Q JEE ADVANCE 2010

A binary star consists of two stars A (mass $2.2 \mathrm{M}_{\mathrm{s}}$ ) and B (mass $11 \mathrm{M}_{\mathrm{s}}$ ), where $\mathrm{M}_{\mathrm{s}}$...

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Q JEE ADVANCE 2010

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m...

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When two progressive waves $y_1=4 \sin (2 x-6 t)$ and $y_2=3 \sin \left(2 x-6 t-\frac{\pi}{2}\right)$ are superimposed, the amplitude of...

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Q JEE ADVANCE 2010

Two spherical bodies A (radius 6 cm ) and B (radius 18 cm ) are at temperature $\mathrm{T}_1$ and $\mathrm{T}_2$,...

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Q JEE ADVANCE 2010

When two identical batteries of internal resistance $1 \Omega$ each are connected in series across a resistor R, the rate...

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Q JEE ADVANCE 2010

An $\alpha$ - particle and a proton are accelerated from rest by a potential difference of 100 V . After...

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Q JEE ADVANCE 2010

The focal length of a thin biconvex lens is 20 cm . When an object is moved from a distance...

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Q JEE ADVANCE 2010

A stationary source is emitting sound at a fixed frequency $f_0$, which is reflected by two cars approaching the source....

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Q JEE ADVANCE 2010

Gravitational acceleration on the surface of a planet is $\frac{\sqrt{6}}{11} \mathrm{~g}$, where g is the gravitational acceleration on the surface...

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Q JEE ADVANCE 2010

A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat $=3.36 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1}$ )...

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Q JEE ADVANCE 2010

When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$ it performs...

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Q JEE ADVANCE 2010

When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$ it performs...

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Q JEE ADVANCE 2010

When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$ it performs...

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Q JEE ADVANCE 2010

Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is...

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Q JEE ADVANCE 2010

Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is...

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Q JEE ADVANCE 2010

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an...

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Q JEE ADVANCE 2010

A few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on...

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Q JEE ADVANCE 2010

A student uses a simple pendulum of exactly 1 m length to determine g , the acceleration due to gravity....

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Q JEE ADVANCE 2010

One mole of an ideal gas in initial state $A$ undergoes a cyclic process ABCA , as shown in the...

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Q JEE ADVANCE 2010

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg . After their collision,...

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Q JEE ADVANCE 2010

A real gas behaves like an ideal gas if its

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Q JEE ADVANCE 2010

Consider a thin square sheet of side L and thickness t , made of a material of resistivity $\rho$. The...

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Q JEE ADVANCE 2010

A thin uniform annular disc (see figure) of mass M has outer radius 4 R and inner radius 3R. The...

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Q JEE ADVANCE 2010

A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block...

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Q JEE ADVANCE 2010

A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in...

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Q JEE ADVANCE 2010

An AC voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance...

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Q JEE ADVANCE 2010

To Verify Ohm's law, a student is provided with a test resistor $R_T$, a high resistance $R_1$, a small resistance...

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Q JEE ADVANCE 2010

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature....

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Q JEE Advance 2010

The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron...

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Q JEE Advance 2010

The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron...

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Q JEE Advance 2010

The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron...

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Q JEE Advance 2010

When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of...

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Q JEE Advance 2010

When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of...

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Q JEE Advance 2010

When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of...

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Q JEE Advance 2010

At time $\mathrm{t}=0$, a battery of 10 V is connected across points A and B in the given circuit. If...

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Q JEE Advance 2010

A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas...

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Q JEE Advance 2010

To determine the half life of a radioactive element, a student plots a graph of $\ell \mathrm{n}\left|\frac{\mathrm{dN}(\mathrm{t})}{\mathrm{dt}}\right|$ versus t ....

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Q JEE Advance 2010

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed...

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Q JEE Advance 2010

A large glass slab $(\mu=5 / 3)$ of thickness 8 cm is placed over a point source of light on...

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Q JEE Advance 2010

A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long...

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Q JEE Advance 2010

A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens...

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Q JEE Advance 2010

A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale...

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Q JEE Advance 2010

A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric...

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Q JEE Advance 2010

A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $\sigma$ per unit area. It...

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Q JEE Advance 2010

A block of mass 2 kg is free to move along the x -axis. It is at rest and from...

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Q JEE ADVANCE 2010

If the distance between the plane $A x-2 y+z=d$ and the plane containing the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is $\sqrt{6}$,...

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Q JEE ADVANCE 2010

The line $2 x+y=1$ is tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If this line passes through the point of intersection of...

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Q JEE ADVANCE 2010

If $\vec{a}$ and $\vec{b}$ are vectors in space given by $\vec{a}=\frac{\hat{i}-2 \hat{j}}{\sqrt{5}}$ and $\vec{b}=\frac{2 \hat{i}+\hat{j}+3 \hat{k}}{\sqrt{14}}$, then the value of...

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Q JEE ADVANCE 2010

The maximum value of the expression $\frac{1}{\sin ^2 \theta+3 \sin \theta \cos \theta+5 \cos ^2 \theta}$ is

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Q JEE ADVANCE 2010

The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{\mathrm{n} \pi}{5}$ for $...

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Q JEE ADVANCE 2010

Let $f$ be a real-valued differentiable function on $R$ (the set of all real numbers) such that $f(1)=1$. If the...

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Q JEE ADVANCE 2010

The number of all possible values of $\theta$, where $0

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Q JEE ADVANCE 2010

Let $S_k, k=1,2, \ldots ., 100$, denote the sum of the infinite geometric series whose first term is $\frac{k-1}{k!}$ and...

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Q JEE ADVANCE 2010

Let p be an odd prime number and $\mathrm{T}_{\mathrm{p}}$ be the following set of $2 \times 2$ matrices : $$...

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Q JEE ADVANCE 2010

Let p be an odd prime number and $\mathrm{T}_{\mathrm{p}}$ be the following set of $2 \times 2$ matrices : $$...

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Q JEE Advance 2010

Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.The equation...

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Q JEE Advance 2010

Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.The orthocentre...

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Q JEE ADVANCE 2010

The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$. Equation of the circle with AB...

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Q JEE ADVANCE 2010

Let p be an odd prime number and $\mathrm{T}_{\mathrm{p}}$ be the following set of $2 \times 2$ matrices : $$...

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Q JEE Advance 2010

Tangents are drawn from the point $P(3,4)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points $A$ and $B$.The coordinates...

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Q JEE ADVANCE 2010

The circle $x^2+y^2-8 x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points $A$ and $B$. Equation of a common tangent with...

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Q JEE Advance 2010

Consider the polynomial $\mathrm{f}(\mathrm{x})=1+2 \mathrm{x}+3 \mathrm{x}^2+4 \mathrm{x}^3$. Let s be the sum of all distinct real roots of $\mathrm{f}(\mathrm{x})$ and...

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Q JEE Advance 2010

Consider the polynomial $\mathrm{f}(\mathrm{x})=1+2 \mathrm{x}+3 \mathrm{x}^2+4 \mathrm{x}^3$. Let s be the sum of all distinct real roots of $\mathrm{f}(\mathrm{x})$ and...

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Q JEE Advance 2010

Consider the polynomial $\mathrm{f}(\mathrm{x})=1+2 \mathrm{x}+3 \mathrm{x}^2+4 \mathrm{x}^3$. Let s be the sum of all distinct real roots of $\mathrm{f}(\mathrm{x})$ and...

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Q JEE ADVANCE 2010

Let $A$ and $B$ be two distinct points on the parabola $y^2=4 x$. If the axis of the parabola touches...

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Q JEE ADVANCE 2010

Let ABC be a triangle such that $\angle \mathrm{ACB}=\frac{\pi}{6}$ and let $\mathrm{a}, \mathrm{b}$ and c denote the lengths of the...

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Q JEE Advance 2010

Consider a triangle ABC and let $\mathrm{a}, \mathrm{b}$ and c denote the lengths of the sides opposite to vertices $...

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Q JEE Advance 2010

Two parallel chords of a circle of radius 2 are at a distance $\sqrt{3}+1$ apart. If the chords subtend at...

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Q JEE Advance 2010

Let k be a positive real number and let $...

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Q JEE Advance 2010

Let f be a function defined on R (the set of all real numbers) such that $\mathrm{f}^{\prime}(\mathrm{x})=2010(\mathrm{x}-2009)(\mathrm{x}-2010)^2 (x-2011)^3(x-2012)^4$, for all...

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Q JEE Advance 2010

Let $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \ldots, \mathrm{a}_{11}$ be real numbers satisfying $\mathrm{a}_1=15,27-2 \mathrm{a}_2>0$ and $\mathrm{a}_{\mathrm{k}}=2 \mathrm{a}_{\mathrm{k}-1}-\mathrm{a}_{\mathrm{k}-2}$ for $\mathrm{k}=3,4, \ldots$, 11. If...

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Q JEE Advance 2010

Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal...

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Q JEE Advance 2010

Let f be a real-valued function defined on the interval $(-1,1)$ such that $e^{-x} f(x)=2+\int_0^x \sqrt{t^4+1} d t$, for all...

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Q JEE Advance 2010

For $r=0,1, \ldots, 10$, let $A_r, B_r$ and $C_r$ denote, respectively, the coefficient of $x^r$ in the expansions of $(1+x)^{10}$,...

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Q JEE Advance 2010

Two adjacent sides of a parallelogram ABCD are given by $\overrightarrow{A B}=2 \hat{i}+10 \hat{j}+11 \hat{k}$ and $\overrightarrow{A D}=-\hat{i}+2 \hat{j}+2 \hat{k}$....

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Q JEE Advance 2010

A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and...

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Q JEE Advance 2010

If the distance of the point $\mathrm{P}(1,-2,1)$ from the plane $\mathrm{x}+2 \mathrm{y}-2 \mathrm{z}=\alpha$, where $\alpha>0$, is 5 , then the...

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Q JEE ADVANCE 2010

The value(s) of $\int_0^1 \frac{x^4(1-x)^4}{1+x^2} d x$ is (are)

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Let $z_1$ and $z_2$ be two distinct complex numbers and let $z=(1-t) z_1+t z_2$ for some real number $t$ with...

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Q JEE ADVANCE 2010

Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{\mathrm{x}}{3}=\frac{\mathrm{y}}{4}=\frac{\mathrm{z}}{2}$ and...

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Q JEE ADVANCE 2010

If the angles $\mathrm{A}, \mathrm{B}$ and C of a triangle are in an arithmetic progression and if $\mathrm{a}, \mathrm{b}$ and...

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Q JEE ADVANCE 2010

Let $f, g$ and $h$ be real-valued functions defined on the interval $[0,1]$ by $f(x)=e^{x^2}+e^{-x^2}, g(x) =x e^{x^2}+e^{-x^2}$ and $...

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Q JEE ADVANCE 2010

Let $p$ and $q$ be real numbers such that $p \neq 0, p^3 \neq q$ and $p^3 \neq-q$. If $\alpha$...

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Q JEE ADVANCE 2010

The value of $\lim _{x \rightarrow 0} \frac{1}{x^3} \int_0^x \frac{t \ln (1+t)}{t^4+4} d t$ is

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Q JEE ADVANCE 2010

The number of $3 \times 3$ matrices $A$ whose entries are either 0 or 1 and for which the system...

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Q JEE ADVANCE 2010

Let $P, Q, R$ and $S$ be the points on the plane with position vectors $...

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Q JEE ADVANCE 2010

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. A fair die is thrown three times....

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Q JEE ADVANCE 2010

The value of n in the molecular formula $\mathrm{Be}_{\mathrm{n}} \mathrm{Al}_2 \mathrm{Si}_6 \mathrm{O}_{18}$ is

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Q JEE ADVANCE 2010

Based on VSEPR theory, the number of 90 degree $\mathrm{F}-\mathrm{Br}-\mathrm{F}$ angles in $\mathrm{BrF}_5$ is

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Q JEE ADVANCE 2010

Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is

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Q JEE ADVANCE 2010

Amongst the following, the total number of compound soluble in aqueous NaOH is

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Q JEE ADVANCE 2010

In the scheme given below, the total number of intra molecular aldol condensation products formed from ' Y ' is

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Q JEE ADVANCE 2010

The total number of cyclic isomers possible for a hydrocarbon with the molecular formula $\mathrm{C}_4 \mathrm{H}_6$ is

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Q JEE ADVANCE 2010

The total number of basic groups in the following form of lysine is

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The number of neutrons emitted when ${ }_{92}^{235} \mathrm{U}$ undergoes controlled nuclear fission to ${ }_{34}^{142} \mathrm{Xe}$ and $...

