List of top Mathematics Questions asked in MHT CET

If \( \tan \theta = \dfrac{1}{3} \), then find \( \cos 2\theta \).

If rectangles are inscribed in a circle of radius \( r \) units, then the dimensions of the rectangle which has maximum area are

The differential equation of the family of curves \( y = e^{x} (A \cos x + B \sin x) \), where \( A \) and \( B \) are arbitrary constants, is

Evaluate the integral \[ \int_{0}^{1} \tan^{-1}\!\left( \frac{2x - 1}{1 + x - x^2} \right) dx \]

If \( \frac{1}{4}, a, b, \frac{1}{19} \) form a harmonic progression (H.P.), then the values of \( a \) and \( b \) are respectively

The sum of first four terms of a G.P. is $160$ and the common ratio is $3$, then the $4^{\text{th}}$ term is

The letters of the word 'LOGARITHM' are arranged at random. The probability that the arrangement starts with a vowel and ends with a consonant is

A metal wire \(108\) meters long is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are

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

If \( \sin(y + z - x) \), \( \sin(z + x - y) \), and \( \sin(x + y - z) \) are in A.P., then

The domain of the real valued function \[ f(x) = \frac{x + 2}{9 - x^2} \] is

If the radius of a circle \( x^2 + y^2 - 4x + 6y - k = 0 \) is 5, then \( k = \)

The displacement of a particle at the time \( t \) is given by \[ s = \sqrt{1 + t}, \quad \text{then its acceleration } a \text{ is proportional to} \]

The length of the perpendicular to the plane \[ \vec r \cdot (i - 2j + 3k) = 14 \] from the origin is

If \( \cosec\theta + \cot\theta = 5 \), then \( \sin\theta = \)

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

The foot of the perpendicular drawn from the origin to the plane \( x + y + 3z - 4 = 0 \) is

If \( f(x) = \frac{2x + 3}{3x - 2}, \, x \neq \frac{2}{3}, \) then the function \( f \circ f \) is

The area of the region bounded by the curve \( y = x^2 + 1 \), the lines \( x = 1 \), \( x = 2 \), and the x-axis is

The function \( f(x) = \log x - \frac{2x}{x+2} \) is increasing for all:

The rate of decay of mass of a certain substance at time \( t \) is proportional to the mass at that instant. The time during which the original mass of \( m_0 \) gram will be left to \( m_1 \) gram is
\[ k \text{ is constant of proportionality} \]

The joint equation of the lines through the origin trisecting angles in the first and third quadrant is

If \( f(x) = [x]^2 - 5[x] + 6 = 0 \), where \( [x] \) denotes the greatest integer function, then \( x \in \)

The equation of the line passing through the point \( (2, 3, -4) \) and perpendicular to the XOZ plane is

If \[ x = \log t, \quad y + 1 = \frac{1}{t}, \] then \[ e^{-x} \frac{d^2 x}{dy^2} + \frac{dx}{dy} = \]