List of top Mathematics Questions asked in COMEDK UGET

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

The value of $a^{\log_b c} - c^{\log_b a}$, where $a, b, c>0$ but $a, b, c \neq 1$, 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 \( \lim_{x \to \infty} \left( 1 + \frac{a}{x} + \frac{b}{x^2} \right)^{2x} = e^2 \), then:

If for any \( 2 \times 2 \) square matrix \( A \), \( A(\text{adj} A) = \begin{bmatrix} 8 & 0 \\ 0 & 8 \end{bmatrix} \), then find the value of \( \det(A) \).

If \( A = \begin{bmatrix} 2 - k & 2 \\ 1 & 3 - k \end{bmatrix} \) is a singular matrix, then the value of \( 5k - k^2 \) is:

If \( A = \begin{bmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{bmatrix} \), then \( |A| \cdot \text{adj}(A) \) is equal to:

If \( A = \{3, 5, 7\} \) and \( B = \{1, 2, 3, 5\} \), then \( A \times B \cap B \times A \) is equal to:

The argument of \( \dfrac{1 - i\sqrt{3}}{1 + i\sqrt{3}} \) is:

\( (i + \sqrt{3})^{100} + (i - \sqrt{3})^{100} + 2^{100} \) is equal to:

The total number of terms in the expansion of \( (x + y)^{100} + (x - y)^{100} \):

The coefficient of \( x^{20} \) in the expansion of \( (1 + 3x + 3x^2 + x^3)^{20} \):

Evaluate the integral \( \int \frac{1}{x \sqrt{ax^2 - x^2}} \, dx \)

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

Evaluate the integral \( 3 \int \frac{3^x}{\sqrt{1 - 9^x}} \, dx \)

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