List of top Mathematics Questions asked in COMEDK UGET

Evaluate the integral \( 3 \int \frac{3^x}{\sqrt{1 - 9^x}} \, dx \)
Maximum value of \( z = 12x + 3y \), subject to constraints \( x \geq 0, y \geq 0, x + y \leq 5 \) and \( 3x + y \leq 9 \) is
Evaluate the integral \( \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x \, dx \)
The solution of the differential equation \( \frac{d^2y}{dx^2} = 0 \) represents
The equation of the pair of angle bisectors of the line \( x^2 - 4xy - 5y^2 = 0 \) is:
The solution of the differential equation \( \frac{dy}{dx} + \sqrt{\frac{1 - y^2}{1 - x^2}} = 0 \) is
The solution of the differential equation \( x \frac{dy}{dx} = \cot y \) is
The distance of point \( (1, 2) \) from line \( x + y + 2 = 0 \) measured along the line parallel to \( 2x - y = 5 \) is equal to:
If \( \sin A + \sin B = a \) and \( \cos A + \cos B = b \), then \( \cos(A + B) \) equals?
The slope of lines which makes an angle \( 45^\circ \) with the line \( 2x - y = -7 \)
What is \( \frac{\cos \theta}{1 - \tan \theta} + \frac{\sin \theta}{1 - \cot \theta} \) equal to?
Find the general solution of \( \sin 2x + \cos x = 0 \).
Total number of elements in the power set of a set $A$ containing 17 elements is
If 2 and 3 are intercepts of a line \( L = 0 \), then the distance of \( L \equiv 0 \) from the origin is
If \( f(x) + 2f(1 - x) = x^2 + 5 \) for all real values of \( x \), then \( f(x) \) is given by:
If \( U_{n+1} = 3U_n - 2U_{n-1} \) and \( U_0 = 2, U_1 = 3 \), then \( U_n \) is equal to
Evaluate $\left[i^{22} + \left(\dfrac{1}{i}\right)^{25}\right]^3$
If \( 4^n + 15n + P \) is divisible by 9 for all \( n \in \mathbb{N} \), then the least negative integral value of \( P \) is
\( (2^{3n} - 1) \) is divisible by
If \( S = \frac{2^2 - 1}{2} + \frac{3^2 - 2}{6} + \frac{4^2 - 3}{12} + \ldots\) \text{ upto 10 terms, then S is equal to}
\( \sum_{n=1}^{m} n \cdot n! \) is equal to
The first and fifth terms of an A.P. are -14 and 2 respectively and the sum of its $n$ terms is 40. The value of $n$ is
Five persons A, B, C, D and E are in queue at a shop. The probability that A and B are always together is.
If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fail is.
The probability of choosing randomly a number \( c \) from the set \( \{1, 2, 3, \dots, 9\} \) such that the quadratic equation \( x^2 + 4x + c = 0 \) has real roots, is