Q JEE Advance 2008

Match the compounds in Column I with their characteristic test(s)/reactions(s) given in Column II. Indicate your answer by darkening the...

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Q JEE Advance 2008

Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening...

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Q JEE Advance 2008

Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening...

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Q JEE Advance 2008

A t tertiary alcohol H upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J...

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Q JEE Advance 2008

A t tertiary alcohol H upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J...

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Q JEE Advance 2008

The nuclear charges (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho(r)$ [charge per unit...

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Q JEE Advance 2008

A t tertiary alcohol H upon acid catalysed dehydration gives a product I. Ozonolysis of I leads to compounds J...

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Q JEE Advance 2008

The nuclear charges (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho(r)$ [charge per unit...

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Q JEE Advance 2008

The nuclear charges (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $\rho(r)$ [charge per unit...

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Q JEE Advance 2008

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top...

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A uniform thin cylindrical disk of mass $M$ and radius $R$ is attached to two id enthical massless springs of...

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Q JEE Advance 2008

A uniform thin cylindrical disk of mass $M$ and radius $R$ is attached to two id enthical massless springs of...

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Q JEE Advance 2008

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top...

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Q JEE Advance 2008

A uniform thin cylindrical disk of mass $M$ and radius $R$ is attached to two id enthical massless springs of...

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Q JEE Advance 2008

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top...

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Q JEE Advance 2008

STATEMENT-1 : Aniline on reaction with $\mathrm{NaNO}_2 / \mathrm{HCl}$ at $0^{\circ} \mathrm{C}$ followed by coupling with $\beta$-naphthol gives a dark...

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Q JEE Advance 2008

STATEMENT-1 For an observer looking out through the window of a fast moving train, the nearby objects appear to move...

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Q JEE Advance 2008

STATEMENT-1: There is a natural asymmetry between converting work to heat and converting heat to work and STATEMENT-2: No process...

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STATEMENT-1: The geometrical isomers of the complex $\left[\mathrm{M}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]$ are optically inactive. and STATEMENT-2: Both geometrical isomers of the complex...

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Q JEE Advance 2008

STATEMENT-1 The sensitivity of a moving-coil galvanometer is increased by placing a suitable magnetic material as a core inside the...

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Q JEE Advance 2008

STATEMENT-1: $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right] \mathrm{SO}_4$ is paramagnetic. and STATEMENT-2: The Fe in $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_5 \mathrm{NO}\right] \mathrm{SO}_4$ has three unpaired electrons.

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Q JEE Advance 2008

STATEMENT-1 For practical purposes, the earth is used as a reference at zero potential in electrical circuits. and STATEMENT-2 The...

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Q JEE Advance 2008

Cellulose upon acetylation with excess acetic anhydride/ $\mathrm{H}_2 \mathrm{SO}_4$ (catalytic) gives cellulose triacetate whose structure is

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Q JEE Advance 2008

STATEMENT -1 It is easier to pull a heavy object than to push it on a level ground. and STATEMENT...

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Q JEE Advance 2008

A radioactive sample S 1 having an activity of $5 \mu \mathrm{Ci}$ has twice the number of nuclei as another...

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Q JEE Advance 2008

The correct stability order for the following species is

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Q JEE Advance 2008

Consider a system of three charges $\frac{\mathrm{q}}{3}, \frac{\mathrm{q}}{3}$ and $-\frac{2 \mathrm{q}}{3}$ placed at points $\mathrm{A}, \mathrm{B}$ and C , respectively,...

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Q JEE Advance 2008

A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \mathrm{~cm} /$ s...

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Q JEE Advance 2008

In the following reaction sequence, the correct structures of E, F and G are

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A block (B) attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure...

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Q JEE Advance 2008

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is...

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Q JEE Advance 2008

Among the following, the coloured compound is

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Q JEE Advance 2008

The IUPAC name of $\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{NiCl}_4\right]$ is

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Q JEE Advance 2008

A bob of mass M is suspended by a massless string of length L . The horizontal velocity V at...

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Q JEE Advance 2008

Both $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$ and $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ are diamagnetic. The hybridisations of nickel in these complexes, respectively are

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Q JEE Advance 2008

A parallel plate capacitor C with plates of unit area and separation s is filled with a liquid of dielectric...

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Q JEE Advance 2008

Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions...

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Q JEE Advance 2008

Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate...

