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JEE ADVANCE 2011

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE ADVANCE 2011
Match the statements given in Column I with the intervals/union of intervals given in Column II
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Q JEE ADVANCE 2011
Match the statements given in Column I with the values given in Column II
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Q JEE ADVANCE 2011
Let M be a $3 \times 3$ matrix satisfying $$ \mathbf{M}\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]=\left[\begin{array}{c} -1 \\ 2...
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Q JEE ADVANCE 2011
Let $y^{\prime}(x)+y(x) g^{\prime}(x)=g(x) g^{\prime}(x), y(0)=0, x \in \mathbb{R}$, where $f^{\prime}(x)$ denotes $\frac{d f(x)}{d x}$ and $g(x)$ is a given nonconstant...
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Q JEE ADVANCE 2011
The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is
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Q JEE ADVANCE 2011
Let $\omega=\mathrm{e}^{\mathrm{i} \mathrm{x} / 3}$, and $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{x}, \mathrm{y}, \mathrm{z}$ be non-zero complex numbers such that $$ \begin{aligned}...
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Q JEE ADVANCE 2011
The straight line $2 x-3 y=1$ divides the circular region $x^2+y^2 \leq 6$ into two parts. If $$ S=\left\{\left(2, \frac{3}{4}\right),\left(\frac{5}{2},...
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Q JEE ADVANCE 2011
Let $\mathrm{a}=-\hat{\mathrm{i}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=-\hat{\mathrm{i}}+\mathrm{j}$ and $\dot{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ be three given vectors. If $\dot{\mathrm{r}}$ is a vector such that $...
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Q JEE ADVANCE 2011
Let L be a normal to the parabola $\mathrm{y}^2=4 \mathrm{x}$. If L passes through the point $(9,6)$, then L is...
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Q JEE ADVANCE 2011
Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the...
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Q JEE ADVANCE 2011
Let $f:(0,1) \rightarrow \mathbb{R}$ be defined by $f(x)=\frac{b-x}{1-b x}$, where be is a constant such that $0
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Q JEE ADVANCE 2011
If $f(x)=\left\{\begin{array}{cc}-x-\frac{\pi}{2}, & x \leq-\frac{\pi}{2} \\ -\cos x, & -\frac{\pi}{2}
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Q JEE ADVANCE 2011
The circle passing through the point $(-1,0)$ and touching the $y$-axis at $(0,2)$ also passes through the point
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Q JEE ADVANCE 2011
Let $\omega \neq 1$ be a cube root of unity and S be the set of all non-singular matrices of...
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Q JEE ADVANCE 2011
A value of $b$ for which the equations $$ \begin{aligned} & x^2+b x-1=0 \\ & x^2+x+b=0 \end{aligned} $$ have one...
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Q JEE ADVANCE 2011
Let $P(6,3)$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If the normal at the point $P$ intersects the $x$-axis at...
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Q JEE ADVANCE 2011
Let $(x, y)$ be any point on the parabola $y^2=4 x$. Let $P$ be the point that divides the line...
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Q JEE ADVANCE 2011
Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x \in \mathbb{R}$. Then the set of all $x$ satisfying ( $...
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Q JEE Advance 2011
The minimum value of the sum of real numbers $\mathrm{a}^{-5}, \mathrm{a}^{-4}, 3 \mathrm{a}^{-3}, 1, \mathrm{a}^8$ and $\mathrm{a}^{10}$ with $\mathrm{a}>0$ is
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Q JEE Advance 2011
If $z$ is any complex number satisfying $|z-3-2 i| \leq 2$, then the minimum value of $|2 z-6+5 i|$ is
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Q JEE Advance 2011
Let $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \ldots, \mathrm{a}_{100}$ be an arithmetic progression with $\mathrm{a}_1=3$ and $\mathrm{S}_{\mathrm{p}}=\sum_{\mathrm{i}=1}^{\mathrm{p}} \mathrm{a}_{\mathrm{i}}, 1 \leq \mathrm{p} \leq 100$....
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Q JEE Advance 2011
The positive integer value of $\mathrm{n}>3$ satisfying the equation $\frac{1}{\sin \left(\frac{\pi}{\mathrm{n}}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{\mathrm{n}}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{\mathrm{n}}\right)}$ is
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Q JEE Advance 2011
Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function such that $f(1)=2$. If $6 \int_1^x f(t) d t=3 x f(x)-x^3$...
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Q JEE Advance 2011
Let $f(\theta)=\sin \left(\tan ^{-1}\left(\frac{\sin \theta}{\sqrt{\cos 2 \theta}}\right)\right)$, where $-\frac{\pi}{4}
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Q JEE Advance 2011
Consider the parabola $y^2=8 x$. Let $\Delta_1$ be the area of the triangle formed by the end points of its...
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Q JEE Advance 2011
Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $...
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Q JEE Advance 2011
Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $...
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Q JEE Advance 2011
Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $...
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Q JEE ADVANCE 2011
Let $f:[-1,2] \rightarrow[0, \infty)$ be a continuous function such that $f(x)=f(1-x)$ for all $x \in[-1,2]$. Let $...
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Q JEE ADVANCE 2011
If $\lim _{x \rightarrow 0}\left[1+x \ln \left(1+b^2\right)\right]^{1 / x}=2 b \sin ^2 \theta, b>0$ and $\theta \in(-\pi, \pi]$, then the...
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Q JEE Advance 2011
Let $\mathrm{U}_1$ and $\mathrm{U}_2$ be two urns such that $\mathrm{U}_1$ contains 3 white and 2 red balls, and $\mathrm{U}_2$ contains...
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Q JEE Advance 2011
Let $\mathrm{U}_1$ and $\mathrm{U}_2$ be two urns such that $\mathrm{U}_1$ contains 3 white and 2 red balls, and $\mathrm{U}_2$ contains...
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Q JEE ADVANCE 2011
Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency...
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Q JEE ADVANCE 2011
One mole of a monatomic gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II...
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Q JEE Advance 2011
Let M and N be two $3 \times 3$ non-singular skew symmetric matrices such that $\mathrm{MN}=\mathrm{NM}$. If $\mathrm{P}^{\mathrm{T}}$ denotes the...
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Q JEE Advance 2011
Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+4 y^2=4$. If the hyperbola passes...
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Q JEE Advance 2011
The vector(s) which is/are coplanar with vectors $\hat{i}+\hat{j}+2 \hat{k}$ and $\hat{i}+2 \hat{j}+\hat{k}$, and perpendicular to the vector $\hat{i}+\hat{j}+\hat{k}$ is/are
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Q JEE Advance 2011
Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a function such that $\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y}), \forall \mathrm{x}, \mathrm{y} \in \mathrm{R}$. If $\mathrm{f}(\mathrm{x})$ is differentiable...
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Q JEE Advance 2011
Let the straight line $x=b$ divides the area enclosed by $y=(1-x)^2, y=0$ and $x=0$ into two parts $...
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Q JEE ADVANCE 2011
Water (with refractive index $=\frac{4}{3}$ ) in a tank is 18 cm deep. Oil of refractive index $\frac{7}{4}$ lies on...
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Q JEE ADVANCE 2011
Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is
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Q JEE Advance 2011
Let $\alpha$ and $\beta$ be the roots of $x^2-6 x-2=0$, with $\alpha>\beta$. If $a_n=\alpha^n-\beta^n$ for $n \geq 1$, then the...
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Q JEE Advance 2011
A straight line L through the point $(3,-2)$ is inclined at an angle $60^{\circ}$ to the line $\sqrt{3} \mathrm{x}+\mathrm{y}=1$. If...
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Q JEE Advance 2011
The value of $\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}} \frac{x \sin x^2}{\sin x^2+\sin \left(\ln 6-x^2\right)} d x$ is
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Q JEE Advance 2011
Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. A vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$, whose projection...
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Q JEE Advance 2011
Let $P=\{\theta: \sin \theta-\cos \theta=\sqrt{2} \cos \theta\}$ and $Q=\{\theta: \sin \theta+\cos \theta=\sqrt{2} \sin \theta\}$ be two sets. Then
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Q JEE Advance 2011
Let $\left(x_0, y_0\right)$ be solution of the following equations $$ \begin{aligned} (2 \mathrm{x})^{\ln 2} & =(3 \mathrm{y})^{\ln 3} \\ 3^{\ln...
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Q JEE Advance 2011
A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface...
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Q JEE Advance 2011
The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^9 \mathrm{~s}$. The...
