Q JEE Advance2007

Match the statements in Column I with the properties Column II and indicate your answer by darkening the appropriate bubbles...

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Q JEE Advance2007

Let $(\mathrm{x}, \mathrm{y})$ be such that $$ \sin ^{-1}(a x)+\cos ^{-1}(y)+\cos ^{-1}(b x y)=\frac{\pi}{2} . $$ Match the statements in...

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Q JEE Advance2007

Let $f(x)=\frac{x^2-6 x+5}{x^2-5 x+6}$. Match the conditions / expressions in Column I with statements in Column II and indicate your...

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Q JEE Advance2007

Let $\mathrm{A}_1, \mathrm{G}_1, \mathrm{H}_1$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $...

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Q JEE Advance2007

Let $\mathrm{A}_1, \mathrm{G}_1, \mathrm{H}_1$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $...

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Q JEE Advance2007

If a continuous $f$ defined on the real line $R$, assumes positive and negative values in $R$ then the equation...

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Q JEE Advance2007

If a continuous $f$ defined on the real line $R$, assumes positive and negative values in $R$ then the equation...

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Q JEE Advance2007

If a continuous $f$ defined on the real line $R$, assumes positive and negative values in $R$ then the equation...

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Q JEE Advance2007

STATEMENT -1 : The curve $\mathrm{y}=\frac{-\mathrm{x}^2}{2}+\mathrm{x}+1$ is symmetric with respect to the line $\mathrm{x}=1$. because STATEMENT -2 : A parabola...

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Q JEE Advance2007

Lines $\mathrm{L}_1: \mathrm{y}-\mathrm{x}=0$ and $\mathrm{L}_2: 2 \mathrm{x}+\mathrm{y}=0$ intersect the line $\mathrm{L}_3: \mathrm{y}+2=0$ at P and Q , respectively. The bisector...

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Q JEE Advance2007

Consider the planes $3 x-6 y-2 z=15$ and $2 x+y-2 z=5$. STATEMENT -1 : The parametric equations of the line...

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Q JEE Advance2007

Let $f(x)=2+\cos x$ for all real $x$. STATEMENT -1 : For each real $t$, there exists a point $c$ in...

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Q JEE Advance2007

Let $\mathrm{E}^{\mathrm{c}}$ denote the complement of an event E . Let $\mathrm{E}, \mathrm{F}, \mathrm{G}$ be pairwise independent events with $\mathrm{P}(\mathrm{G})>0$...

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Q JEE Advance2007

The differential equation $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}$ determines a family of circles with

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Q JEE Advance2007

Let $\mathrm{O}(0,0), \mathrm{P}(3,4), \mathrm{Q}(6,0)$ be the vertices of the triangle OPQ . The point R inside the triangle OPQ is...

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Q JEE Advance2007

Let ABCD be a quadrilateral with area 18 , with side AB parallel to the side CD and $\mathrm{AB}=2 \mathrm{CD}$....

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Q JEE Advance2007

If $|z|=1$ and $z \neq \pm 1$, then all the values of $\frac{z}{1-z^2}$ lie on

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Q JEE Advance2007

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in...

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Q JEE Advance2007

$\frac{d^2 x}{d y^2}$ equals

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Q JEE Advance2007

Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$. Which one of the following is correct?

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Q JEE Advance2007

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer...

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Q JEE Advance2007

Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkenin the appropriate bubbles...

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Q JEE Advance2007

Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer...

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Q JEE Advance2007

Redox reactions play a pivotal role in chemistry and biology. The values of standard redox potential ( $\mathrm{E}^{\circ}$ ) of...

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Q JEE Advance2007

Redox reactions play a pivotal role in chemistry and biology. The values of standard redox potential ( $\mathrm{E}^{\circ}$ ) of...

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Q JEE Advance2007

Redox reactions play a pivotal role in chemistry and biology. The values of standard redox potential ( $\mathrm{E}^{\circ}$ ) of...

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Q JEE Advance2007

Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction...

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Q JEE Advance2007

Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction...

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Q JEE Advance2007

Reimer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction...

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Q JEE Advance2007

STATEMENT-1: Glucose gives a reddish-brown precipitate with Fehling's solution. because STATEMENT-2: Reaction of glucose with Fehling's solution gives CuO and...

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Q JEE Advance2007

STATEMENT-1: Band gap in germanium is small. because STATEMENT-2: The energy spread of each germanium atomic energy level is infinitesimally...

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Q JEE Advance2007

STATEMENT-1: Alkali metals dissolves in liquid ammonia to give blue solution because STATEMENT-2: Alkali metals in liquid ammonia give solvated...

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Q JEE Advance2007

STATEMENT-1: Molecules that are not superimposable on their mirror images are chiral because STATEMENT-2: All chiral molecules have chiral centres.

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Q JEE Advance2007

A solution of metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give...

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Q JEE Advance2007

The number of stereoisomers obtained by bromination of trans-2-butene is

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Q JEE Advance2007

Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles...

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Q JEE Advance2007

A positron is emitted from ${ }^{23} \mathrm{Na}_{11}$. The ratio of the atomic mass and atomic number of the resulting...

