List of practice Questions

In which of the following thermodynamic processes, the total amount of heat supplied to the system is only used to rise the temperature?
The set of all real values of \( c \) for which the equation \[ zz' + (4 - 3i)z + (4+3i)z + c = 0 \] represents a circle is:
The molar specific heat capacity of a diatomic gas at constant pressure is \( C \). The molar specific heat capacity of a monatomic gas at constant volume is
Electric field intensity and electric potential at a point due to a point charge are 600 V/m and -3600 V respectively. The distance of the point from the charge and the magnitude of the charge are:
A parallel plate capacitor has two square plates of side 5 cm separated by 15 mm. A Pyrex glass slab of dielectric constant \(K = 4.5\) and thickness 10 mm is placed between the plates. The capacitance of the capacitor is:

In the given LCR series circuit the quality factor is


 

The hybridization of aluminum in the complexes X and Y respectively is: 

If the circle S = 0 cuts the circles x2 + y2 - 2x + 6y = 0, x2 + y2 - 4x - 2y + 6 = 0, and x2 + y2 - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

Identify the autocatalytic reaction from the following:
If the area of the triangle formed by the straight lines \(-15x^2 + 4xy + 4y^2 = 0\) and \(x = a\) is \(200 \, {sq. units}\), then \(|a| =\)

Evaluate the integral \( \int \frac{dx}{\sqrt{\sin^3 x \cdot \cos (x - \alpha)}} \):

The speed of the electron in a hydrogen atom in the \( n = 3 \) level is:

Which of the following general reactions is an example for heterogeneous catalysis?
The real valued function \( f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) \) defined by \( f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| \) is:

If \( a \) is in the 3rd quadrant, \( \beta \) is in the 2nd quadrant such that \( \tan \alpha = \frac{1}{7}, \sin \beta = \frac{1}{\sqrt{10}} \), then \[ \sin(2\alpha + \beta) = \]
Match the following (\( f \) is the number of degrees of freedom): \includegraphics[]{100.png}
If \( \vec{i} - 2\vec{j} + 3\vec{k}, 2\vec{i} + 3\vec{j} - \vec{k}, -3\vec{i} - \vec{j} - 2\vec{k} \) are the position vectors of three points A, B, C respectively, then A, B, C:
P is a point on \( x + y + 5 = 0 \), whose perpendicular distance from \( 2x + 3y + 3 = 0 \) is \( \sqrt{13} \), then the coordinates of P are:
If \[ a^2 x^4 + b^2 y^4 = c^6, \] then the maximum value of \( xy \) is:
Hydrolysis of an alkyl bromide X (C\(_4\)H\(_9\)Br) follows first-order kinetics. Reaction of X with Mg in dry ether followed by treatment of D\(_2\)O gave Y. What is Y?
If \[ \cos \alpha + 4 \cos \beta + 9 \cos \gamma = 0 \quad \text{and} \quad \sin \alpha + 4 \sin \beta + 9 \sin \gamma = 0, \] then \[ 81 \cos (2\gamma - 2\alpha) - 16 \cos (2\beta - 2\alpha) = ? \]
A force of \( (4\hat{i} + 2\hat{j} + \hat{k}) \) N is acting on a particle of mass \( 2 \) kg displaces the particle from a position of \( (2\hat{i} + 2\hat{j} + \hat{k}) \) m to a position of \( (4\hat{i} + 3\hat{j} + 2\hat{k}) \) m. The work done by the force on the particle in joules is:
If \( \omega \) is the cube root of unity, then: \[ \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} = \frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} \]
If the period of the function \( f(x) = \frac{\tan 5x \cos 3x}{\sin 6x} \) is \( \alpha \), then find \( f \left( \frac{\alpha}{8} \right) \):