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Q JEE Advance 2011
A block is moving on an inclined plane making an angle $45^{\circ}$ with the horizontal and the coefficient of friction...
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Q JEE ADVANCE 2011
A block of mass 0.18 kg is attached to a spring of force-constant $2 \mathrm{~N} / \mathrm{m}$. The coefficient of...
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Q JEE Advance 2011
Four point charges, each of $+q$, are rigidly fixed at the four corners of a square planar soap film of...
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Q JEE ADVANCE 2011
A train is moving along a straight line with a constant acceleration ' $a$ '. A boy standing in the...
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A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in freespace....
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A series R-C combination is connected to an AC voltage of angular frequency $\omega=500$ radian/s. If the impedance of the...
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Q JEE ADVANCE 2011
A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric...
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Q JEE ADVANCE 2011
Which of the following statement(s) is/are correct?
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A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity...
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Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $\mathrm{d}_{\mathrm{B}}$ are connected by a...
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Q JEE ADVANCE 2011
A long insulated copper wire is closely wound as a spiral of ' N ' turns. The spiral has inner...
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Q JEE ADVANCE 2011
A satellite is moving with a constant speed ' $V$ ' in a circular orbit about the earth. An object...
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A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence $\theta$. The reflected...
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A wooden block performs SHM on a frictionless surface with frequency, $\mathrm{v}_0$. The block carries a charge +Q on its...
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Q JEE ADVANCE 2011
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured...
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A ball of mass 0.2 kg rests on a vertical post of height 5 m . A bullet of mass...
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Q JEE ADVANCE 2011
Which of the field patterns given below is valid for electric field as well as for magnetic field?
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Q JEE ADVANCE 2011
Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column...
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Q JEE ADVANCE 2011
Match the transformations in column I with appropriate options in column II
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Q JEE ADVANCE 2011
The number of hexagonal faces that are present in a truncated octahedron is
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In 1 L saturated solution of $\mathrm{AgCl}\left[\mathrm{K}_{\mathrm{sp}}(\mathrm{AgCl})=1.6 \times 10^{-10}\right], 0.1 \mathrm{~mol}$ of $\mathrm{CuCl}\left[\mathrm{K}_{\mathrm{sp}}(\mathrm{CuCl})=1.0 \times 10^{-6}\right]$ is added. The resultant concentration...
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Q JEE ADVANCE 2011
The volume (in mL ) of $0.1 \mathrm{M} \mathrm{AgNO}_3$ required for complete precipitation of chloride ions present in 30 mL...
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Q JEE ADVANCE 2011
Among the following, the number of compounds than can react with $\mathrm{PCl}_5$ to give $\mathrm{POCl}_3$ is $...
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Q JEE ADVANCE 2011
The total number of contributing structure showing hyperconjugation (involving $\mathrm{C}-\mathrm{H}$ bonds) for the following carbocation is
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The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compound is
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Q JEE Advance 2011
Steel wire of lenght ' L ' at $40^{\circ} \mathrm{C}$ is suspended from the ceiling and then a mass '...
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Q JEE Advance 2011
Four solid spheres each of diameter $\sqrt{5} \mathrm{~cm}$ and mass 0.5 kg are placed with their centers at the corners...
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Q JEE Advance 2011
A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in...
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Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the...
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Q JEE Advance 2011
Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the...
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Q JEE Advance 2011
Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the...
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Q JEE Advance 2011
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive...
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Q JEE Advance 2011
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive...
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Q JEE Advance 2011
An electron and a proton are moving on straight parallel paths with same velocity. They enter a semiinfinite region of...
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A composite block is made of slabs $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and E of different thermal conductivities (given in terms...
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A spherical metal shell $A$ of radius $R_A$ and a solid metal sphere $B$ of radius $R_B\left(
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The equilibrium $$ 2 \mathrm{Cu}^{\prime} \rightleftharpoons \mathrm{Cu}^{\circ}+\mathrm{Cu}^{\prime \prime} $$ in aqueous medium at $25^{\circ} \mathrm{C}$ shifts towards the left in...
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Q JEE ADVANCE 2011
For the first order reaction $$ 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightarrow 4 \mathrm{NO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) $$
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The correct functional group X and the reagent/reaction conditions Y in the following scheme are
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Reduction of the metal centre in aqueous permanganate ion involves
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A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m...