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Q JEE Advance 2010

The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $\mathrm{S}_1$ with one radial node. Upon absorbing light the ion...

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The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $\mathrm{S}_1$ with one radial node. Upon absorbing light the ion...

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Q JEE Advance 2010

The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $\mathrm{S}_1$ with one radial node. Upon absorbing light the ion...

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Q JEE Advance 2010

Two aliphatic aldehydes P and Q react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R , which...

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Q JEE ADVANCE 2010

The concentration of R in the reaction $\mathrm{R} \rightarrow \mathrm{P}$ was measured as a function of time and the following...

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Q JEE Advance 2010

Two aliphatic aldehydes P and Q react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R , which...

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Q JEE Advance 2010

Two aliphatic aldehydes P and Q react in the presence of aqueous $\mathrm{K}_2 \mathrm{CO}_3$ to give compound R , which...

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Q JEE Advance 2010

$$ \text { Total number of geometrical isomers for the complex }\left[\mathrm{RhCl}(\mathrm{CO})\left(\mathrm{PPh}_3\right)\left(\mathrm{NH}_3\right)\right] \text { is } $$

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Q JEE Advance 2010

The total number of dirpotic acids among the following is$$ \begin{array}{ccccc} \mathrm{H}_3 \mathrm{PO}_4 & \mathrm{H}_2 \mathrm{SO}_4 & \mathrm{H}_3 \mathrm{PO}_3 &...

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Q JEE Advance 2010

One mole of an ideal gas is taken from $a$ to $b$ along two paths denoted by the solid and...

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Q JEE Advance 2010

Among the following, the number of elements showing only one non-zero oxidation state is $...

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Q JEE ADVANCE 2010

A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL and 25.0 mL....

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Q JEE Advance 2010

Silver (atomic weight $=108 \mathrm{~g} \mathrm{~mol}^{-1}$ ) has a density of $10.5 \mathrm{~g} \mathrm{~cm}^{-3}$. The number of silver atoms on...

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Q JEE ADVANCE 2010

Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores...

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Q JEE Advanced 2010

The species having pyramidal shape is

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Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores...

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Q JEE Advance 2010

In the reaction the structure of the

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Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores...

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Q JEE ADVANCE 2010

The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting...

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Q JEE Advance 2010

The complex showing a spin-only magnetic moment of 2.82 B.M. is

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Q JEE Advance 2010

The packing efficiency of the two-dimensional square unit cell shown below is

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Q JEE ADVANCE 2010

The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting...

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Q JEE ADVANCE 2010

Among the following, the intensive property is (properties are)

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Q JEE Advance 2010

Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule $B_2$ is

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Q JEE ADVANCE 2010

The reagent(s) used for softening the temporary hardness of water is(are)

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Q JEE ADVANCE 2010

Aqueous solutions of $\mathrm{HNO}_3, \mathrm{KOH}, \mathrm{CH}_3 \mathrm{COOH}$, and $\mathrm{CH}_3 \mathrm{COONa}$ of identical concentrations are provided. The pair (s) of solutions...

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Q JEE ADVANCE 2010

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The ionization isomer of $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}$ is

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Q JEE ADVANCE 2010

In the Newman projection for 2,2-dimethylbutane

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Q JEE Advance 2010

The compounds P, Q and S

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Q JEE ADVANCE 2010

The correct structure of ethylenediaminetetraacetic acid (EDTA) is

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Q JEE ADVANCE 2010

The bond energy (in $\mathbf{k c a l ~ m o l}^{-\mathbf{1}}$ ) of a $\mathrm{C}-\mathrm{C}$ single bond is approximately

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Q JEE ADVANCE 2010

The species which by definition has ZERO standard molar enthalpy of formation at 298 K is

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Q JEE ADVANCE 2010

Plots showing the variation of the rate constant ( $k$ ) with temperature ( $T$ ) are given below. The...

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Q JEE ADVANCE 2010

The correct statement about the following disaccharide is

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Q JEE ADVANCE 2010

In the reaction the products are

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Q JEE ADVANCE 2010

The synthesis of 3 – octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an...

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