List of practice Questions

What is the ratio \( \frac{C_p}{C_v} \) for a monatomic and diatomic gas?
The ideal gas equation is given by \( PV = nRT \). Which of the following statements is correct for an ideal gas?
The root mean square velocity (\(v_{\text{rms}}\)) of a gas is given by:
Arrange the following substances in decreasing order of their boiling points:
What is the depression in the freezing point?
In a BCC (Body-Centered Cubic) structure, the radius of the atoms is:
What is the maximum oxidation state of an element in the periodic table?
Which of the following represents the Stephan Reaction?
The half-life of a 1st order reaction is 1 hr. What is the fraction of the reactant remaining after 3 hours?
Which has the highest first ionization energy?
The value of \( \sqrt{3} \csc 20^\circ - \sec 20^\circ \) is:
The integral \( \int \frac{\csc x}{\cos^2\left(1 + \log \tan \frac{x}{2}\right)} \, dx \) is equal to:
A committee of 11 members is to be formed out of 8 males and 5 females. If \( m \) is the number of ways the committee is formed with at least 6 males and \( n \) is the number of ways with at least 3 females, then:
A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:
Using the rules in logic, write the negation of the following: \[ (p q) \land (q \lor \sim r) \]
The equation of the plane passing through the point \( (1, 1, 1) \) and perpendicular to the planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \) is:
If \( AX = B \), where \[ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix}, \] then \( 2x + y - z \) is:
The equation \( (\cos p - 1)x^2 + (\cos p)x + \sin p = 0 \), where \( x \) is a variable with real roots. Then the interval of \( p \) may be any one of the following:
Maximize \( z = x + y \) subject to: \[ x + y \leq 10, \quad 3y - 2x \leq 15, \quad x \leq 6, \quad x, y \geq 0. \] Find the maximum value.
Two monkeys off mass 10 kg and 8 kg are moving along a vertical light rope the former climbing up with an acceleration of 2 m/second square while the latter coming down with a uniform velocity of 2 m/sec square find the tension in the rope at the fixed support
Total genetic content of an organism is called
How many ATP molecules are needed as an initial investment in the glycolytic cycle (normal glycolysis)?
Which disease is primarily spread by female Anopheles mosquitoes?
What will be the acceleration due to gravity at a depth \( d \), where \( g \) is the acceleration due to gravity on the surface of the Earth?
For two events A and B, if \(P(A) = P(A/B) = \frac{1}{4}\) and \(P(B/A) = \frac{1}{2}\), then which of the following is not true?