List of top Mathematics Questions asked in COMEDK UGET

Let $ \alpha $ and $ \beta $ be the distinct roots of $ ax^2 + bx + c = 0 $, then $ \lim_{x \to \alpha} \frac{1 - \cos(ax^2 + bx + c)}{(x - \alpha)^2} $ is equal to:

If $ A = \begin{bmatrix} 0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x \end{bmatrix} $ is a singular matrix, then $ x $ is equal to

If the straight lines $ \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{-t} \quad \text{and} \quad \frac{x - 1}{t} = \frac{y - 4}{2} = \frac{z - 5}{1} \quad \text{are intersecting, then $ t $ can have:} $
The sum of the order and degree of the differential equation $ \left( \frac{d^5y}{dx^5} \right) + 4 \left( \frac{d^4y}{dx^4} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 - 1 $
In the expansion of $ \left( \frac{1}{x} + x \sin x \right)^{10} $, the coefficient of the 6th term is equal to $ 7^7g $, then the principal value of $ x $ is.
The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is
For an examination a candidate has to select 7 questions from three different groups A, B and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection if he has to select at least 2 questions from each group?
The function $ f(x) = \tan^{-1}(\sin x + \cos x) $ is an increasing function in.
Suppose we have three cards identical in form except that both sides of the first card are coloured red, both sides of the second are coloured black, and one side of the third card is coloured red and the other side is coloured black. The three cards are mixed and a card is picked randomly. If the upper side of the chosen card is coloured red, what is the probability that the other side is coloured black?
The points on the $x\text{-axis whose perpendicular distance from the line } \frac{x}{3} + \frac{y}{4} = 1 \text{ is 4 units are}$
In the parabola $y^2 = 4ax$ the length of the latus rectum is 6 units and there is a chord passing through its vertex and the negative end of the latus rectum. Then the equation of the chord is

If the matrix $ A $ is such that $ A \begin{pmatrix} -1 & 2 \\ 3 & 1 \end{pmatrix} = \begin{pmatrix} -4 & 1 \\ 7 & 7 \end{pmatrix} \text{ then } A \text{ is equal to} $

The turning point of the function $ y = \frac{ax-b}{(x-1)(x-4)} $ at the point $ P(2, -1) $ is
Evaluate the following expression: $ \sqrt{2 + \sqrt{2} + \sqrt{2 + 2 \cos(2\theta)}} \quad \text{where} \quad \theta \in \left[ -\frac{\pi}{8}, \frac{\pi}{8} \right] $

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix} \quad \text{and} \quad A \, \text{adj} \, A = A A^t, \quad \text{then} \, 5a + b \, \text{is equal to}$ 
 

Which of the following relations on the set of real numbers $ \mathbb{R} $ is an equivalence relation?
The value of $ \lim_{x \to 1} \frac{x^{15} - 1}{x^{10} - 1} $ is:
If two positive numbers are in the ratio $ 3 + 2\sqrt{2} : 3 - 2\sqrt{2} $, then the ratio between their A.M (arithmetic mean) and G.M (geometric mean) is:
The domain of the function $ y = \frac{1}{\log_{10}(3 - x)} + \sqrt{x + 7} $ is:

The solution set for the inequality $ 13x - 5 \leq 15x + 4<7x + 12;  x \in W $

What is the nature of the function $ f(x) = x^3 - 3x^2 + 4x $ on real numbers?
If $ \frac{dy}{dx} = y + 3 \quad \text{and} \quad y(0) = 2, \quad \text{then} \quad y(\log 2) \text{ is equal to:} $
If $ y = \sin^{-1} \left( \frac{5x + 12\sqrt{1 - x^2}}{13} \right) $ then $ \frac{dy}{dx} $ equals
Evaluate: $ \cos^{-1} \left( \cos \frac{35\pi}{18} \right) - \sin^{-1} \left( \sin \frac{35\pi}{18} \right) $
What is the probability of a randomly chosen 2-digit number being divisible by 3?