List of practice Questions

Evaluate the limit: \[ \lim_{x \to 2} \frac{(x^3 - 8) \sin(x - 2)}{x^2 - 4x + 4} \]
Find the range of \( f(x) = \log_e(4x^2 - 4x + 1) \)
Evaluate the integral: \[ \int \frac{\sin(2x)}{\sin(x)} \, dx \]
Equation of line through (0, 0, 1) and (1, 1, 0)
Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)
What is the ratio of de Broglie wavelength of the particles if their kinetic energy are 0.002 eV and 2 eV respectively?
If \[ (a - 2)^2 + (b - 2)^2 + (c - 2)^2 = 0, \text{ then } a + b + c = \]
Equation of line through (0, 0, 1) and (1, 1, 0)
Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)
What is the ratio of de Broglie wavelength of the particles if their kinetic energy are 0.002 eV and 2 eV respectively?
The position of body varies as \[ S = 9t^2 - 6t. \text{ What is the time at which the body becomes at rest?} \]
Given: \[ \frac{197}{96} X \to \frac{197}{95} Y + Z + V \quad \text{what is Z?} \]
Galvanometer can be converted into a voltmeter by connecting...
What is the dimension of \[ \frac{M B}{K T} \] where \( M \) represents magnetic moment, \( K \) represents the Boltzmann constant, \( B \) represents the magnetic field, and \( T \) represents temperature?
If force is 500 N and instantaneous velocity is 20 m/s, what is the instantaneous power?
The tennis ball of mass 120 g moving with a velocity of 20 m/s towards gets by a rocket of velocity and the final speed becomes 30 m/s with direction reversed. If the time of contact is 0.01 s, what is the average force acting on the ball?
For an ideal gas of molar mass \( M \), the slope of the graph between the rms speed \( V \) and \( \sqrt{T} \) where \( T \) represents the temperature is...
Relation between Azimuthal quantum number and magnetic quantum number
Maximum magnetic moment shown by:
Molecule with 2\( \sigma \) and 2\( \pi \) bonds:
Number of valence electrons in Germanium?
Which of the following contains 2 primary –OH groups in its structure?
Name of the reaction in which benzoyl chloride is converted to benzaldehyde is
Benzene when treated with Br\(_2\) in the presence of FeBr\(_3\), gives 1,4-dibromobenzene and 1,2-dibromobenzene. Which type of reaction is this?
Alkali metal with highest first ionization enthalpy is: