List of top Mathematics Questions asked in MHT CET

If two numbers \( p \) and \( q \) are chosen randomly from the set \( \{1, 2, 3, 4\} \) with replacement, what is the probability that \( p^2 \geq 4q \)?
Marks of 5 students of a group are \( 8, 12, 13, 15, 22 \). Find the variance.
If \( x = a(\cos \theta + \theta \sin \theta), \, y = a(\sin \theta - \theta \cos \theta) \), then \( \frac{d^2 y}{dx^2} \) equals
If one of the lines given by \( 6x^2 - xy + 4cy^2 = 0 \) is \( 3x + 4y = 0 \), then \( c \) equals
Evaluate the following limit: \[ \lim_{\theta \to -\frac{\pi}{4}} \frac{\cos\theta + \sin\theta}{\theta + \frac{\pi}{4}}. \]
Let the foot of the perpendicular from the point \( (1, 2, 4) \) on the line \( \frac{x+2}{4} = \frac{y-1}{2} = \frac{z+1}{3} \) be \( P \). Then the distance of \( P \) from the plane \( 3x + 4y + 12z + 23 = 0 \) is:
The equation of a circle with center \( (5, 4) \) and touching the \( Y \)-axis is:
The point on the line \( 4x - y - 2 = 0 \) which is equidistant from the points \( (-5, 6) \) and \( (3, 2) \) is
The number of all four-digit numbers which begin with 4 and end with either zero or five is
\( \int_{\pi/11}^{9\pi/22} \frac{dx}{1 + \sqrt{\tan x}} \) is equal to:
If \( f(x) = |x| - |1| \), then points where \( f(x) \) is not differentiable, is/are:
Let \( p: \) I am brave, \( q: \) I will climb the Mount Everest. The symbolic form of a statement, 'I am neither brave nor I will climb the Mount Everest' is:
Let \( \vec{a} = \hat{i} + 2\hat{j} + \hat{k}, \, \vec{b} = \hat{i} - \hat{j} + \hat{k}, \, \text{and} \, \vec{c} = \hat{i} + \hat{j} - \hat{k} \). A vector in the plane of \( \vec{a} \) and \( \vec{b} \) whose projection on \( \vec{c} \) is \( \frac{1}{\sqrt{3}} \), is:
If \( \mathbf{a} = \mathbf{i} + 2\mathbf{j} - 3\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} - 3\mathbf{j} - 5\mathbf{k} \), then:
The maximum value of \(\frac{\log(x)}{x}\) is:

The sides of a triangle are \(\sin\alpha\), \(\cos\alpha\), and \(\sqrt{1+\sin\alpha\cos\alpha}\) for some \(0 < \alpha < \frac{\pi}{2}\). Then, the greatest angle of the triangle is:

If the curve \(y^2 = 6x\) and \(9x^2 + by^2 = 16\) intersect each other at right angles, then the value of \(b\) is:
The value of the integral \( \int_0^2 |2x - 3| \, dx \) is:
If \(\alpha + \beta = \frac{\pi}{2}\) and \(\beta + \gamma = \alpha\), then the value of \(\tan\alpha\) is:
If the mean and variance of a Binomial variate \(X\) are 2 and 1 respectively, then the probability that \(X\) takes a value greater than 1 is:
The particular solution of the differential equation \(e \frac{dy}{dx} = (x + 1)\), \(y(0) = 3\), is:
The value of the integral \( \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \) is:
The length of the perpendicular drawn from the point \((1, 2, 3)\) to the line \((X - 6)/3 = (y - 7)/2 = (Z - 7)/-2\) is:
Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:
If \(|\mathbf{a}| = \sqrt{3}, |\mathbf{b}| = 5, |\mathbf{b}||\mathbf{c}| = 10\), the angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\pi/3\), and \(\mathbf{a}\) is perpendicular to \(\mathbf{b} \times \mathbf{c}\), then the value of \(|\mathbf{a} \times (\mathbf{b} \times \mathbf{c})|\) is: