List of practice Questions

A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?
Which of the following has the maximum size?
What is the time period of a simple pendulum of length \( L \) and acceleration due to gravity \( g \)?
In a sound wave, the displacement of the air particles follows the equation \( y = A \cos(kx - \omega t) \). What is the wave velocity?
In the reaction \( 2A + B \rightarrow C \), if the rate law is \( \text{Rate} = k[A]^2[B] \), what is the overall order of the reaction?
Which of the following compounds exhibits ionic bonding?
In an oxidation-reduction reaction, what happens to the oxidation state of the central atom in \( \text{MnO}_4^- \) when it is reduced to \( \text{Mn}^{2+} \)?
In the reaction \( 2\text{H}_2\text{O}_2 \rightarrow 2\text{H}_2\text{O} + \text{O}_2 \), what is the role of potassium iodide (KI) in this reaction?
What is the hybridization of the central atom in the molecule \( \text{SO}_3 \)?
Which of the following is the correct order of acidic strength for the following compounds: HNO\(_3\), HClO\(_4\), and HClO\(_3\)?
Compare boiling point of given solutions:
(i) \( 10^{-4} \) NaCl
(ii) \( 10^{-3} \) NaCl
(iii) \( 10^{-2} \) NaCl
(iv) \( 10^{-4} \) urea
Find the dimensions of \( \frac{B}{\mu_0} \)
In a resistive circuit, the power dissipated by a resistor \( R \) when a current \( I \) flows through it is given by \( P = I^2 R \). What happens to the power when the current is doubled?
What is the solution to the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) with the initial condition \( y(1) = 2 \)?
What is the sum of the infinite series \( S = \sum_{n=0}^{\infty} \frac{1}{3^n} \)?
If the equation of a circle is \( 4x^2 + 4y^2 - 12x + 8y = 0 \), what is the radius of the circle?
Find the value of the integral \( \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx \).
For \([ \text{NiCl}_4 ]^{2-}\), what is the charge on the metal and shape of the complex respectively?
In the context of the photoelectric effect, what is the threshold frequency \( f_0 \) for a metal if the work function is \( \phi = 2 \, \text{eV} \)?

Shown below is an image that shows the step-by-step process of folding a white color fabric. The folded fabric is dipped into color at three corners P, Q, and R as indicated in the image. What will be the resultant fabric after unfolding?

Which arrangement of tiles will create the image shown on the left? Tiles can be rotated but not flipped.

Which option will replace the question mark? 

A circular disc and a sphere of the same diameter are floating above the ground. The circular disc is parallel to the ground. Which option shows the CORRECT set of shadows on the ground when seen from the top? 

Shown on the left is an image. Which option is the correct profile of the image? 

Which option is the mirror image of the sentence shown on the left?