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A meter bridge is set up as shown, to determine an unknown resistance ' X ' using a standard 10...
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Consider the following cell reaction: $$ 2 \mathrm{Fe}_{(\mathrm{s})}+\mathrm{O}_{2(\mathrm{~g})}+4 \mathrm{H}_{(\mathrm{aq})}^{+} \rightarrow 2 \mathrm{Fe}_{(\mathrm{aq})}^{2+}+2 \mathrm{H}_2 \mathrm{O}_{(f)} \mathrm{E}^{\circ}=1.67 \mathrm{~V} $$ At $...
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Q JEE Advance 2011
A $2 \mu \mathrm{~F}$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after...
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Passing $\mathrm{H}_2 \mathrm{~S}$ gas into a mixture of $\mathrm{Mn}^{2+}, \mathrm{Ni}^{2+}, \mathrm{Cu}^{2+}$ and $\mathrm{Hg}^{2+}$ ions in an acidified aqueous solution precipitates
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5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be $\mathrm{T}_1$,...
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$...
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Oxidation states of the metal in the minerals haematite and magnetite, respectively, are
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Consider an electric field $\vec{E}=E_0 \hat{x}$ where $E_0$ is a constant. The flux through the shaded area (as shown in...
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The following carbohydrate is
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The major product of the following reaction is
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The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561 \mathrm{~A}^0$. The wavelength of...
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Amongst the compounds given, the one that would form a brilliant colored dye on treatment with $\mathrm{NaNO}_2$ in dil. HCl...
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The freezing point (in ${ }^{\circ} \mathrm{C}$ ) of a solution containing 0.1 g of $\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6(\mathrm{Mol}\right.$. Wt. 329) in 100...
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A police car with a siren of frequency 8 kHz is moving with uniform velocity $36 \mathrm{~km} / \mathrm{hr}$ towards...
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The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic KOH is
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To an evacuated vessel with movable piston under external pressure of $1 \mathrm{~atm}, 0.1 \mathrm{~mol}$ of He and 1.0 mol...
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Reaction of $\mathrm{Br}_2$ with $\mathrm{Na}_2 \mathrm{CO}_3$ in aqueous solution gives sodium bromide and sodium bromate with evolution of $\mathrm{CO}_2$ gas....
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The maximum number of electrons that can have principal quantum number, $\mathrm{n}=3$, and spin quantum number, $\mathrm{m}_{\mathrm{s}}=-\frac{1}{2}$, is
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The work function $(\phi)$ of some metals is listed below. The number of metals which will show photoelectric effect when...
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A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes $47.0 \%$...
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The difference in the oxidation numbers of the two types of sulphur atoms in $\mathrm{Na}_2 \mathrm{~S}_4 \mathrm{O}_6$ is
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When a metal rod $\mathbf{M}$ is dipped into an aqueous colourless concentrated solution of compound $\mathbf{N}$, the solution turns light...
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When a metal rod $\mathbf{M}$ is dipped into an aqueous colourless concentrated solution of compound $\mathbf{N}$, the solution turns light...
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When a metal rod $\mathbf{M}$ is dipped into an aqueous colourless concentrated solution of compound $\mathbf{N}$, the solution turns light...
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An acyclic hydrocarbon $\mathbf{P}$, having molecular formula $\mathrm{C}_6 \mathrm{H}_{10}$, gave acetone as the only organic product through the following sequence...
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An acyclic hydrocarbon $\mathbf{P}$, having molecular formula $\mathrm{C}_6 \mathrm{H}_{10}$, gave acetone as the only organic product through the following sequence...
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The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)
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According to kinetic theory of gases
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Extraction of metal from the ore cassiterite involves
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Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations...
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Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations...
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$\mathrm{AgNO}_3$ (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot...
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Among the following compounds, the most acidic is
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The major product of the following reaction is
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Geometrical shapes of the complexes formed by the reaction of $\mathrm{Ni}^{2+}$ with $\mathrm{Cl}^{-}, \mathrm{CN}^{-}$and $\mathrm{H}_2 \mathrm{O}$, respectively, are
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Bombardment of aluminium by $\alpha$-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products $...
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Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density $...
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Extra pure $\mathrm{N}_2$ can be obtained by heating
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