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Q JEE Advance 2008

A vibrating string of certain length $\ell$ under a tension T resonates with a mode corresponding to the first overtone...

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Q JEE Advance 2008

A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II,...

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Q JEE Advance 2008

Solubility product constants $\left(\mathrm{K}_{s p}\right)$ of salts of types $\mathrm{MX}, \mathrm{MX}_2$ and $\mathrm{M}_3 \mathrm{X}$ at temperature " T " are...

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Q JEE Advance 2008

Consider the function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$ defined by Let $\mathrm{g}(\mathrm{x})=\int_0^{\mathrm{e}^{\mathrm{x}}} \frac{\mathrm{f}^{\prime}(\mathrm{t})}{1+\mathrm{t}^2} \mathrm{dt}$ Which of the following is true?

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Q JEE Advance 2008

Consider the function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$ defined by Which of the following is true?

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Q JEE Advance 2008

Consider the function $f:(-\infty, \infty) \rightarrow(-\infty, \infty)$ defined by Which of the following is true?

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Q JEE Advance 2008

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...

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Q JEE Advance 2008

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...

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Q JEE Advance 2008

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...

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Q JEE Advance 2008

Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$ The distance of the point (1,...

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Q JEE Advance 2008

Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$ The shortest distance between $\mathrm{L}_1$ and...

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Q JEE Advance 2008

In the following sequence, products I, J and L are formed. K represents a reagent. The structure of product L...

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Q JEE Advance 2008

Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$ The unit vector perpendicular to both...

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Q JEE Advance 2008

In the following sequence, products I, J and L are formed. K represents a reagent. $...

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Q JEE Advance 2008

In the following sequence, products I, J and L are formed. K represents a reagent. The structure of the product...

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Q JEE Advance 2008

Suppose four distinct positive numbers $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \mathrm{a}_4$ are in G.P. Let $\mathrm{b}_1=\mathrm{a}_1, \mathrm{~b}_2=\mathrm{b}_1+\mathrm{a}_2, \mathrm{~b}_3=\mathrm{b}_2+ \mathrm{a}_3$ and $\mathrm{b}_4=\mathrm{b}_3+\mathrm{a}_4$. STATEMENT-1:...

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Q JEE Advance 2008

There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...

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Q JEE Advance 2008

Let a solution $y=y(x)$ of the differential equation $x \sqrt{x^2-1} d y-y \sqrt{y^2-1} d x=0$ satisfy $y(2)=\frac{2}{\sqrt{3}}$. STATEMENT-1 : $...

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Q JEE Advance 2008

There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...

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Q JEE Advance 2008

Consider $$ \begin{aligned} & L_1: 2 x+3 y+p-3=0 \\ & L_2: 2 x+3 y+p+3=0 \end{aligned} $$ where $p$ is a...

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Q JEE Advance 2008

There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...

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Q JEE Advance 2008

Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $...

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Q JEE Advance 2008

STATEMENT-1: $\quad \mathrm{Pb}^{4+}$ compounds are stronger oxidizing agents than $\mathrm{Sn}^{4+}$ compounds. and STATEMENT-2: The higher oxidation states for the group...

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Q JEE Advance 2008

STATEMENT-1: Bromobenzene upon reaction with $\mathrm{Br}_2 / \mathrm{Fe}$ gives 1,4 - dibromobenzene as the major product. and STATEMENT-2: In bromobenzene,...

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Q JEE Advance 2008

STATEMENT-1: The plot of atomic number ( y -axis) versus number of neutrons ( x -axis) for stable nuclei shows...

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Q JEE Advance 2008

A small block of mass $M$ moves on a frictionless surface of an inclined plane, as shown in figure. The...

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Q JEE Advance 2008

A small block of mass $M$ moves on a frictionless surface of an inclined plane, as shown in figure. The...

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Q JEE Advance 2008

STATEMENT-1: For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero. and STATEMENT-2: At constant temperature and...

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Q JEE Advance 2008

Let the function $\mathrm{g}:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $\mathrm{g}(\mathrm{u})=2 \tan ^{-1}\left(\mathrm{e}^{\mathrm{u}}\right)-\frac{\pi}{2}$. Then, g is

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Q JEE Advance 2008

A small block of mass $M$ moves on a frictionless surface of an inclined plane, as shown in figure. The...

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Q JEE Advance 2008

A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{3}{3}\right)$ is trapped inside a liquid of density $\rho_{\ell}$ (see figure). Assume that...