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Q JEE Advance2007

Among the following metal carbonyls, the $\mathrm{C}-\mathrm{O}$ bond order is lowest in

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Q JEE Advance2007

Consider a reaction $\mathrm{aG}+\mathrm{bH} \rightarrow$ Products. When concentration of both the reactants G and H is doubled, the rate increases...

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Q JEE Advance2007

Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E . Compound E on further treatment...

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Q JEE Advance2007

For the process $\mathrm{H}_2 \mathrm{O}(\mathrm{l})(1$ bar, 373 K$) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})(1$ bar, 373 K$)$, the correct set of thermodynamic parameters...

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Q JEE Advance2007

Among the following, the least stable resonance structure is

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Q JEE Advance2007

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match...

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Q JEE Advance2007

Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting...

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Q JEE Advance2007

Column I describe some situations in which a small object moves. Column II describes some characteristics of these motions. Match...

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Two trains A and B are moving with speeds $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$ respectively in...

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Q JEE Advance2007

Two trains A and B are moving with speeds $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$ respectively in...

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Q JEE Advance2007

Two trains A and B are moving with speeds $20 \mathrm{~m} / \mathrm{s}$ and $30 \mathrm{~m} / \mathrm{s}$ respectively in...

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Q JEE Advance2007

The figure shows a surface XY separating two transparent media, medium -1 and medium -2. The lines ab and cd...

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Q JEE Advance2007

The figure shows a surface XY separating two transparent media, medium -1 and medium -2. The lines ab and cd...

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Q JEE Advance2007

STATEMENT-1 A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging...

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Q JEE Advance2007

STATEMENT-1 The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5...

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Q JEE Advance2007

STATEMENT-1 If there is no external torque on a body about its center of mass, then the velocity of the...

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STATEMENT-1 A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current...

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A particle moves in the $X-Y$ plane under the influence of a force such that its linear momentum is $...

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Q JEE Advance2007

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The...

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Q JEE Advance2007

In the experiment to determine the speed of sound using a resonance column,

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Q JEE Advance2007

Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right)$ and $\left(0,0, \frac{-a}{2}\right)$, respectively. The work done...

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Q JEE Advance2007

A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method....

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Q JEE Advance2007

Electrons with de-Broglie wavelength $\lambda$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted Xrays...

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Q JEE Advance2007

A small object of uniform density rolls up a curved surface with an initial velocity v . It reaches up...

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Q JEE Advance2007

A magnetic field $\vec{B}=B_0 \hat{j}$ exists in the region $a

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Q JEE Advance2007

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown...

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Q JEE Advance2007

Let $V_r$ denote the sum of the first $r$ terms of an arithmetic progression (A.P.) whose first term is $r$...

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Q JEE Advance2007

Let $V_r$ denote the sum of the first $r$ terms of an arithmetic progression (A.P.) whose first term is $r$...

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Q JEE Advance2007

Let $V_r$ denote the sum of the first $r$ terms of an arithmetic progression (A.P.) whose first term is $r$...

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Q JEE Advance2007

Consider the circle $x^2+y^2=9$ and the parabola $y^2=8 x$. They intersect at $P$ and $Q$ in the first and the...

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Q JEE Advance2007

Consider the circle $x^2+y^2=9$ and the parabola $y^2=8 x$. They intersect at $P$ and $Q$ in the first and the...

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Q JEE Advance2007

Consider the circle $x^2+y^2=9$ and the parabola $y^2=8 x$. They intersect at $P$ and $Q$ in the first and the...

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Q JEE Advance2007

Tangents are drawn from the point $(17,7)$ to the circle $x^2+y^2=169$. STATEMENT-1: The tangents are mutually perpendicular. because STATEMENT -...

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Q JEE Advance2007

Let $\mathrm{H}_1, \mathrm{H}_2, \ldots, \mathrm{H}_{\mathrm{n}}$ be mutually exclusive and exhaustive events with $\mathrm{P}\left(\mathrm{H}_{\mathrm{i}}\right)>0, \mathrm{i}=1,2, \ldots, \mathrm{n}$. Let E be any...

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Q JEE Advance2007

Let $\mathrm{F}(\mathrm{x})$ be an indefinite integral of $\sin ^2 \mathrm{x}$. STATEMENT -1: The function $\mathrm{F}(\mathrm{x})$ satisfies $\mathrm{F}(\mathrm{x}+\pi)=\mathrm{F}(\mathrm{x})$ for all real...

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Q JEE Advance2007

Let the vectors $\overrightarrow{\mathrm{PQ}}, \overrightarrow{\mathrm{QR}}, \overrightarrow{\mathrm{RS}}, \overrightarrow{\mathrm{ST}}, \overrightarrow{\mathrm{TU}}$ and $\overrightarrow{\mathrm{UP}}$ represent the sides of a regular hexagon. STATEMENT -1 :...

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Q JEE Advance2007

$\lim _{x \rightarrow \frac{\pi}{4}} \frac{\int_2^{\sec ^2 x} f(t) d t}{x^2-\frac{\pi^2}{16}}$ equals

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Q JEE Advance2007

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the...

