 3, \quad x, y \geq 0 \] contains

Let \( x \) be the length of each of the equal sides of an isosceles triangle and \( \theta \) be the angle between these sides. If \( x \) is increasing at the rate \( \frac{1}{2} \) m/hour and \( \theta \) is increasing at the rate \( \frac{\pi}{3} \) rad/hour, then the rate at which area of the triangle is increasing when \( x = 12 \) m and \( \theta = \frac{\pi}{4} \) is