Chapterwise Topic Mastery Arena

A parallel plate capacitor with plate area $A$ and separation $d$ is charged to a potential difference $V_0$ and then disconnected from the battery. A dielectric slab of dielectric constant $K = 4$ and thickness $t = d/2$ is inserted between the plates. What is the new potential difference across the plates?

Light of wavelength $\lambda = 310\text{ nm}$ is incident on a metallic surface having work function $\Phi = 2.4\text{ eV}$. If the stopping potential for the emitted photoelectrons is $V_s$ volts, find the value of $V_s$ in volts. (Take $hc = 1240\text{ eV}\cdot\text{nm}$)

According to Molecular Orbital Theory (MOT), which of the following diatomic species is diamagnetic and has a fractional bond order of $2.5$?

Benzaldehyde when treated with concentrated aqueous $\text{NaOH}$ undergoes disproportionation. The organic product that gives an immediate turbidity with Lucas reagent at room temperature is:

For the cell $\text{Zn}(s) | \text{Zn}^{2+}(0.01\text{ M}) || \text{Cu}^{2+}(1.0\text{ M}) | \text{Cu}(s)$, the standard EMF $E^\circ_{cell} = 1.10\text{ V}$. Find the cell EMF $E_{cell}$ in volts at $298\text{ K}$. (Take $\frac{2.303 RT}{F} = 0.06$)

Evaluate the definite integral $I = \int_0^{\pi/2} \frac{\sin^3 x}{\sin^3 x + \cos^3 x} dx$.

The shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}$ is:

If $A$ is a $3 \times 3$ non-singular matrix such that $|A| = 4$, find the value of $|\text{adj}(2A)|$.

A uniform solid sphere of mass $M$ and radius $R$ is placed on a rough horizontal surface with coefficient of static friction $\mu_s$. A horizontal force $F$ is applied at a height $h$ above the center of the sphere ($0 \le h \le R$). Which of the following statements is/are CORRECT?

Match the phenomena in List I with their corresponding governing physical principles in List II: **List I:** (P) Brewster’s angle reflection (Q) Optical fiber propagation (R) Rainbow formation (S) Mirage formation **List II:** (1) Total internal reflection (2) Polarization by reflection (3) Refraction and dispersion with internal reflection (4) Atmospheric temperature gradient and refraction

For the octahedral coordination complex $[\text{Co}(\text{en})_2\text{Cl}_2]^+$, where $\text{en} = \text{ethylenediamine}$, which of the following statements is/are CORRECT?

Let $f(x) = x^3 - 3x^2 + 6x - 2\sin x$ for all $x \in \mathbb{R}$. Which of the following statements is/are TRUE?

In a dihybrid test cross between a heterozygous round yellow pea plant ($RrYy$) and a wrinkled green plant ($rryy$), what is the expected phenotypic ratio in the progeny?

In C4 plants (e.g. Maize, Sugarcane), the primary $\text{CO}_2$ acceptor is present in the mesophyll cells. It is:

In a standard Electrocardiogram (ECG), the QRS complex represents:

In Assisted Reproductive Technology (ART), Zygote Intra-Fallopian Transfer (ZIFT) involves the transfer of:

A uniform copper wire of resistance $R = 16\,\Omega$ is stretched uniformly such that its length increases by $25\%$. Assuming the density remains constant, what is the new resistance of the wire?

What is the osmotic pressure (in atm) of a $0.1\text{ M}$ aqueous solution of $\text{CaCl}_2$ at $300\text{ K}$, assuming complete dissociation? ($R = 0.0821\text{ L}\cdot\text{atm/mol}\cdot\text{K}$)

If $A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$, find $A^{-1}$.

The length of the tangent from the point $(4, 5)$ to the circle $x^2 + y^2 - 4x - 6y + 4 = 0$ is:

An electric pump lifts $1200\text{ kg}$ of water to a height of $10\text{ m}$ in $20\text{ seconds}$. If $g = 10\text{ m/s}^2$ and efficiency is $80\%$, what is the electrical power input to the pump?

Ozonolysis of an alkene produces Acetone and Acetaldehyde in equimolar amounts. The IUPAC name of the starting alkene is: