List of practice Questions

Calculate the number density of free carriers in silver, assuming that each atom contributes one carrier. The density of silver is \( 10.5 \times 10^3 \, \text{kg/m}^3 \) and the atomic weight is 107.8.

Identify the major product C formed in the following reaction sequence: 
product C

Find the integrating factor of the differential equation \( \sin x \frac{dy}{dx} - y \cos x = 1 \):
When 54 g of ice at \(-20^\circ C\) is mixed with 25 g of steam at \(100^\circ C\), then the final mixture at thermal equilibrium contains:
Which enzyme converts glucose and fructose both into ethanol?
The range of the real valued function \( f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} \) is:
What is meant by 'relaxation time' of free electrons in a conductor? Show that the resistance of a conductor can be expressed by \( R = \frac{mL}{n e^2 \tau A} \), where symbols have their usual meanings.
If X, Y and XY are matrices of order 2 × 3, m × n, and 2 × 5 respectively, then the number of elements in matrix Y is:
The greatest integer function defined by \( f(x) = [x] \), \( 1 < x < 3 \) is not differentiable at \( x = \):
A ball falls freely from rest from a height of 6.25 m onto a hard horizontal surface. If the ball reaches a height of 81 cm after the second bounce from the surface, the coefficient of restitution is:
The first member of the Paschen series in the hydrogen spectrum is of wavelength \( 18800 \, \text{Å} \). What is the short wavelength limit of the Paschen series?
Let \(k\in R\). If \(\)\(\)\(\)\(\lim\limits_{x→0+}(\sin(\sin kx)+\cos x+x)^{\frac{2}{x}}=e^6\), then the value of k is
How is democracy a legitimate government? Explain with examples.


What is the correct IUPAC name for the following compound?


What is the major product formed when phenol is treated with sodium dichromate (\( \text{Na}_2\text{Cr}_2\text{O}_7 \)) and sulfuric acid (\( \text{H}_2\text{SO}_4 \))?

Consider the statements P and P: Client’s Preliminary Estimate is used for budgeting costs toward the end of planning and design phase. Q: Client’s Detailed Estimate is used for controlling costs during the execution of the project. Which one of the following options is CORRECT?
The energy of an electron in the ground state (n=1) for He+ ion is -xJ, then that for an electron in n=2 state for Be3+ ion in J is:
Match the minerals in Group I with their highest order of interference color in Group II (for 0.03 mm mineral thickness).
Group IGroup II
P. Sillimanite1. First order
Q. Quartz2. Second order
R. Muscovite3. Greater than third order
S. Calcite4. Third order variegated
The camber prescribed by the I.R.C. for cement concrete or high type bituminous roads in percentage is

Identify the ulcer:
ulcer

A 30-year-old female presented with swelling in the neck. What is the next step in evaluation?
How does a skin graft derive its nutrition on day 3?
Identify the structure marked in the intraoperative image of congenital inguinal hernia:
What is the negative pressure in VAC dressing?

A 12-year-old child presented with sudden severe onset of scrotal pain after a history of trauma 6 hours before. Intraoperative image is given. What is the likely diagnosis?