List of practice Questions

Find the pH if \( pK_b \), \([ \text{base} ]\), and \([ \text{salt} ]\) are given.
In 2-chloro-3,4-dimethylhexane, how many chiral carbon atoms are present?
From the options given below, which one of the following is a primary amine?
Which of the following alkanes is tertiary?
If the lines \( \frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4} \) and \( \frac{x-3}{1} = \frac{y - 9/2}{2} = z/1 \) intersect, then the value of \( k \) is:
The distribution function \( F(X) \) of a discrete random variable \( X \) is given. Then \( P[X = 4] + P[X = 5] \):
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]
If \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \), then \( A^{-1} \) is:
If \( B = \begin{bmatrix} 3 & a & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then \( a \) is equal to:
The statement \( (p \wedge (\sim q)) \vee ((\sim p) \wedge q) \vee ((\sim p) \wedge (\sim q)) \) is equivalent to:
Which of the following is a logic gate that gives an output of 1 when the inputs are different?
What is the overtone of a vibrating string?
How do you find the amplitude of a simple harmonic oscillator?
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: