List of top Mathematics Questions asked in COMEDK UGET

Find $ nC_{21} $, if $ nC_{10} = nC_{12} $
The differential equation of all non-vertical lines in a plane is
The solution of the differential equation $ \frac{dy}{dx} \tan y = \sin(x + y) + \sin(x - y) $ is
The general solution of $ \left( \frac{dy}{dx} \right)^2 = 1 - x^2 - y^2 + x^2y^2 $ is
If the sum of 12th and 22nd terms of an AP is 100, then the sum of the first 33 terms of an AP is
If two lines $ L_1 : \frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4} $ and $ L_2 : \frac{x-3}{1} = \frac{y-k}{2} = z $ intersect at a point, then $ 2k $ is equal to
If a number $ n $ is chosen at random from the set \{11, 12, 13, ..., 30\, then, the probability that $ n $ is neither divisible by 3 nor divisible by 5, is}
A five-digit number is formed by using the digits 1, 2, 3, 4, 5 with no repetition. The probability that the numbers 1 and 5 are always together, is
The integral $ \int \frac{x \, dx}{2(1+x^2)^{3/2}} $ is equal to
The integral $ \int \frac{4x^2}{\sqrt{1-16x^2}} \, dx \text{ is equal to} $
The integral $ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^2 x \, dx \text{ is equal to} $
The angle between the vectors $ a = \hat{i} + 2 \hat{j} + 2 \hat{k} \quad \text{and} \quad b = \hat{i} + 2 \hat{j} - 2 \hat{k} \quad \text{is} $
If the vectors $ \mathbf{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \quad \mathbf{b} = \hat{i} + 2\hat{j} - \hat{k}, \quad \mathbf{c} = m\hat{i} - \hat{j} + 2\hat{k} $ are coplanar, then the value of $ m $ is
If $ A \text{ is a matrix of order 4 such that } A(\text{adj } A) = 10 I, \text{ then } |\text{adj } A| \text{ is equal to} $

The feasible region for the inequalities $ x + 2y \geq 4, \quad 2x + y \leq 6, \quad x \geq 0, \quad y \geq 0 $

A number $ n $ is chosen at random from $ s = \{1, 2, 3, ..., 50\} $. Let $ A = \{n \in s : n \text{ is a square} \} $, $ B = \{n \in s : n \text{ is a prime}\} $, and $ C = \{n \in s : n \text{ is a square} \} $. Then, correct order of their probabilities is
The value of $ \lim_{x \to \infty} \left( \frac{x^2 - 2x + 1}{x^2 - 4x + 2} \right)^{2x} \text{ is} $
The points of intersection of circles $ (x + 1)^2 + y^2 = 4 \quad \text{and} \quad (x - 1)^2 + y^2 = 9 \quad \text{are} \quad (a, \pm b), \quad \text{then} \quad (a, b) \quad \text{equals to} $
The value of $ \lim_{x \to 0} \frac{e^{ax} - e^{bx}}{2x} \text{ is equal to} $
The slope of the tangent to the curve, $ y = x^2 - xy $ at $ (1, \frac{1}{2}) $ is
Shade the feasible region for the inequalities
\( 6x + 4y \leq 120 \), \( 3x + 10y \leq 180 \), \( x, y \geq 0 \) in a rough figure.
If \( \lim_{x \to 0} \frac{(1 + a^3)^x + 8e^{1/x}}{1 + (1 - b^3)^x e^{1/x}} = 2 \), then:
The approximate value of \( (0.007)^{1/3} \) is:
Let \( f(x) = a - (x-3)^{8/9} \), then the maxima of \( f(x) \) is:

If the derivative of the function \( f(x) = \begin{cases} b x^2 + ax + 4; & x \geq -1 \\ a x^2 + b; & x < -1 \end{cases} \) is everywhere continuous, then