List of top Questions asked in COMEDK UGET

In Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in a liquid of refractive index \( \frac{4}{3} \) without changing the geometrical arrangement, the new fringe width will be:

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:
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?
A DC ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through the circuit, the DC ammeter shows 6A. When AC current flows through the circuit, what is the average reading in DC ammeter and the AC ammeter, if DC and AC currents flow simultaneously through the circuit?
A bullet of mass \( m \) hits a mass \( M \) and gets embedded in it. If the block rises to a height \( h \) as a result of this collision, the velocity of the bullet before collision is
A particle of mass \( m \) is moving in a horizontal circle of radius \( r \) under a centripetal force given by \( \left( \frac{-K}{r^2} \right) \), where \( K \) is a constant. Then
The height at which the acceleration due to gravity becomes \( \frac{g}{16} \) (where \( g \) is the acceleration due to gravity on the surface of the earth) in terms of \( R \), if \( R \) is the radius of the Earth.
Which of the following series spectrum of hydrogen atom lies in ultraviolet region?