The correct molecular orbital diagram for $\mathrm{F}_2$ molecule in the ground state is :

Consider the following statements related to colloids. (I) Lyophobic colloids are not formed by simple mixing of dispers

In the following reactions, $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ are the major products. The correct

A disaccharide $\mathbf{X}$ cannot be oxidised by bromine water. The acid hydrolysis of $\mathbf{X}$ leads to a laevorot

The complex(es), which can exhibit the type of isomerism shown by $\left[\operatorname{Pt}\left(\mathrm{NH}_3\right)_2 \

Atoms of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$ form face-centred cubic (fcc) unit cell of edge length $\math

In the following reactions, $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ are the major products. The correct

$\mathrm{H}_2 \mathrm{S}$ (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this re

Among $\left[\mathrm{I}_3\right]^{+},\left[\mathrm{SiO}_4\right]^{4-}, \mathrm{SO}_2 \mathrm{Cl}_2, \mathrm{XeF}_2, \mat

Consider the following molecules: $\mathrm{Br}_3 \mathrm{O}_8, \mathrm{~F}_2 \mathrm{O}, \mathrm{H}_2 \mathrm{S}_4 \math

For $\mathrm{He}^{+}$, a transition takes place from the orbit of radius $105.8 \mathrm{pm}$ to the orbit of radius $26.

$50 \mathrm{~mL}$ of 0.2 molal urea solution (density $=1.012 \mathrm{~g} \mathrm{~mL}^{-1}$ at $300 \mathrm{~K}$ ) is m

The reaction of 4-methyloct-1-ene $(\mathbf{P}, 2.52 \mathrm{~g})$ with $\mathrm{HBr}$ in the presence of $\left(\mathrm

The value of entropy change, $S_\beta-S_\alpha$ (in $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ ), at $300 \mathrm{~

$$ \text { The value of enthalpy change, } \mathrm{H}_\beta-\mathrm{H}_\alpha \text { (in } \mathrm{J} \mathrm{mol}^{-1}

The number of heteroatoms present in one molecule of $\mathbf{R}$ is _________. [Use : Molar mass (in $\left.\mathrm{g}

The total number of carbon atoms and heteroatoms present in one molecule of $\mathbf{S}$ is _________. [Use : Molar mass

Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function such that $f(1)=\frac{1}{3}$ and $3 \int\limits_

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probab

For any $y \in \mathbb{R}$, let $\cot ^{-1}(y) \in(0, \pi)$ and $\tan ^{-1}(y) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\ri

Let the position vectors of the points $P, Q, R$ and $S$ be $\vec{a}=\hat{i}+2 \hat{j}-5 \hat{k}, \vec{b}=3 \hat{i}+6 \h

Let $M=\left(a_{i j}\right), i, j \in\{1,2,3\}$, be the $3 \times 3$ matrix such that $a_{i j}=1$ if $j+1$ is divisible

Let $f:(0,1) \rightarrow \mathbb{R}$ be the function defined as $f(x)=[4 x]\left(x-\frac{1}{4}\right)^2\left(x-\frac{1}{

Let $S$ be the set of all twice differentiable functions $f$ from $\mathbb{R}$ to $\mathbb{R}$ such that $\frac{d^2 f}{d

For $x \in \mathbb{R}$, let $\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the minimum value of the

For $x \in \mathbb{R}$, let $y(x)$ be a solution of the differential equation $\left(x^2-5\right) \frac{d y}{d x}-2 x y

Let $X$ be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in $X$ while 02244 and 44

Let $A_1, A_2, A_3, \ldots, A_8$ be the vertices of a regular octagon that lie on a circle of radius 2 . Let $P$ be a po

Let $R=\left\{\left(\begin{array}{lll}a & 3 & b \\ c & 2 & d \\ 0 & 5 & 0\end{array}\right): a, b, c, d \in\{0,3,5,7,11,

Let $C_1$ be the circle of radius 1 with center at the origin. Let $C_2$ be the circle of radius $r$ with center at the

$$ \text { Let } a \text { be the area of the triangle } A B C \text {. Then the value of }(64 a)^2 \text { is } $$ :

$$ \text { Then the inradius of the triangle } A B C \text { is } $$ :

Let $p_i$ be the probability that a randomly chosen point has $i$ many friends, $i=0,1,2,3,4$. Let $X$ be a random varia

Two distinct points are chosen randomly out of the points $A_1, A_2, \ldots, A_{49}$. Let $p$ be the probability that th

An electric dipole is formed by two charges $+q$ and $-q$ located in $x y$-plane at $(0,2) \mathrm{mm}$ and $(0,-2) \mat

Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant

A particle of mass $m$ is moving in the $x y$-plane such that its velocity at a point $(x, y)$ is given as $\overrightar

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The inte

A monochromatic light wave is incident normally on a glass slab of thickness $d$, as shown in the figure. The refractive

An annular disk of mass $M$, inner radius $a$ and outer radius $b$ is placed on a horizontal surface with coefficient of

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E}=30(2

A thin circular coin of mass $5 \mathrm{gm}$ and radius $4 / 3 \mathrm{~cm}$ is initially in a horizontal $x y$-plane. T

A rectangular conducting loop of length $4 \mathrm{~cm}$ and width $2 \mathrm{~cm}$ is in the $x y$-plane, as shown in t

A string of length $1 \mathrm{~m}$ and mass $2 \times 10^{-5} \mathrm{~kg}$ is under tension $T$. When the string vibrat

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius

In a radioactive decay process, the activity is defined as $A=-\frac{d N}{d t}$, where $N(t)$ is the number of radioacti

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P-V$ diagrams below. In cyc

When only $S_2$ is emitting sound and it is at $Q$, the frequency of sound measured by the detector in $\mathrm{Hz}$ is

Consider both sources emitting sound. When $S_2$ is at $R$ and $S_1$ approaches the detector with a speed $4 \mathrm{~m}

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _________ $\mathrm{gm

When the chimney is closed using a cap at the top, a pressure difference $\Delta P$ develops between the top and the bot