List of top Questions asked in MHT CET

Two wires 'A' and 'B' of equal lengths are connected in left and right gaps of a meter bridge, respectively. The null point is obtained at 40 cm from the left end. Diameters of the wires 'A' and 'B' are in the ratio 3:1, the ratio of specific resistance of 'A' to that of 'B' is

A parallel combination of pure inductor and capacitor is connected across a source of alternating e.m.f. \( e \). The currents flowing through an inductor and capacitor are \( i_L \) and \( i_C \) respectively. In this parallel resonant circuit, the condition for currents \( i, i_L, i_C \) (i.e. \( i \) = net r.m.s. current in the circuit) is

The frequency of two tuning forks A and B are 1.5% more and 2.5% less than that of the tuning fork C. When A and B are sounded together, 12 beats are produced in 1 second. The frequency of tuning fork C is

A ball of mass \( m \) is attached to the free end of an inextensible string of length \( \ell \). Let \( T \) be the tension in the string. The ball is moving in a horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be

The maximum velocity of the photoelectron emitted by the metal surface is \( v \). Charge and mass of the photoelectron is denoted by \( e \) and \( m \) respectively. The stopping potential in volt is

A stationary body explodes into two parts of masses \( M_1 \) and \( M_2 \). They move in opposite directions with velocities \( v_1 \) and \( v_2 \). The ratio of their kinetic energies is

Evaluate the integral \[ \int \frac{dx}{\sqrt{(x - 1)(x - 2)}} = \text{?}

The potential differences that must be applied across the parallel and series combination of 3 identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in parallel to series combination is

The unit vector \( (ai + bj) \) is perpendicular to \( (i + j) \). The value of 'b' is

Figure shows three forces \( F_1, F_2, F_3 \) acting along the sides of an equilateral triangle. If the total torque acting at point 'O' (centre of the triangle) is zero then the magnitude of \( F_3 \) is

A pipe open at one end has length 0.8 m. At the open end of the tube a string 0.5 m long is vibrating in its 1st overtone and resonates with the fundamental frequency of the pipe. If tension in the string is 50 N, the mass of the string is (speed of sound = 320 m/s)

If the dimensions of a physical quantity are given by \( [L^{-1} M^0 T^1] \), then the physical quantity is

The equation of the circle whose end points of a diameter are the centres of the circles \[ x^2 + y^2 + 2x - 4y + 1 = 0 \quad \text{and} \quad x^2 + y^2 - 8x + 6y + 17 = 0 \] is

The area of the region bounded by the curve \( y = 4x - x^2 \) and the x-axis is

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

If \[ f(x) = \left[ \tan \left( \frac{\pi}{4} + x \right) \right]^{\frac{1}{x}} \quad \text{if} \quad x \neq 0 \] \[ f(x) = k \quad \text{if} \quad x = 0 \] is continuous at \( x = 0 \), then \( k = \)

The equation of a line passing through the point \( (2, 4, 6) \) and parallel to the line \[ 3x + 4 = 4y - 1 = 1 - 4z \] is

If \[ \tan u = \frac{\sqrt{1 - x}}{\sqrt{1 + x}}, \quad \cos v = 4x^3 - 3x, \quad \text{then} \quad \frac{du}{dv} = \text{?}

If \[ \mathbf{a} = 2\hat{i} + 3\hat{j} - \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} - 4\hat{k}, \quad \mathbf{c} = \hat{i} + \hat{j} + \hat{k} \] then \( (\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{a} \times \mathbf{c}) = \)

If the vectors \( \hat{i} + 2\hat{j} + \hat{k} \) and \( \hat{i} + 6\hat{j} + 4\hat{k} \) are collinear, then the values of \( x \) and \( y \) are respectively

The focal distance of the point \( (4, 4) \) on the parabola with vertex at \( (0, 0) \) and symmetric about the y-axis is

The equation of the plane passing through the points \( (2, 3, 1), (4, -5, 3) \) and parallel to the y-axis is

The maximum value of the function \( \frac{\log x}{x}, x \neq 0 \) is

If for the harmonic progression, \( t_7 = \frac{1}{10}, \, t_{12} = \frac{1}{25}, \) then \( t_{20} = \)

If \( A \) and \( B \) are independent events such that odds in favour of \( A \) is 2:3 and odds against \( B \) is 4:5, then \( P(A \cap B) = \)