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Q JEE Advance2007

The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\lambda^2 \hat{k}$ are...

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Q JEE Advance2007

Let $\alpha, \beta$ be the roots of the equation $x^2-p x+r=0$ and $\frac{\alpha}{2}, 2 \beta$ be the roots of the...

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Q JEE Advance2007

The number of solutions of the pair of equations $$ \begin{aligned} & 2 \sin ^2 \theta-\cos 2 \theta=0 \\ &...

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Q JEE Advance2007

Let $f(x)$ be differentiable on the interval $(0, \infty)$ such that $f(1)=1$, and $$ \lim _{t \rightarrow x} \frac{t^2 f(x)-x^2...

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Q JEE Advance2007

The tangent to the curve $\mathrm{y}=\mathrm{e}^{\mathrm{x}}$ drawn at the point $\left(\mathrm{c}, \mathrm{e}^{\mathrm{c}}\right)$ intersects the line joining the points $\left(\mathrm{c}-1, \mathrm{e}^{\mathrm{c}-1}\right)$...

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Q JEE Advance2007

A hyperbola, having the transverse axis of length $2 \sin \theta$, is confocal with the ellipse $3 x^2+4 y^2=12$. Then...

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Q JEE Advance2007

Match the chemical substances in Column-I with type of polymers/type of bonds in Column-II. Indicate your answer by darkening the...

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Q JEE Advance2007

Match gases under specified conditions listed in Column-I with their properties/laws in Column-II. Indicate your answer by darkening the appropriate...

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Q JEE Advance2007

Match the complexes in Column-I with their properties listed in Column-II. Indicate your answer by darkening t appropriate bubbles of...

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The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the...

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The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the...

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Q JEE Advance2007

The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the...

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Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately $6.023 \times 10^{23}$ ) are present...

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Q JEE Advance2007

Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately $6.023 \times 10^{23}$ ) are present...

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Q JEE Advance2007

Chemical reactions involve interaction of atoms and molecules. A large number of atoms/molecules (approximately $6.023 \times 10^{23}$ ) are present...

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Q JEE Advance2007

STATEMENT-1: In water, orthoboric acid behaves as a weak monobasic acid. because STATEMENT-2: In water, orthoboric acid acts as a...

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STATEMENT-1: Boron always forms covalent bond. because STATEMENT-2: The small size of $\mathrm{B}^{3+}$ favours formation of covalent bond.

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STATEMENT-1: Micelles are formed by surfactant molecules above the critical micellar concentration (CMC). because STATEMENT-2: The conductivity of a solution...

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STATEMENT-1: p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid. because STATEMENT-2: o-Hydroxybenzoic acid has intramolecular hydrogen bonding.

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Q JEE Advance2007

The reagent(s) for the following conversion,

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Extraction of zinc from zinc blende is achieved by

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The percentage of p -character in the orbitals forming $\mathrm{P}-\mathrm{P}$ bonds in $\mathrm{P}_4$ is

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Q JEE Advance2007

The species having bond order different from that in CO is

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Q JEE Advance2007

The value of $\log _{10} \mathrm{~K}$ for a reaction $\mathrm{A} \rightleftharpoons \mathrm{B}$ is (Given : $...

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Q JEE Advance2007

Among the following, the paramagnetic compound is

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Q JEE Advance2007

When 20 g of naphthoic acid $\left(\mathrm{C}_{11} \mathrm{H}_8 \mathrm{O}_2\right)$ is dissolved in 50 g of benzene $\left(\mathrm{K}_{\mathrm{f}}=1.72 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$,...

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Q JEE Advance2007

In the following reaction,

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Q JEE Advance2007

The number of structural isomers for $\mathrm{C}_6 \mathrm{H}_{14}$ is

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Q JEE Advance2007

(C)olumn I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives...

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Q JEE Advance2007

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your...

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Q JEE Advance2007

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed...

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Q JEE Advance2007

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and...

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Q JEE Advance2007

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and...

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Q JEE Advance2007

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and...

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A fixed thermally conducting cylinder has a radius R and height $\mathrm{L}_0$. The cylinder is open at its bottom and...

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Q JEE Advance2007

While the piston is at a distance 2 L from the top, the hole at the top is sealed. The...

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A fixed thermally conducting cylinder has a radius R and height $\mathrm{L}_0$. The cylinder is open at its bottom and...

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A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to...

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STATEMENT-1 If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change....

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Q JEE Advance2007

The formula connecting $u$, $v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very...

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Q JEE Advance2007

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere...

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Two particle of mass $m$ each are tied at the ends of a light string of length 2a. The whole...

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A ray of light travelling in water is incident on its surface open to air. The angle of incidence is...

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A resistance of $2 \Omega$ is connected across one gap of a metre-bridge (the length of the wire is 100...

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Q JEE Advance2007

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm . The smallest wavelength in the...

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Q JEE Advance2007

In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places...

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In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The...

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A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius Both the cylinders...

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A circuit is connected as shown in the figure with the switch S open. When the switch is closed the...

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