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Q JEE Advance 2008

A particle $P$ starts from the point $z_0=1+2 i$, where $i=\sqrt{-1}$. It moves first horizontally away from origin by 5...

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Q JEE Advance 2008

A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{3}{3}\right)$ is trapped inside a liquid of density $\rho_{\ell}$ (see figure). Assume that...

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Q JEE Advance 2008

A solution of colourless salt $\mathbf{H}$ on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after...

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Q JEE Advance 2008

Consider a branch of the hyperbola $x^2-2 y^2-2 \sqrt{2} x-4 \sqrt{2} y-6=0$ with vertex at the point $A$. Let $B$...

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Q JEE Advance 2008

A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{3}{3}\right)$ is trapped inside a liquid of density $\rho_{\ell}$ (see figure). Assume that...

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Q JEE Advance 2008

The correct statement (s) concerning the structures E, F and G is (are)

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Q JEE Advance 2008

The area of the region between the curves $y=\sqrt{\frac{1+\sin x}{\cos x}}$ and $y=\sqrt{\frac{1-\sin x}{\cos x}}$ bounded by the lines $x=0$...

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Q JEE Advance 2008

The correct statement (s) about the compound given below is (are)

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In a mixture of $\mathrm{H}-\mathrm{He}^{+}$gas ( $\mathrm{He}^{+}$is singly ionized He atom), H atoms and $\mathrm{He}^{+}$ions are excited to their respective...

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Q JEE Advance 2008

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A...

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Q JEE Advance 2008

A gas described by van der Waal’s equation

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Aqueous solutions of $\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ on reaction with $\mathrm{Cl}_2$ gives

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Q JEE Advance 2008

In a mixture of $\mathrm{H}-\mathrm{He}^{+}$gas ( $\mathrm{He}^{+}$is singly ionized He atom), H atoms and $\mathrm{He}^{+}$ions are excited to their respective...

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Q JEE Advance 2008

In a mixture of $\mathrm{H}-\mathrm{He}^{+}$gas ( $\mathrm{He}^{+}$is singly ionized He atom), H atoms and $\mathrm{He}^{+}$ions are excited to their respective...

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Q JEE Advance 2008

Hyperconjugation involves overlap of the following orbitals

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Consider three points. $P=(-\sin (\beta-\alpha),-\cos \beta), Q=(\cos (\beta-\alpha), \sin \beta)$ and $R=(\cos (\beta-\alpha+\theta), \sin (\beta-\theta))$, where $0

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Q JEE Advance 2008

STATEMENT-1 An astronaut in an orbiting space station above the Earth experiences weightlessness. and STATEMENT-2 An object moving around the...

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Q JEE Advance 2008

The major product of the following reaction is

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STATEMENT-1 In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put...

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Q JEE Advance 2008

Let non-collinear unit vectors â and $\hat{b}$ form an acute angle. A point P moves so that at any time...

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STATEMENT-1 Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously...

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Q JEE Advance 2008

Under the same reaction conditions, initial concentration of $1.386 \mathrm{~mol} \mathrm{dm}^{-3}$ of a substance becomes half in 40 seconds and...

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Q JEE Advance 2008

Let $g(x)=\log f(x)$ where $f(x)$ is a twice differentiable positive function on $(0, \infty)$ such that $f(x+1)= \mathrm{x} \mathrm{f}(\mathrm{x})$. Then,...

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Q JEE Advance 2008

2.5 mL of $\frac{2}{5} \mathrm{M}$ weak monoacidic base $\left(\mathrm{K}_{\mathrm{b}}=1 \times 10^{-12}\right.$ at $\left.25^{\circ} \mathrm{C}\right)$ is titrated with $\frac{2}{15} \mathrm{M} \mathrm{HCl}$...

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Q JEE Advance 2008

Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of

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STATEMENT-1 The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain...

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Q JEE Advance 2008

A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as...

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Q JEE Advance 2008

Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use...

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Q JEE Advcance 2008

The balls, having linear momenta $\overrightarrow{\mathrm{p}}_1=\mathrm{p} \hat{\mathrm{i}}$ and $\overrightarrow{\mathrm{p}}_2=-\mathrm{p} \hat{\mathrm{i}}$, undergo a collision in free space. There is no external...

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Q JEE Advance 2008

In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light...

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Q JEE Advance 2008

Figure shows three resistor configurations R1, R2 and R3 connected to 3V battery. If the power dissipated by the configuration...

