JEE Advanced 2011 · 10 Apr 2011 · Paper 1

Q1.A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is $320\mathrm{m}/\mathrm{s}$. The frequency of the siren heard by the car driver is

Q2.5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be ${\mathrm{T}}_1$, the work done in the process is

Q3.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 the figure) due to this field is

Q4.The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561\mathring{A}$. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

Q5.A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) …

Q6.A meter bridge is set-up as shown, to determine an unknown resistance 'X' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of 'X' is

Q7.A $2\mu \mathrm{F}$ capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is

Q8.A spherical metal shell A of radius ${\mathrm{R}}_{\mathrm{A}}$ and a solid metal sphere B of radius ${\mathrm{R}}_{\mathrm{B}}\left(<{\mathrm{R}}_{\mathrm{A}}\right)$ are kept far apart and each is given charge '+Q'. Now they are connected by a thin metal wire. Then

Q11.A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius 'R' (< L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc …

Q12.Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase …

Q13.Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase …

Q14.Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider some simple dynamical systems in one-dimension. For such systems, phase …

Q15.A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of free electrons, each of mass 'm'. When the ele …

Q16.A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of free electrons, each of mass 'm'. When the ele …

Q17.A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of $0.3\mathrm{m}/{\mathrm{s}}^2$. The coefficient of friction between the ground and t …

Q18.A block is moving on an inclined plane making an angle $45^{\circ }$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define …

Q19.Four point charges, each of $+q$, are rigidly fixed at the four corners of a square planar soap film of side 'a'. The surface tension of the soap film is $\gamma$. The system of charges and planar film are in equilibrium, and $a=k{\left[\frac{q^2}{\gamma }\right]}^{1/N}$, …

Q20.Steel wire of length 'L' at $40^{\circ }\mathrm{C}$ is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is …

Q21.The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^9\mathrm{s}$. The mass of an atom of this radioisotope is $10^{-25}\mathrm{kg}$. The mass (in mg) of the radioactive sample is

Q22.A long circular tube of length 10 m and radius 0.3 m carries a current $I$ along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as …

Q23.Four solid spheres each of diameter $\sqrt{5}\mathrm{cm}$ and mass 0.5 kg are placed with their centers at the corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is $\mathrm{N}\times 10^{-4}\mathrm{kg}-{\mathrm{m}}^2$, …

Q1.Extra pure ${\mathrm{N}}_2$ can be obtained by heating

Q2.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

Q3.Bombardment of aluminum by $\alpha$-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products X, Y and Z respectively are,

Q4.Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density $1.15\mathrm{g}/\mathrm{mL}$. The molarity of the solution is

Q5.${\mathrm{AgNO}}_3$ (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance ( $\Lambda$ ) versus the volume of ${\mathrm{AgNO}}_3$ is

Q6.Among the following compounds, the most acidic is

Q8.Extraction of metal from the ore cassiterite involves

Q9.The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)

Q10.According to kinetic theory of gases

Q12.When a metal rod $\mathbf{M}$ is dipped into an aqueous colourless concentrated solution of compound $\mathbf{N}$, the solution turns light blue. Addition of aqueous NaCl to the blue solution gives a white precipitate $\mathbf{O}$. Addition of aqueous ${\mathrm{NH}}_3$ di …

Q16.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 of reactions, in which $\mathbf{Q}$ is an intermediate organic compound.

The structure of the compound …

Q17.The difference in the oxidation numbers of the two types of sulphur atoms in ${\mathrm{Na}}_2{\mathrm{S}}_4{\mathrm{O}}_6$ is

Q18.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. The number of sodium bromide molecules involved in the balanced chemical equation is

Q19.The maximum number of electrons that can have principal quantum number, $n=3$, and spin quantum number, $m_{\mathrm{s}}=-1/2$, is

Q20.The work function ( $\varphi$ ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is
| Metal | Li | Na | K | Mg | Cu | Ag | Fe | Pt | W || --- | --- | --- | --- | --- | --- | --- | --- | - …

Q21.To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm . at $0^{\circ }\mathrm{C}$ ) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases a …

Q22.The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentylhexane using alcoholic KOH is

Q23.A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes 47.0 % to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is

Q1.Let $(x_0,y_0)$ be the solution of the following equations

Then $x_0$ is

Q2.The value of ${\int }_{\sqrt{\ln 2}}^{\sqrt{\ln 3}}\frac{x\sin x^2}{\sin x^2+\sin \left(\ln 6-x^2\right)}dx$ is

Q3.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 on $\vec{c}$ is $\frac{1}{\sqrt{3}}$, is given by

Q4.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

Q6.Let $\alpha$ and $\beta$ be the roots of $x^2-6x-2=0$, with $\alpha >\beta$. If $a_n={\alpha }^n-{\beta }^n$ for $n\ge 1$, then the value of $\frac{a_{10}-2a_8}{2a_9}$ is

Q7.A straight line $L$ through the point $(3,-2)$ is inclined at an angle $60^{\circ }$ to the line $\sqrt{3}x+y=1$. If $L$ also intersects the $x$-axis, then the equation of $L$ is

Q8.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

Q10.Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+4y^2=4$. If the hyperbola passes through a focus of the ellipse, then

Q12.Let $a,b$ and $c$ be three real numbers satisfying

If the point $P(a,b,c)$, wi …

Q13.Let $a,b$ and $c$ be three real numbers satisfying

Let $\omega$ be a solution of …

Q14.Let $a,b$ and $c$ be three real numbers satisfying

Let $b=6$, with $a$ and …

Q15.Let $U_1$ and $U_2$ be two urns such that $U_1$ contains 3 white and 2 red balls, and $U_2$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $U_1$ and put into $U_2$. However, if tail appears then 2 bal …

Q16.Let $U_1$ and $U_2$ be two urns such that $U_1$ contains 3 white and 2 red balls, and $U_2$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $U_1$ and put into $U_2$. However, if tail appears then 2 bal …

Q17.Consider the parabola $y^2=8x$. Let ${\Delta }_1$ be the area of the triangle formed by the end points of its latus rectum and the point $P\left(\frac{1}{2},2\right)$ on the parabola, and ${\Delta }_2$ be the area of the triangle formed by drawing tangents at $P$ and …

Q19.The positive integer value of $n>3$ satisfying the equation

is

Q21.If $z$ is any complex number satisfying $|z-3-2i|\le 2$, then the minimum value of $|2z-6+5i|$ is

Q22.The minimum value of the sum of real numbers $a^{-5},a^{-4},3a^{-3},1,a^8$ and $a^{10}$ with $a>0$ is