Chapterwise Topic Mastery Arena

A uniform solid sphere of mass $M = 2\text{ kg}$ and radius $R = 0.5\text{ m}$ rolls without slipping on a horizontal surface with linear center-of-mass velocity $v = 10\text{ m/s}$. Calculate its total kinetic energy in Joules.

A parallel plate capacitor with plate separation $d$ and plate area $A$ is filled with two dielectric slabs of dielectric constants $K_1 = 3$ and $K_2 = 6$, each of thickness $d/2$ in series. What is the equivalent capacitance $C$ in terms of $C_0 = \frac{\varepsilon_0 A}{d}$?

For the spontaneous isothermal expansion of an ideal gas into a vacuum (Joule free expansion), which set of thermodynamic variables is strictly correct?

Determine the spin-only magnetic moment (in Bohr Magnetons, rounded to one decimal place) of the complex ion $[\text{Fe}(\text{H}_2\text{O})_6]^{2+}$. (Given $\sqrt{24} \approx 4.9$)

Evaluate the definite integral: $I = \int_{0}^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}} \, dx$

Let $A$ be a $3 \times 3$ invertible matrix with real entries such that $\det(A) = 4$. If $B = \text{adj}(2A)$, calculate the value of $\det(B)$.

A conducting circular loop of radius $r$ and resistance $R$ is placed in a uniform magnetic field $\vec{B} = B_0 \cos(\omega t) \hat{k}$ perpendicular to the plane of the loop. Which of the following statements is/are correct?

Consider the solvolysis reaction of $(R)\text{-2-bromobutane}$ in aqueous ethanol $(\text{H}_2\text{O}/\text{EtOH})$. Which of the following statements is/are correct?

In $C_4$ plants (e.g. Maize, Sugarcane), the primary $\text{CO}_2$ acceptor is present in which cells and catalyzed by which enzyme?

During the generation and conduction of an action potential in an axon, the rapid depolarization phase is caused by:

In an unbiased $p\text{-}n$ junction diode at thermal equilibrium, the depletion region contains:

The eccentricity of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is $e = \frac{1}{2}$. If the length of its latus rectum is 6, what is the length of its major axis $2a$?

A ray of light traveling in water $(\mu_w = 4/3)$ is incident on the water-air boundary. What is the critical angle $\theta_c$ for total internal reflection?