List of top Questions asked in COMEDK UGET

The equation of a plane passing through the line of intersection of the planes \( x + 2y + 3z = 2 \) and \( x - y + z = 3 \) and at a distance \( \frac{2}{\sqrt{3}} \) from the point \( (3, 1, -1) \) is:
The integral of \( \int \frac{dx}{x^2[1 + x^4]^{3/4}} \) is:
The integral \( \int \frac{2^x}{\sqrt{1 - 4^x}} \, dx \) is equal to:
The point of intersection of the lines \( \frac{x - 1}{3} = \frac{y - 2}{-3} = \frac{z - 3}{4} \) and \( \frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z - 1}{-2} \) is:
The integral \( \int_{\pi/2}^{-\pi/2} \sin x \, dx \) is:
The angle between the lines \( 2x = 3y - z \) and \( 6x = -y - 4z \) is:
The line \( \frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5} \) is parallel to the plane:
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:
Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).
The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:
Evaluate: \( 8^{\log_5 5} \)
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:
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 \([\vec{a} \, \vec{b} \, \vec{c}]\).
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 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 \( \mathbf{b} \).
The maximum value of \( x + y \) subject to \[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \] is:
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:
Which of the following series of transitions in the spectrum of hydrogen atom fall in the visible region?
The Lyman series of hydrogen spectrum lies in which region?
Which of the following conditions are favourable for chemisorption?
Arrange the hydrides of group 15 in correct decreasing order of reducing nature: