A closed vessel contains $10 \mathrm{~g}$ of an ideal gas $\mathbf{X}$ at $300 \mathrm{~K}$, which exerts $2 \mathrm{~at

At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid $\left(\mathrm{HNO}_2\r

Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is

Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two co

Among the following, the correct statement(s) for electrons in an atom is(are)

Reaction of iso-propylbenzene with $\mathrm{O}_2$ followed by the treatment with $\mathrm{H}_3 \mathrm{O}^{+}$forms phen

The option(s) in which at least three molecules follow Octet Rule is(are)

Consider the following volume-temperature $(\mathrm{V}-\mathrm{T})$ diagram for the expansion of 5 moles of an ideal mon

Consider the following reaction, $$ 2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mat

Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. $\mathrm{NaOH}$ solution, gives $\ma

Among $\mathrm{V}(\mathrm{CO})_6, \mathrm{Cr}(\mathrm{CO})_5, \mathrm{Cu}(\mathrm{CO})_3, \mathrm{Mn}(\mathrm{CO})_5, \m

In the following reaction sequence, the major product $\mathbf{P}$ is formed. Glycerol reacts completely with excess $\

Among the following complexes, the total number of diamagnetic species is ___________. $\left[\mathrm{Mn}\left(\mathrm{N

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of t

Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone

List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with t

List-I contains various reaction sequences and List-II contains different phenolic compounds. Match each entry in List-I

Let $f(x)$ be a continuously differentiable function on the interval $(0, \infty)$ such that $f(1)=2$ and $$ \lim\limit

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student kno

Let $\frac{\pi}{2} $$ \left(\sin \frac{11 x}{2}\right)(\sin 6 x-\cos 6 x)+\left(\cos \frac{11 x}{2}\right)(\sin 6 x+\c

Consider the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let $S(p, q)$ be a point in the first quadrant such that $\frac{p^

Let $S=\{a+b \sqrt{2}: a, b \in \mathbb{Z}\}, T_1=\left\{(-1+\sqrt{2})^n: n \in \mathbb{N}\right\}$, and $T_2=\left\{(1+

Let $\mathbb{R}^2$ denote $\mathbb{R} \times \mathbb{R}$. Let $$ S=\left\{(a, b, c): a, b, c \in \mathbb{R} \text { and

Let $\mathbb{R}^3$ denote the three-dimensional space. Take two points $P=(1,2,3)$ and $Q=(4,2,7)$. Let $\operatorname{d

Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{1 / 6} \sqrt{6}}$. If $x, y \in \mathbb{R}$ are such that $$ \begin{aligned} & 3

Let $f(x)=x^4+a x^3+b x^2+c$ be a polynomial with real coefficients such that $f(1)=-9$. Suppose that $i \sqrt{3}$ is a

Let $S=\left\{A=\left(\begin{array}{lll}0 & 1 & c \\ 1 & a & d \\ 1 & b & e\end{array}\right): a, b, c, d, e \in\{0,1\}\

A group of 9 students, $s_1, s_2, \ldots, s_9$, is to be divided to form three teams $X, Y$, and $Z$ of sizes 2,3 , and

Let $\overrightarrow{O P}=\frac{\alpha-1}{\alpha} \hat{i}+\hat{j}+\hat{k}, \overrightarrow{O Q}=\hat{i}+\frac{\beta-1}{\

Let $X$ be a random variable, and let $P(X=x)$ denote the probability that $X$ takes the value $x$. Suppose that the poi

Let $\alpha$ and $\beta$ be the distinct roots of the equation $x^2+x-1=0$. Consider the set $T=\{1, \alpha, \beta\}$. F

Let the straight line $y=2 x$ touch a circle with center $(0, \alpha), \alpha>0$, and radius $r$ at a point $A_1$. Let $

Let $\gamma \in \mathbb{R}$ be such that the lines $L_1: \frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3}$ and $L_2: \frac{x

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be functions defined by $$ f(x)=\

A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, P

An infinitely long wire, located on the $z$-axis, carries a current $I$ along the $+z$-direction and produces the magnet

Two beads, each with charge $q$ and mass $m$, are on a horizontal, frictionless, non-conducting, circular hoop of radius

A block of mass $5 \mathrm{~kg}$ moves along the $x$-direction subject to the force $F=(-20 x+10) \mathrm{N}$, with the

A particle of mass $m$ is moving in a circular orbit under the influence of the central force $F(r)=-k r$, corresponding

Two uniform strings of mass per unit length $\mu$ and $4 \mu$, and length $L$ and $2 L$, respectively, are joined at poi

A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature

The specific heat capacity of a substance is temperature dependent and is given by the formula $C=k T$, where $k$ is a c

A disc of mass $M$ and radius $R$ is free to rotate about its vertical axis as shown in the figure. A battery operated m

A point source $\mathrm{S}$ emits unpolarized light uniformly in all directions. At two points $\mathrm{A}$ and $\mathrm

A source (S) of sound has frequency $240 \mathrm{~Hz}$. When the observer (O) and the source move towards each other at

Two large, identical water tanks, 1 and 2 , kept on the top of a building of height $H$, are filled with water up to hei

A thin uniform rod of length $L$ and certain mass is kept on a frictionless horizontal table with a massless string of l

One mole of a monatomic ideal gas undergoes the cyclic process $\mathrm{J} \rightarrow \mathrm{K} \rightarrow \mathrm{L}

Four identical thin, square metal sheets, $S_1, S_2, S_3$ and $S_4$, each of side $a$ are kept parallel to each other wi

A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $\theta_0$. The ray

The circuit shown in the figure contains an inductor $L$, a capacitor $C_0$, a resistor $R_0$ and an ideal battery. The