List of top Mathematics Questions asked in COMEDK UGET

If the standard deviation of \( 0,1,2,3,\ldots,9 \) is \( k \), then the standard deviation of \( 10,11,12,13,\ldots,19 \) will be:

Kiran purchased 3 pencils, 2 notebooks and one pen for INR 41. From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for INR 29, while Shreya purchased 3 pencils, 2 notebooks and 2 pens for INR 44. The above situation can be represented in matrix form as \( AX = B \). Then \( \text{adj}(A) \) is equal to

The value of \( \frac{\sin^2 20^\circ + \cos^4 20^\circ}{\sin^4 20^\circ + \cos^2 20^\circ} \) is :

A function \( f \) from the set of natural numbers to integers defined by \[ f(n) = \begin{cases} \frac{n-1}{2}, & \text{when } n \text{ is odd} -\frac{n}{2}, & \text{when } n \text{ is even} \end{cases} \] is

Position vector of \( P \) and \( Q \) are \( \hat{i} + 3\hat{j} - 7\hat{k} \) and \( 5\hat{i} - 2\hat{j} + 4\hat{k} \) respectively. Then the cosine of the angle between \( \overrightarrow{PQ} \) and the y-axis is

Evaluate the limit \[ \lim_{x \to 1} \frac{(\sqrt{x-1})(2x-3)}{2x^2 + x - 3} \]

Shortest distance between the lines \( \vec{r} = (8 + 3\lambda)\hat{i} - (9 + 16\lambda)\hat{j} + (10 + 7\lambda)\hat{k} \) and \( \vec{r} = 15\hat{i} + 29\hat{j} + 5\hat{k} + \mu(3\hat{i} + 8\hat{j} - 5\hat{k}) \) is

Domain of the function \[ f(x) = \sqrt{\sin^{-1}(2x) + \frac{\pi}{6}} \text{ for real values of } x \]

The cofactor of the element \( a_{21} \) in the expansion of \[ \Delta = \begin{vmatrix} 1 & 4 & 4 -3 & 5 & 9 2 & 1 & 2 \end{vmatrix} \] is

If for real values of \( x \), \( \cos \theta = x + \frac{1}{x} \), then x is

The value of \( \tan^{-1} \left( \tan \frac{7\pi}{6} \right) \text{ is:} \)

The inequality representing the following graph is

If \( |\mathbf{a}| = 2\sqrt{2} \) and \( |\mathbf{b}| = 3 \) and the angle between \( \mathbf{a} \) and \( \mathbf{b} \) is \( \frac{\pi}{4} \), and if a parallelogram is constructed with adjacent sides \( \mathbf{p} = 2\mathbf{a} - 3\mathbf{b} \) and \( \mathbf{q} = \mathbf{a} + \mathbf{b} \), then the product of the lengths of both diagonals is:

In a triangle \( ABC \), the coordinates of the vertex \( A \) are \( (1, 2) \). Equations of the median through \( B \) and \( C \) are respectively \( x + y = 5 \) and \( x = 4 \). Then the equation of side \( AB \) is:

The radius of the circle passes through the foci of a conic \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \) and has its centre at \( (0, 3) \), then the diameter of the circle is ---

In the interval \( (0, 1) \), the function \( f(x) = x^2 - x + 1 \) is

Let \( A \) and \( G \) denote the arithmetic mean and geometric mean of positive real numbers \( 5^x \) and \( 5^{1 - x} \). Then the minimum value of the expression \[ 5^x + 5^{1 - x}, \text{ where } x \in \mathbb{R}, \text{ is:} \]

If \( A = \{1, 2, 4\} \), \( B = \{2, 4, 5\} \), \( C = \{2, 5\} \), then \[ (A - B) \cap (B - C) = \]

Evaluate the integral:
\[ \int \frac{dx}{x \sqrt{4x^2 - 9}} \]

The line \( AB \) passes through the point \( P(-4, 3) \) and the portion of the line intercepted between the axes is divided internally in the ratio 5:3 by the point \( P \). Given that the point \( A \) lies on the x-axis and \( B \) lies on the y-axis, then the x-intercept of the line is

If \( Q(1, 0, 1) \) is the image of the point \( P(a, b, c) \) in the line \( \frac{x + 1}{2} = \frac{y - 3}{-2} = \frac{z}{-1} \), then \( a + b + c \) is equal to:

The complex number \( \frac{1 + 7i}{(2 - i)^2 \) lies in}