List of top Mathematics Questions asked in MHT CET

If \( \sin^{-1} x + \cos^{-1} y = \frac{3\pi}{10} \), then the value of \( \cos^{-1} x + \sin^{-1} y \) is:
If \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix} \] and \[ A^{-1} = \frac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ -8 & 6 & 2c \\ 5 & -3 & 1 \end{bmatrix}, \] then the values of \( a \) and \( c \) are respectively:
The variance of the first 50 even natural numbers is:
If \(\alpha + \beta = \frac{\pi}{2}\) and \(\beta + \gamma = \alpha\), then the value of \(\tan\alpha\) is:
One of the principal solutions of \( \sqrt{3} \sec x = -2 \) is equal to:
\( \sin^{-1}[\sin(-600^\circ)] + \cot^{-1}(-\sqrt{3}) = \)
A lot of 100 bulbs contains 10 defective bulbs. Five bulbs are selected at random from the lot and are sent to the retail store. Then the probability that the store will receive at most one defective bulb is:
If the lines \( \frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4} \) and \( \frac{x-3}{1} = \frac{y - 9/2}{2} = z/1 \) intersect, then the value of \( k \) 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:
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 distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]
The number of ways of distributing \( 500 \) dissimilar boxes equally among \( 50 \) persons is
Marks of 5 students of a group are \( 8, 12, 13, 15, 22 \). Find the variance.

Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to

Evaluate \( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \):

The area of the region \( \{(x, y): 0 \leq y \leq x^2 + 1, \, 0 \leq y \leq x + 1, \, 0 \leq x \leq 2\ \) is:}

Define \( f(x) = \begin{cases} x^2 + bx + c, & x< 1 \\ x, & x \geq 1 \end{cases} \). If f(x) is differentiable at x=1, then b−c is equal to

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:
The number of all four-digit numbers which begin with 4 and end with either zero or five is
The line whose vector equations are \(\vec{r}_1 = 2\hat{i} - 3\hat{j} + 7\hat{k} + \lambda(2\hat{i} + p\hat{j} + 5\hat{k})\) and \(\vec{r}_2 = \hat{i} + 2\hat{j} + 3\hat{k} + \mu(3\hat{i} - p\hat{j} + p\hat{k})\) are perpendicular for all values of \(\lambda\) and \(\mu\). The value of \(p\) is:

If \( X \) is a random variable such that \( P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6} \), and \( P(X = 0) = \frac{1}{3} \), then the mean of \( X \) is

The solution of the differential equation \( \sqrt{1 - y^2} \, dx + x \, dy - \sin^{-1} y \, dy = 0 \) is:
Which of the following is correct?
The solution of the differential equation \( y^2 dx + (x^2 - xy + y^2) dy = 0 \) is
Let the following system of equations: $$ kx + y + z = 1, \quad x + ky + z = k, \quad x + y + kz = k^2 $$ have no solution. Find $|k|$: