List of top Questions asked in COMEDK UGET

In the network shown in figure, the equivalent capacitance between points P and Q is 

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 the derivative of the function \( f(x) = \begin{cases} b x^2 + ax + 4; & x \geq -1 \\ a x^2 + b; & x < -1 \end{cases} \) is everywhere continuous, then
 

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:

Which of the following are not path functions? 
I. H - T S 
II. W 
III. q 
IV. q + W 
 

A newly prepared radioactive nuclide has a decay constant of 6.93 s\(^{-1}\). What is the half-life of the nuclide?
\( (i + \sqrt{3})^{100} + (i - \sqrt{3})^{100} + 2^{100} \) 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 \( (1 + 3x + 3x^2 + x^3)^{20} \):
X and Y in the following reactions are:
(CH3–CH2)2C=O → HCN/KCN → X → LiAlH4 → (CH3)2C(OH)CH2NH2

Identify the product formed in the given reaction. 

Which of the following artificial sweeteners can be used in soft drinks only?
The equilibrium constant, \(K_C\) for \(3C_2H_2(g) \rightleftharpoons C_6H_6(g)\) is 4 L\(^2\)mol\(^{-2}\). If the equilibrium concentration of benzene is 0.5 mol/L, then what is the value of concentration of ethylene?
Find the product formed for the given reaction.
\[ C_6H_5CHO + H_3C-CH_2CHO \xrightarrow{\text{Dil. NaOH/Δ}} \text{Product} \]
If \( \theta \) be the angle between the vectors \( a = 2\hat{i} + 2\hat{j} - \hat{k} \) and \( b = 6\hat{i} - 3\hat{j} + 2\hat{k} \), then
Five persons A, B, C, D and E are in queue at a shop. The probability that A and B are always together is.
Speed of electromagnetic wave in a medium having relative permittivity \( \epsilon_r \) and relative permeability \( \mu_r \) is (speed of light in air, \( c = 3 \times 10^8 \, \text{m/s} \))
The solution of the differential equation \( \frac{d^2y}{dx^2} = 0 \) represents