Concentration of $\mathrm{H}_{2} \mathrm{SO}_{4}$ and $\mathrm{Na}_{2} \mathrm{SO}_{4}$ in a solution is $1 \mathrm{M}$

An aqueous solution is prepared by dissolving $0.1 \mathrm{~mol}$ of an ionic salt in $1.8 \mathrm{~kg}$ of water at $35

Consider the strong electrolytes $Z_{m} X_{n}, U_{m} Y_{p}$ and $V_{m} X_{n}$. Limiting molar conductivity ( $\Lambda^{0

The reaction of $\mathrm{Xe}$ and $\mathrm{O}_{2}{F}_{2}$ gives a $\mathrm{Xe}$ compound $\mathbf{P}$. The number of mol

Thermal decomposition of $\mathrm{AgNO}_{3}$ produces two paramagnetic gases. The total number of electrons present in

The number of isomeric tetraenes (NOT containing $s p$-hybridized carbon atoms) that can be formed from the following re

The number of $-\mathrm{CH}_{2}-$ (methylene) groups in the product formed from the following reaction sequence is _____

The total number of chiral molecules formed from one molecule of $\mathbf{P}$ on complete ozonolysis $\left(\mathrm{O}_{

To check the principle of multiple proportions, a series of pure binary compounds $\left(\mathrm{P}_{\mathrm{m}} \mathr

The correct option(s) about entropy (S) is(are) $[\mathrm{R}=$ gas constant, $\mathrm{F}=$ Faraday constant, $\mathrm{T}

The compound(s) which react(s) with $\mathrm{NH}_{3}$ to give boron nitride (BN) is(are)

The correct option(s) related to the extraction of iron from its ore in the blast furnace operating in the temperature r

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

Among the following, the correct statement(s) about polymers is(are)

Atom $\mathrm{X}$ occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing

The reaction of $\mathrm{HClO}_{3}$ with $\mathrm{HCl}$ gives a paramagnetic gas, which upon reaction with $\mathrm{O}_{

The reaction of $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ and $\mathrm{NaCl}$ in water produces a precipitate that d

Treatment of D-glucose with aqueous $\mathrm{NaOH}$ results in a mixture of monosaccharides, which are

Let $\alpha$ and $\beta$ be real numbers such that $-\frac{\pi}{4}If $\sin (\alpha+\beta)=\frac{1}{3}$ and $\cos (\alpha

If $y(x)$ is the solution of the differential equation $$ x d y-\left(y^{2}-4 y\right) d x=0 \text { for } x > 0, y(1)

The greatest integer less than or equal to $$ \int_{1}^{2} \log _{2}\left(x^{3}+1\right) d x+\int_{1}^{\log _{2} 9}\lef

The product of all positive real values of $x$ satisfying the equation $$ x^{\left(16\left(\log _{5} x\right)^{3}-68 \l

If $$ \beta=\lim \limits_{x \to 0} \frac{e^{x^{3}}-\left(1-x^{3}\right)^{\frac{1}{3}}+\left(\left(1-x^{2}\right)^{\frac{

Let $\beta$ be a real number. Consider the matrix $$ A=\left(\begin{array}{ccc} \beta & 0 & 1 \\ 2 & 1 & -2 \\ 3 & 1 &

Consider the hyperbola $$ \frac{x^{2}}{100}-\frac{y^{2}}{64}=1 $$ with foci at $S$ and $S_{1}$, where $S$ lies on the

Consider the functions $f, g: \mathbb{R} \rightarrow \mathbb{R}$ defined by $$ f(x)=x^{2}+\frac{5}{12} \quad \text { an

Let $P Q R S$ be a quadrilateral in a plane, where $Q R=1, \angle P Q R=\angle Q R S=70^{\circ}, \angle P Q S=15^{\circ}

Let $$ \alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)} $$ Let $g:[0,1] \rightarrow

Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both r

Let $G$ be a circle of radius $R>0$. Let $G_{1}, G_{2}, \ldots, G_{n}$ be $n$ circles of equal radius $r>0$. Suppose eac

Let $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let $$ \be

For $x \in \mathbb{R}$, let the function $y(x)$ be the solution of the differential equation $$ \frac{d y}{d x}+12 y=\c

Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how ma

If $M=\left(\begin{array}{rr}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{array}\right)$, then which of

Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-II contains 24 red, 9 blue and 15 green balls, Box-III

For positive integer $n$, define $$ f(n)=n+\frac{16+5 n-3 n^{2}}{4 n+3 n^{2}}+\frac{32+n-3 n^{2}}{8 n+3 n^{2}}+\frac{48

A particle of mass $1 \mathrm{~kg}$ is subjected to a force which depends on the position as $\vec{F}=$ $-k(x \hat{\imat

In a radioactive decay chain reaction, ${ }_{90}^{230} \mathrm{Th}$ nucleus decays into ${ }_{84}^{214} \mathrm{Po}$ nuc

Two resistances $R_{1}=X \Omega$ and $R_{2}=1 \Omega$ are connected to a wire $A B$ of uniform resistivity, as shown in

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$, electron mass

Consider a configuration of $n$ identical units, each consisting of three layers. The first layer is a column of air of

A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$, and a h

On a frictionless horizontal plane, a bob of mass $m=0.1 \mathrm{~kg}$ is attached to a spring with natural length $l_{0

An object and a concave mirror of focal length $f=10 \mathrm{~cm}$ both move along the principal axis of the mirror with

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_{A}=1$, within which the electrostatic cha

In Circuit-1 and Circuit- 2 shown in the figures, $R_{1}=1 \,\Omega, R_{2}=2 \,\Omega$ and $R_{3}=3 \,\Omega$. $P_{1}$

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma=$ $\frac{5}{3}$. T

A disk of radius $\mathrm{R}$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center

A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_{2}$. The other slit

In the given $P-V$ diagram, a monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is first compressed adiabatically from st

A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted pho

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 \mathrm{~mm}$.

Which one of the following options represents the magnetic field $\vec{B}$ at $\mathrm{O}$ due to the current flowing in