Q JEE Advance2022

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{48-3 n-3 n^2}{12 n+3 n^2}+\ldots+\frac{25 n-7...

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

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If $M=\left(\begin{array}{cc}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{array}\right)$, then which of the following matrices is equal to $M^{2022}$ ?

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

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For $\mathrm{x} \in \mathbb{R}$, let the function $\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $$ \frac{\mathrm{dy}}{\mathrm{dx}}+12 \mathrm{y}=\cos \left(\frac{\pi}{12} \mathrm{x}\right),...

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Let $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ and $\hat{\mathrm{k}}$ be the unit vectors along the three positive coordinate axes. Let $$ \begin{aligned} & a=3...

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Let G be a circle of radius $\mathrm{R}>0$. Let $\mathrm{G}_1, \mathrm{G}_{2 e a v e} \mathrm{G}_2$ be n circles of...

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

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Let $$ \sum_{k=1}^{\text {sam }}\left(\frac{-}{6}\right) $$ Let $g_a[0,1] \rightarrow \mathbb{R}$ be the function defined by $$ g(\mathrm{x})=2^{\alpha \mathrm{x}}+2^{\alpha(1-\mathrm{x})} $$ Then,...

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Let PQRS be a quadrilateral in a plane, where $\mathrm{QR}=1, \angle \mathrm{PQR}=\angle \mathrm{QRS}=70^{\circ}, \angle \mathrm{PQS}=15^{\circ}$ and $\angle \mathrm{PRS}=40^{\circ}$. If $...

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Consider the functions $f, g: \mathbb{R} \rightarrow \mathbb{R}$ defined by $$ f(x)=x^{\circ}+{ }_{12}^5 \text { and } g(x)=\left\{\begin{array}{cc} \left\{\left(1-\frac{4|x|}{0-1}\right)\right. &...

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Consider the hyperbola $$ \frac{x^{+}}{100}-\frac{y^{-}}{64}=1 $$ with foci at S and $\mathrm{S}_1$, where S lies on the positive x -axis....

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Treatment of D-glucose with aqueous NaOH resuts in a mixture of monosaccharides, which are

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The reaction of $\mathrm{Pb}\left(\mathrm{NO}_3\right)_2$ and NaCl in water produces a precipitate that dissolves upon the addintion of HCl of appropriate...

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The reaction of $\mathrm{HClO}_3$ with HCl gives a paramagnetic gas, which upon reaction with $\mathrm{O}_3$ produces

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Atom X occupies the fcc lattice sites as well alternate tetrahedral voids of the same lattice. The packing efficiency (in...

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LIST-I contains metal species and LIST-II contains their properties. Match each metal species in LIST-I with their properties in LIST-II,...

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Among the following, the correct statements about polymers is(are)

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LIST-I contains compounds and LIST-II contains reactionsMatch each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the...

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

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Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. $\mathrm{X}_{\mathrm{s}}$ and...

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

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

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

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The compounds which reacts with $\mathrm{NH}_3$ to give boron nitride $(\mathrm{BN})$ is(are)

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Consider the ellipse $$ \frac{x^2}{4}+\frac{y^2}{3}=1 $$ Let $\mathrm{H}(\alpha, 0), 0

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

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The treatment of galena with $\mathrm{HNO}_3$ produces a gas that is

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Let $p, q, r$ be non-zero real numbers that are, respectively, the $10^{\text {th }}, 100^{\text {th }}$ and $...

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The electrochemical extraction of aluminum from bauxite ore involves

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To check the principle of multiple proportions, a series of pure binary conmpouds ( $\mathrm{P}_{\mathrm{m}} \mathrm{Q}_{\mathrm{n}}$ ) were analyzed and...

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

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The total number of chiral molecules formed from one molecule of $\mathbf{P}$ on complete ozonolysis $\quad\left(\mathrm{O}_3\right.$, $\mathrm{Zn} / \mathrm{H}_2 \mathrm{O}$...

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Consider the following lists:The correct option is:

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For diatomic molecules, the correct statement ( $s$ ) about the molecular orbitals formed by the overlap of two $...

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

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If the reaction sequence given below is carried out with 15 moles of acetylene, the amount of the product D...

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

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Let $S$ be the reflection of a point $Q$ with respect to the plane given by $$ \vec{r}=-(t+p) \hat{i}+\hat{j}+(1+p) \hat{k}...

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If $$ \beta=\lim _{x \rightarrow 0} \frac{e^{r^3}-\left(1-x^{\frac{2}{3}}\right)^{\frac{1}{3}}\left((1-x)^2-1\right) \sin x}{x \sin ^2 x} $$ then the value of $6 \beta$ is...

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

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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...

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

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

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Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1=7$ and common difference 8 . Let $...