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Q JEE Advance 2008

Students I, II and III perform an experiment for measuring the acceleration due to gravity ( g ) using a...

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A spherically symmetric gravitational system of particles has a mass density $...

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An ideal gas is expanding such that $\mathrm{PT}^2=$ constant. The coefficient of volume expansion of the gas is

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Q JEE Advance 2008

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

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Q JEE Advance 2008

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is...

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Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be three sets of complex numbers as defined below $$ \begin{aligned} & A=\{z: \operatorname{Im} z \geq...

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Q JEE Advance 2008

Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be three sets of complex numbers as defined below $$ \begin{aligned} & A=\{z: \operatorname{Im} z \geq...

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Q JEE Advance 2008

Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be three sets of complex numbers as defined below $$ \begin{aligned} & A=\{z: \operatorname{Im} z \geq...

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Q JEE Advance 2008

A circle $C$ of radius 1 is inscribed in an equilateral triangle $P Q R$. The points of contact of...

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Q JEE Advance 2008

A circle $C$ of radius 1 is inscribed in an equilateral triangle $P Q R$. The points of contact of...

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Q JEE Advance 2008

A circle $C$ of radius 1 is inscribed in an equilateral triangle $P Q R$. The points of contact of...

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Q JEE Advance 2008

Consider the functions defined implicitly by the equation $y^3-3 y+x=0$ on various intervals in the real line. If $...

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Q JEE Advance 2008

Consider the functions defined implicitly by the equation $y^3-3 y+x=0$ on various intervals in the real line. If $...

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Q JEE Advance 2008

Consider the functions defined implicitly by the equation $y^3-3 y+x=0$ on various intervals in the real line. If $...

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Consider three planes $$ \begin{aligned} & P_1: x-y+z=1 \\ & P_2: x+y-z=-1 \\ & P_3: x-3 y+3 z=2 . \end{aligned}...

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Q JEE Advance 2008

Let $f$ and $g$ be real valued functions defined on interval $(-1,1)$ such that $g^{\prime \prime}(x)$ is continuous, $...

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Consider the system of equations $$ \begin{aligned} & x-2 y+3 z=-1 \\ & -x+y-2 z=k \\ & x-3 y+4 z=1...

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Consider the system of equations $\mathrm{ax}+\mathrm{by}=0, \mathrm{cx}+\mathrm{dy}=0$, where $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} \in\{0,1\}$. STATEMENT -1 : The probability that the...

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Q JEE Advance 2008

Let $\mathrm{S}_{\mathrm{n}}=\sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{\mathrm{n}}{\mathrm{n}^2+\mathrm{kn}+\mathrm{k}^2}$ and $\mathrm{T}_{\mathrm{n}}=\sum_{\mathrm{k}=0}^{\mathrm{n}-1} \frac{\mathrm{n}}{\mathrm{n}^2+\mathrm{kn}+\mathrm{k}^2}$ for $\mathrm{n}=1,2,3, \ldots$. Then,

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Let $\mathrm{P}\left(\mathrm{x}_1, \mathrm{y}_1\right)$ and $\mathrm{Q}\left(\mathrm{x}_2, \mathrm{y}_2\right), \mathrm{y}_1

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A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and...

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Let $\mathrm{f}(\mathrm{x})$ be a non-constant twice differentiable function defined on $(-\infty, \infty)$ such that $\mathrm{f}(\mathrm{x})=\mathrm{f}(1-\mathrm{x})$ and $\mathrm{f}^{\prime}\left(\frac{1}{4}\right)=0$. Then (A) (B)...

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Q JEE Advance 2008

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors $\hat{a}, \hat{b}, \hat{c}$ such...

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Consider the two curves $C_1: y^2=4 x, C_2: x^2+y^2-6 x+1=0$. Then,

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Q JEE Advance 2008

Let $\mathrm{g}(\mathrm{x})=\frac{(\mathrm{x}-1)^{\mathrm{n}}}{\log \cos ^{\mathrm{m}}(\mathrm{x}-1)} ; 0

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Q JEE Advance 2008

The total number of local maxima and local minima of the function $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{ll}(2+\mathrm{x})^3, & -3

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Q JEE Advance 2008

Let $a$ and $b$ be non-zero real numbers. Then, the equation $\left(a x^2+b y^2+c\right)\left(x^2-5 x y+6 y^2\right)=0$ represents

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