List of top Mathematics Questions asked in COMEDK UGET

If $ A $, $ B $, and $ C $ are mutually exclusive and exhaustive events of a random experiment such that $ P(B) = \frac{3}{2} P(A) $ and $ P(C) = \frac{1}{2} P(B) $, then $ P(A \cup C) $ equals to

Three vertices are chosen randomly from the nine vertices of a regular 9-sided polygon. The probability that they form the vertices of an isosceles triangle, is

The lines $ \frac{x-1}{2} = \frac{y-4}{4} = \frac{z-2}{3} \quad \text{and} \quad \frac{1-x}{1} = \frac{y-2}{5} = \frac{3-z}{a} \quad \text{are perpendicular to each other, then} \ a \ \text{equals to} $

The plane $ x - 2y + z = 0 $ is parallel to the line

Given $ \mathbf{a} = 2\hat{i} + \hat{j} - \hat{k}, \quad \mathbf{b} = \hat{i} - \hat{j}, \quad \mathbf{c} = 5\hat{i} - \hat{j} + \hat{k},$ then the unit vector parallel to $\mathbf{a} + \mathbf{b} - \mathbf{c} $ but in the opposite direction is

The maximum value of $ Z = 12x + 13y $, subject to constraints $ x \geq 0, \quad y \geq 0, \quad x + y \leq 5, \quad 3x + y \leq 9 $ is

If $$ A = \begin{pmatrix} k + 1 & 2 \\4 & k - 1 \end{pmatrix}$$ is a singular matrix, then possible values of k are

If $ A = \begin{bmatrix} 2 & 2 \\3 & 4 \end{bmatrix}, \quad \text{then} \quad A^{-1} \text{ equals to} $

The maximum value of Z = 10x + 16y, subject to constraints $ x \geq 0, \quad y \geq 0, \quad x + y \leq 12, \quad 2x + y \leq 20 $

S $ \equiv x^2 + y^2 - 2x - 4y - 4 = 0 $ and $ S' \equiv x^2 + y^2 - 4x - 2y - 16 = 0 $ are two circles. The point $ (-2, -1) $ lies

If $$f(x) = \begin{cases} 2 \sin x & \text{for} \ -\pi \leq x \leq -\frac{\pi}{2}, a \sin x + b & \text{for} \ -\frac{\pi}{2}<x<\frac{\pi}{2}, \cos x & \text{for} \ \frac{\pi}{2} \leq x \leq \pi,\end{cases}$$and it is continuous on $[- \pi, \pi]$, then the values of $ a $ and $ b $ are:

The circle $x^2 + y^2 + 3x - y + 2 = 0$ cuts an intercept on X-axis of length

Let $ f(x) = a + \left( (x - 4) \right)^4 / 9 $, $\text{ then minima of } $ f(x) $\text{ is} $

The approximate value of $ f(5.001) $, $\text{where} $ f(x) = x^3 - 7x^2 + 10 $

The value of $a^{\log_b c} - c^{\log_b a}$, where $a, b, c>0$ but $a, b, c \neq 1$, is

3 and 5 are intercepts of a line $L = 0$, then the distance of $L = 0$ from $(3, 7)$ is

The slope of lines which makes an angle $60^\circ$ with the line $y - 3x + 18 = 0$ is

There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?

If $ A = \{a, b, c\}, B = \{b, c, d\} $ and $ C = \{a, d, c\} $, then $ (A - B) \times (B \cap C) $ is equal to

If $ \cos A = m \cos B $ \text{ and } $ \cot \left( \frac{A+B}{2} \right) = \lambda \tan \left( \frac{B-A}{2} \right), $ \text{ then } $ \lambda \text{ is equal to} $

The expression $ \frac{2 \tan A}{1 - \cot A} + \frac{2 \cot A}{1 - \tan A} $ \text{ can be written as}

The general solution of $ 2 \cos 4x + \sin^2 2x = 0 \text{ is}