List of top Mathematics Questions asked in MHT CET

The derivative of $\cot^{-1}x$ with respect to $\log(1+x^2)$ is

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

If the equation \[ ax^2 + 2hxy + by^2 + 2gx + 2fy = 0 \] has one line as the bisector of the angle between the co-ordinate axes, then \[ (a + b)^2 = 4(h^2 + g^2) \]

If the symbolic form of the switching circuit is \( \sim p \vee ( p \wedge \sim q) \vee q \), then the current flows through the circuit only if:

Two dice are thrown together. The probability that the sum of the numbers is divisible by 2 or 3 is

If the angle between the lines whose direction ratios are \( 4, -3, 5 \) and \( 3, 4, k \) is \( \frac{\pi}{3} \), then \( k = \)

Evaluate $\displaystyle \int \frac{dx}{1+\sqrt{x}}$

If \( f(x) = \sin^{-1} \left( \sqrt{\frac{1 - x}{2}} \right) \), then \[ f'(x) = \]

The area bounded by the parabola \( y^2 = 16x \) and its latus-rectum in the first quadrant is

The coordinates of the foci of the ellipse \( 16x^2 + 9y^2 = 144 \) 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

If the displacement of a particle at time \(t\) is given by \[ s = 3t^2 - 12t + 14, \] then the displacement of the particle when its velocity becomes zero is

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

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

If \( m_1 \) and \( m_2 \) are slopes of the lines represented by \( \left( \sec^2 \theta - \sin^2 \theta \right) x - 2 \tan \theta \, xy + \sin^2 \theta \, y^2 = 0 \), then \( |m_1 - m_2| = \)

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

If the lines given by \( \vec{r} = 2\hat{i} + \lambda(\hat{i} + 2\hat{j} + m\hat{k}) \) and \( \vec{r} = \hat{i} + \mu(2\hat{i} + \hat{j} + 6\hat{k}) \) are perpendicular, then the value of \( m \) is

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

With usual notations, in triangle ABC, \( a = \sqrt{3} + 1 \), \( b = \sqrt{3} - 1 \) and \( \angle C = 60^\circ \), then \( A - B = \)

If \(f'(x) = k(\cos x + \sin x)\) and \(f(0) = 9,\ f\!\left(\dfrac{\pi}{2}\right) = 15\), then \(f(x)=\)

If \( \int x^x (1 + \log x) \, dx = k x^x + c \), then \( k = \)

If \(\sqrt{x} + \sqrt{y} = \sqrt{xy}\), then find \(\dfrac{dy}{dx}\).

With usual notations in \( \triangle ABC \), \(a = 3\), \(c = 2\) and \(\sin C = \dfrac{2}{3}\), then \(\angle A =\)

The derivative of \( f(\tan x) \) w.r.t. \( g(\sec x) \) at \( x = \frac{\pi}{4} \), where \( f'(1) = 2 \) and \( g'( \sqrt{2} ) = 4 \), 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