List of top Mathematics Questions asked in COMEDK UGET

If $ y = \sin^{-1} \left( \frac{5x + 12\sqrt{1 - x^2}}{13} \right) $ then $ \frac{dy}{dx} $ equals
If $ (1 - 4i)^3 = a + ib $, then the value of $ a $ and $ b $ is
If $ I_n = \int_0^\pi \tan^n x \, dx $, for $ n \geq 2 $, then $ I_n + I_{n-2} = $
The integral $ \int e^x \left[ \frac{x^2 + 1}{(x+1)^2} \right] \, dx $
Two finite sets have $ m $ and $ n $ number of elements respectively. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Then the values of $ m $ and $ n $ are respectively.
The area bounded by the curve $ y = \cos x $, $ x = 0 $, and $ x = \pi $ is
The co-ordinate of the foot of the perpendicular from $ P(1, 8, 4) $ on the line joining $ R(0, -1, 3) $ and $ Q(2, -3, -1) $ is
Find the value of 'b' such that the scalar product of the vector $ \hat{i} + \hat{j} + \hat{k} $ with the unit vector parallel to the sum of the vectors $ 2\hat{i} + 4\hat{j} - 5\hat{k} $ and $ b\hat{i} + 2\hat{j} + 3\hat{k} $ is unity.
Value of $ \cos 105^\circ $
If a real number $ a $ is such that $ \int_0^a x \, dx \leq a + 4 $, then what is the range of $ a $?
The general solution of the differential equation $ (1 + \tan y)(dx - dy) + 2x \, dx \, dy = 0 $
The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is
The equation of the circle which touches the x-axis, passes through the point (1, 1) and whose centre lies on the line $ x + y = 3 $ in the first quadrant is
A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?
The general solution of the differential equation $ x \frac{dy}{dx} = y + x \tan\left(\frac{y}{x}\right) $
The value of $ \int \frac{dx}{\sqrt{2ax - x^2}} $
The measure of the angle between the lines $ x = k + 1, \quad y = 2k - 1, \quad z = 2k + 3, \quad k \in \mathbb{R} $ and $ \frac{x-1}{2} = \frac{y+1}{1} = \frac{z-1}{2} $ is:
A number consists of three digits in geometric progression. The sum of the right hand and left hand digits exceeds twice the middle digit by 1 and the sum of left hand and middle digits is two third of the sum of the middle and right hand digits. Then the sum of digits of number is

The shaded region in the Venn diagram represents

Evaluate: $ \cot^{-1} \left( -\frac{3}{\sqrt{3}} \right) - \sec^{-1} \left( -\frac{2}{\sqrt{2}} \right) - \csc^{-1}(-1) - \tan^{-1}(1) $

If $ f(x) = \begin{cases} x, & 0 \leq x \leq 1 \\ 2x - 1, & x > 1 \end{cases} $, then:

If $ y = \sqrt{\sin x + y} $, then find $ \frac{dy}{dx} $ at $ x = 0, y = 1 $.
Let A and B be two events such that $ P(A/B) = \frac{1}{2}, \quad P(B/A) = \frac{1}{3}, \quad \text{and} \quad P(A \cap B) = \frac{1}{6} $ Then, which one of the following is not true?
If $ \hat{i} + \hat{j} - \hat{k} $ and $ 2\hat{i} - 3\hat{j} + \hat{k} $ are adjacent sides of a parallelogram, then length of its diagonal is
If $ \frac{\cos x}{\cos(x - 2y)} = \lambda \quad \text{then} \quad \tan(x - y) \tan y = $