List of top Questions asked in COMEDK UGET

The integral \( \int \frac{2^x}{\sqrt{1 - 4^x}} \, dx \) is equal to:
What will be the equation of the circle whose center is \( (1, 2) \) and which passes through the point \( (4, 6) \)?
The approximate value of \( f(5.001) \), where \( f(x) = x^3 - 7x^2 + 15 \), is:
The line \( \frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5} \) is parallel to the plane:
The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:
Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).
What will be the equation of the circle whose center is \( (1, 2) \) and touches the X-axis?
If \( L = \lim_{x \to 0} \frac{a - \sqrt{a^2 - x^2}}{x^4} \), \( a > 0 \), then:
The coefficients \( a, b, c \) of the quadratic equation \( ax^2 + bx + c = 0 \) are obtained by throwing a die three times. The probability that this equation has equal roots is:
Evaluate: \( 8^{\log_5 5} \)
If for \(\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}\), \(\vec{b} = \hat{i} - 2\hat{j} + \hat{k}\), and \(\vec{c} = -3\hat{i} + \hat{j} + 2\hat{k}\), then find \([\vec{a} \, \vec{b} \, \vec{c}]\).
The vector that must be added to \[ \mathbf{i} - 3\mathbf{j} + 2\mathbf{k} \quad \text{and} \quad 3\mathbf{i} + 6\mathbf{j} - 7\mathbf{k} \] so resultant vector is a unit vector along the X-axis is:
If \( |\mathbf{a}| = 8 \), \( |\mathbf{b}| = 3 \) and \( |\mathbf{a} \times \mathbf{b}| = 12 \), then find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
Write the solution of the following LPP \[ \text{Maximize } Z = x + y \] Subject to \[ 3x + 4y \leq 12, \quad x \geq 0, \quad y \geq 0 \] Which point the value of \( Z \) is maximum?
The maximum value of \( x + y \) subject to \[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \] is:
The Lyman series of hydrogen spectrum lies in which region?
Which of the following series of transitions in the spectrum of hydrogen atom fall in the visible region?
Which of the following conditions are favourable for chemisorption?
The value of \( \Delta G^\circ \) for the phosphorylation of glucose in glycolysis is 13.8 kJ/mol. The value of \( K_C \) at 298 K is:
For decolourisation of 1 mole of KMnO\(_4\), the moles of H\(_2\)O\(_2\) required is:
Arrange the hydrides of group 15 in correct decreasing order of reducing nature:
What would be the molarity of one litre solution of 22.2 g of CaCl\(_2\)?
Calculate the difference between \(C_p\) and \(C_v\) for 10 moles of an ideal gas:
What is the IUPAC name of the following compound? \[ \text{HC}= \text{C} - \text{C} = \text{CH} \]
Which of the following particulate matter is emitted from vehicles?