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Consider the equation $$ \int_1^e \frac{\left(\log _e x\right)^{1 / 2}}{x\left(a-\left(\log _e x\right)^{3 / 2}\right)^2} d x=1, a \in(-\infty, 0) \cup(1,...

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

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Thermal decomposition of $\mathrm{AgNO}_3$ produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of...

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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...

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The reaction of Xe and $\mathrm{O}_2 \mathrm{~F}_2$ gives a Xe compound $\mathbf{P}$. The number of moles of HF produced by...

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

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Consider the strong electrolytes $Z_m X_n, U_m Y_p$ and $V_m X_n$. Limiting molar conductivity $\left(\Lambda^0\right)$ of $U_m Y_p$ and $...

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Dissolving 1.24 g of white phosphorous in boiling NaOH solution in an inert atmosphere gives a gas Q . The...

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Let $l_1, l_2, \ldots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_1$, and let $...

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

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The treatment of an aqueous solution of 3.74 g of $\mathrm{Cu}\left(\mathrm{NO}_3\right)_2$ with excess KI results in a brown solution along...

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The greatest integer less than or equal to $$ \int_1^2 \log _2\left(x^3+1\right) d x+\int_1^{\log _2 9}\left(2^x-1\right)^{\frac{1}{3}} d x $$ is...

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

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A solution is prepared by mixing 0.01 mol each of $\mathrm{H}_2 \mathrm{CO}_3, \mathrm{NaHCO}_3, \mathrm{Na}_2 \mathrm{CO}_3$, and NaOH in 100 mL...

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

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

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The reduction potential ( $\mathrm{E}^0$, in V ) of $\mathrm{MnO}_4^{-}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})$ is $\_\_\_\_$ . [Given $...

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An aqueous solution is prepared by dissolving 0.1 mol of an ionic salt in 1.8 kg of water at $...

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

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2 mol of $\mathrm{Hg}(\mathrm{g})$ is combusted in a fixed volume bomb calorimeter with excess of $\mathrm{O}_2$ at 298 K and...

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Concentration of $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{Na}_2 \mathrm{SO}_4$ in a solution is 1 M and $1.8 \times 10^{-2} \mathrm{M}$, respectively. Molar...

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Considering only the principal values of the inverse trigonometric functions, the value of $$ \frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^2}}+\frac{1}{4} \sin ^{-1}...

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List I contains four combinations of two lenses (1 and 2) whose focal lengths (in cm) are indicated in the...

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

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

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

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

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Six charges are placed around a regular hexagon of side length 𝑎 as shown in the figure. Five of them...

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

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

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The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $\mathrm{R}_1$ to $\mathrm{R}_8$, and two ideal batteries...

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Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is...

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

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

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

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

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

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A solid sphere of mass 1 kg and radius 1 m rolls without slipping on a fixed inclined plane with...

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At time $t=0$, a disk of radius 1 m starts to roll without slipping on a horizontal plane with an...

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In the given P-V diagram, a monoatomic gas $\left(y=\frac{5}{3}\right)$ is first compressed adiabatically from state A state B. Then it...

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A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index...

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

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

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In Circuit-1 and Circuit-2 shown in the figures, $\mathrm{R}_1=1 \Omega, \mathrm{R}_2=2 \Omega$ and $\mathrm{R}_3=3 \Omega$. $P_1$ and $P_2$ are the...

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In the figure, the inner (shaded) region $A$ represents a sphere of radius $\mathrm{r}_{\mathrm{A}}=1$, within which the electrostatic charge density...

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

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

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

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

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

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Two resistances $\mathrm{R}_1=\mathrm{X} \Omega$ and $\mathrm{R}_2=1 \Omega$ are connected to a wire AB of uniform resistivity, as shown in the...

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In a radioactive decay chain reaction, ${ }_{90}^{230} \mathrm{Th}$ nucleus decays into ${ }_{84}^{214} \mathrm{Po}$ nucleus. The ratio of the...

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A particle of mass 1 kg is subjected to a force which depends on the position as $\overline{\mathrm{F}}=-\mathrm{k}(\hat{\mathrm{xi}}+\hat{\mathrm{yj}}) \mathrm{kgms}^{-2}$ with...

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

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In the following circuit $\mathrm{C}_1=12 \mu \mathrm{~F}, \mathrm{C}_2=\mathrm{C}_3=4 \mu \mathrm{~F}$ and $\mathrm{C}_4=\mathrm{C}_5=2 \mu \mathrm{~F}$. The charge stored in $\mathrm{C}_3$ is...

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The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction $...

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Two spherical stars $A$ and $B$ have densities $\rho_A$ and $\rho_B$, respectively. $A$ and $B$ have the same radius, and...

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