List of practice Questions

Which of the following alkanes is tertiary?
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:
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?
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 integral \( \int \frac{\csc x}{\cos^2\left(1 + \log \tan \frac{x}{2}\right)} \, dx \) is equal to:
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:
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?