List of top Questions asked in MHT CET- 2020

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 \( P(A \cap B) = \)

If \[ \mathbf{a} = \hat{i} + \hat{j} + \hat{k}, \quad \mathbf{b} = \hat{i} - \hat{j} + 2\hat{k}, \quad \mathbf{c} = x\hat{i} + \hat{j} + (x - 1)\hat{k} \] If the vector \( \mathbf{c} \) lies in the plane of \( \mathbf{a} \) and \( \mathbf{b} \), then \( x = \)

The approximate value of \( \cot^{-1} (1 \cdot 001) \) is

If the line \( 6x - y - 4 = 0 \) touches the curve \( y^2 = ax^3 + b \) at the point (1, 2), then \( a + b = \)

If \[ \tan^{-1} x + \tan^{-1} y = c \text{ is the general solution of the differential equation} \]

With usual notations, if in \( \triangle ABC \), \( s \) is the semi-perimeter and \( (s - a)(s - b) = (s - c) \), then \( \triangle ABC \) is

Evaluate the integral \[ \int x^3 e^{x^2} \, dx \]

Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt[3]{\sec x}}{\sqrt[3]{\sec x} + \sqrt[3]{\csc x}} \, dx \]

If \[ \cos x + \cos y = -\cos \alpha, \quad \sin x + \sin y = -\sin \alpha, \quad \text{then} \quad \cot \left( \frac{x + y}{2} \right) = \]