List of top Mathematics Questions asked in MHT CET

The eccentricity of the ellipse \[ y^2 + 4x^2 - 12x + 6y + 14 = 0 \] is

The function \[ f(x) = \frac{x + 1}{9x + x^3} \] is

The odds in favour of drawing a king from a pack of 52 playing cards is

Evaluate \[ \tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A = \]

In a \( \triangle ABC \), if \( 2 \cos C = \sin B \cdot \csc A \), then

Evaluate \[ \left[ \sin \left( \tan^{-1} \frac{3}{4} \right) \right]^2 + \left[ \sin \left( \tan^{-1} \frac{4}{3} \right) \right]^2 \]

Evaluate the integral \[ \int \frac{dx}{\cos 2x - \cos^2 x} \]

The straight lines represented by the equation \( 9x^2 - 12xy + 4y^2 = 0 \) are

The length of the latus rectum of the parabola \( x^2 + 2y = 8x - 7 \) is

If \( p, q \) are true statements and \( r \) is a false statement, then which of the following statements is a true statement?

If \( f(x) = \frac{|x|}{x} \) for \( x \neq 0 \) and \( f(x) = 1 \) for \( x = 0 \), then the function is

Out of 100 people selected at random, 10 have common cold. If five persons are selected at random from the group, then the probability that at most one person will have common cold is

Evaluate the integral \[ \int_{-5}^{5} \log \left( \frac{7 - x}{7 + x} \right) \, dx \]

The matrix \( A = \begin{bmatrix} a & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2 \end{bmatrix} \) is not invertible only if \( a = \)

The direction cosines of the line which bisects the angle between the positive direction of Y and Z axes are

The equation of normal to the curve \( y = \sin \left( \frac{\pi x}{4} \right) \) at the point (2, 5) is

Let \( G \) be the centroid of a triangle ABC and \( O \) be any other point in that plane, then \[ OA + OB + OC + OG = \]

\( \cos(36^\circ - A) \cos(36^\circ + A) + \cos(54^\circ + A) \cos(54^\circ - A) = \)

Evaluate \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{\tan x}{\tan x + \cot x} \, dx \]

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290K and the metal temperature drops from 370K to 330K in 10 minutes, then the time required to drop the temperature up to 295K is

For \( f(x) = [x] \), where \( [x] \) is the greatest integer function, which of the following is true, for every \( x \in \mathbb{R} \)?

The points A \( (-a, -b) \), B \( (0, 0) \), C \( (a, b) \) and D \( (a^2, ab) \) are

The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{5} \right) + \tan^{-1} \left( \frac{1}{7} \right) + \tan^{-1} \left( \frac{1}{8} \right) \] is

The cosine of the angle included between the lines \[ \vec{r_1} = (2i + j - 2k) + \lambda (i - 2j - 2k) \quad \text{and} \quad \vec{r_2} = (i + j + 3k) + \mu (3i + 2j - 6k) \] where \( \lambda, \mu \in \mathbb{R} \) is

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is