$2 \mathrm{~mol} \,\mathrm{of}\, \mathrm{Hg}(\mathrm{g})$ is combusted in a fixed volume bomb calorimeter with excess of

The reduction potential $\left(E^{0}\right.$, in $\left.\mathrm{V}\right)$ of $\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \math

A solution is prepared by mixing $0.01 \mathrm{~mol}$ each of $\mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{NaHCO}_{3}, \math

The treatment of an aqueous solution of $3.74 \mathrm{~g}$ of $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}$ with excess

Dissolving $1.24 \mathrm{~g}$ of white phosphorous in boiling $\mathrm{NaOH}$ solution in an inert atmosphere gives a ga

Consider the following reaction. On estimation of bromine in $1.00 \mathrm{~g}$ of $\mathbf{R}$ using Carius method, th

The weight percentage of hydrogen in $\mathbf{Q}$, formed in the following reaction sequence, is ________. [Given: Ato

If the reaction sequence given below is carried out with 15 moles of acetylene, the amount of the product $\mathbf{D}$ f

For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two $2 p_{z}$ orb

The correct option(s) related to adsorption processes is(are)

The electrochemical extraction of aluminum from bauxite ore involves

The treatment of galena with $\mathrm{HNO}_{3}$ produces a gas that is

Considering the reaction sequence given below, the correct statement(s) is(are)

Considering the following reaction sequence, the correct option(s) is(are)

Match the rate expressions in LIST-I for the decomposition of $X$ with the corresponding profiles provided in LIST-II. $

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LIST-I contains metal species and LIST-II contains their properties. .tg {border-collapse:collapse;border-spacing:0;}

Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option. .tg {border-collapse:co

Considering only the principal values of the inverse trigonometric functions, the value of $$ \frac{3}{2} \cos ^{-1} \s

Let $$\alpha$$ be a positive real number. Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ and $$g:(\alpha, \infty) \rightar

In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever, 22

Let $$z$$ be a complex number with a non-zero imaginary part. If $$ \frac{2+3 z+4 z^{2}}{2-3 z+4 z^{2}} $$ is a real n

Let $$\bar{z}$$ denote the complex conjugate of a complex number $$z$$ and let $$i=\sqrt{-1}$$. In the set of complex nu

Let $$l_{1}, l_{2}, \ldots, l_{100}$$ be consecutive terms of an arithmetic progression with common difference $$d_{1}$$

The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $$0,2,3,4,6,7$$ is _______

Let $$A B C$$ be the triangle with $$A B=1, A C=3$$ and $$\angle B A C=\frac{\pi}{2}$$. If a circle of radius $$r>0$$ to

Consider the equation $$ \int_{1}^{e} \frac{\left(\log _{\mathrm{e}} x\right)^{1 / 2}}{x\left(a-\left(\log _{\mathrm{e}}

Let $$a_{1}, a_{2}, a_{3}, \ldots$$ be an arithmetic progression with $$a_{1}=7$$ and common difference 8. Let $$T_{1},

Let $$P_{1}$$ and $$P_{2}$$ be two planes given by $$ \begin{aligned} &P_{1}: 10 x+15 y+12 z-60=0 \\\\ &P_{2}:-2 x+5 y+

Let $$S$$ be the reflection of a point $$Q$$ with respect to the plane given by $$ \vec{r}=-(t+p) \hat{\imath}+t \hat{\

Consider the parabola $$y^{2}=4 x$$. Let $$S$$ be the focus of the parabola. A pair of tangents drawn to the parabola fr

Let $$|M|$$ denote the determinant of a square matrix $$M$$. Let $$g:\left[0, \frac{\pi}{2}\right] \rightarrow \mathbb{R

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Two players, $$P_{1}$$ and $$P_{2}$$, play a game against each other. In every round of the game, each player rolls a fa

Let $$p, q, r$$ be nonzero real numbers that are, respectively, the $$10^{\text {th }}, 100^{\text {th }}$$ and $$1000^

Consider the ellipse $$$ \frac{x^{2}}{4}+\frac{y^{2}}{3}=1 $$$ Let $H(\alpha, 0), 0 .tg {border-collapse:collapse;bo

Two spherical stars $A$ and $B$ have densities $\rho_{A}$ and $\rho_{B}$, respectively. $A$ and $B$ have the same radius

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${ }_{7}^{16} \mathrm{~N}+$ ${ }_{2

In the following circuit $C_{1}=12 \mu F, C_{2}=C_{3}=4 \mu F$ and $C_{4}=C_{5}=2 \mu F$. The charge stored in $C_{3}$ i

A rod of length $2 \mathrm{~cm}$ makes an angle $\frac{2 \pi}{3} \mathrm{rad}$ with the principal axis of a thin convex

At time $t=0$, a disk of radius $1 \mathrm{~m}$ starts to roll without slipping on a horizontal plane with an angular ac

A solid sphere of mass $1 \mathrm{~kg}$ and radius $1 \mathrm{~m}$ rolls without slipping on a fixed inclined plane with

Consider an LC circuit, with inductance $L=0.1 \,\mathrm{H}$ and capacitance $C=10^{-3} \mathrm{~F}$, kept on a plane. T

A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to

A medium having dielectric constant $K>1$ fills the space between the plates of a parallel plate capacitor. The plate

The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_{1}$ to $R_{8}$, and two ideal batte

An ideal gas of density $\rho=0.2 \mathrm{~kg} \mathrm{~m}^{-3}$ enters a chimney of height $h$ at the rate of $\alpha=$

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l&gt

Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$,

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons

A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $x y$-plane with the center of the loop al

List I describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figures. List II gives

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as

List I contains four combinations of two lenses (1 and 2) whose focal lengths (in $\mathrm{cm}$ ) are indicated in the f