List of practice Questions

If the frequency of the cyclotron is doubled, then the radius becomes?
Find the equation of the circle touching the x-axis at \( (9, 0) \) and the line \( y = 14 \).
Evaluate the limit: \[ \lim_{x \to \infty} \frac{\sqrt{\cos^2 x + 3} - \sqrt{\cos^2 x + \sin x + 3}}{x} \]
The velocity is given as \( \mathbf{v} = 3\hat{i} + 3\hat{j} \). Find the acceleration \( \mathbf{a} \).
If \( \sin \alpha = \frac{12}{13} \), and \( \frac{\pi}{6} \leq \alpha \leq \frac{3\pi}{2} \), find \( \tan \alpha \).
Find \( \tan 15^\circ + \tan 45^\circ \).
Evaluate the integral: \[ \int_{\frac{\pi}{10}}^{\frac{2\pi}{5}} \frac{\cot^3 x}{1 + \cot^3 x} \, dx \]
Evaluate the integral: \[ \int \frac{\sin^1 x}{\sqrt{1 - x^2}} \, dx \]
If \( f(x) = \sqrt{x - 3} + 4 \sqrt{5 - x} \), find the domain of \( f(x) \).
If \( f(x) = \cos x \), find the following expression: \[ \frac{1}{2} \left[ f(x + y) + f(y - x) - f(x) \cdot f(y) \right] \]
Given: \[ \sum_{k=0}^{5} \binom{10}{2k} = \alpha \quad \text{and} \quad \sum_{k=0}^{4} \binom{10}{2k+1} = \beta \] \text{Find the value of} \( \alpha - \beta \).
Given the line equation \( Ax + By + C = 0 \), which passes through the point \( (-10, 7) \) and is perpendicular to the line \( 11x - 8y - 16 = 0 \), find \( C \).
Find the domain of the composite function \( f \circ g(x) \) where \( f(x) = \log(5x) \) and \( g(x) = \cos(x) \).
Which one of the following mechanisms is expected to generate tightly linked genes?
You are given a sequence of numbers: 2, 5, 10, 17, ... Identify the pattern and find the next three terms in the sequence. Can you express the nth term of this sequence in a general formula?
Explain the difference between a strong acid and a weak acid. How does the pH of a solution change when a strong acid is added compared to a weak acid?
You are given a set of experimental data for a chemical reaction, including the concentrations of reactants and products at different times. Determine the order of the reaction and the rate constant.
Explain the concept of a limit. Why is it important in calculus?
A graph shows the velocity of an object as a function of time. Describe the motion of the object in detail, including its acceleration and displacement, at different points in time. What does the area under the curve represent?
Explain the difference between work and energy. Give an example where work is done on an object, but its kinetic energy does not change.
The concept of ‘footloose’ labour is associated with _______
Which of the following statement(s) is/are CORRECT?
Which of the following is/are CORRECT with reference to the concept of ‘Little and Great traditions’?
Much before M. N. Srinivas’s concept of ‘sanskritisation’, which of the following scholar(s) framed caste as a process of imitation and social closure?
Which of the following aspect(s) is/are CORRECT about Dalit Panthers in Maharashtra?