List of top Questions asked in MHT CET

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

The statement pattern \( \sim (p \vee q) \vee (\sim p \wedge q) \) is equivalent to

The direction cosines of a line which makes equal acute angles with the co-ordinate axes are

The adjoint of the matrix \[ A = \begin{pmatrix} 2 & 3
-3 & 5 \end{pmatrix} \] is

If \[ y = \left( \frac{x^2 + 1}{x} \right)^x \text{ and } \frac{dy}{dx} = y \left[ g(x) + \log \left( \frac{x^2}{x+1} \right) \right], \text{ then } g(x) = \]

The integral \[ \int_0^{\frac{\pi}{2}} \frac{1 - \cot x}{\csc x + \cos x} \, dx = \]

If the equation \[ ax^2 + hxy + by^2 = 0, \quad c \neq 0 \text{ represents a pair of coincident lines, then} \]

For \( \theta \in \left( 0, \frac{\pi}{2} \right) \), if \( \tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1 \), then \( \theta = \)

If \( f : \mathbb{R} \to \mathbb{R}, g : \mathbb{R} \to \mathbb{R} \) are defined by \[ f(x) = x^2 - 3x + 4 \quad \text{and} \quad g(x) = 2x + 1, \quad \text{then the value of} \quad x \text{ for which} \quad f(x) = f \circ g(x) \text{ is} \]

For the following shaded region, the linear constraints are:

A metal has half-life period of 10 days. A sample originally has a mass of 1000 mg, then the mass remaining after 50 days is

If \[ A = \{ x / x \text{ is a prime number}, 0 \leq x \leq 9 \}, \text{ then the number of elements of the power set of } A \text{ is} \]

If the equation \( ax^2 + hy^2 + cx + cy = 0, c \neq 0 \) represents a pair of lines, then