JEE Advanced 2011 · 10 Apr 2011 · Paper 2

Q1.A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence $\theta$. The reflected ( R ) and transmitted ( T ) intensities, both as function of $\theta$, are plotted. The correct sketch is

Q2.A satellite is moving with a constant speed ' $V$ ' in a circular orbit about the earth. An object of mass ' $m$ ' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object i …

Q3.A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the X-Y plane and a steady current ' $I$ ' flows through the wire. The Z-component of the magnetic field at the cen …

Q4.A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $x_1(t)=A\sin \omega t$ and $x_2(t)=A\sin \left(\omega t+\frac{2\pi }{3}\right)$. Adding a third sinusoidal displacement $x_3(t)=B\sin (\omega t+\varphi )$ brings the mas …

Q5.Which of the field patterns given below is valid for electric field as well as for magnetic field?

Q6.A ball of mass 0.2 kg rests on a vertical post of height 5 m . A bullet of mass 0.01 kg, traveling with a velocity $\mathrm{Vm}/\mathrm{s}$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The bal …

Q7.The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 division …

Q8.A wooden block performs SHM on a frictionless surface with frequency, $v_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\vec{E}$ is switched-on as shown, then the SHM of the block will be

Q9.Two solid spheres A and B of equal volumes but of different densities ${\mathrm{d}}_{\mathrm{A}}$ and ${\mathrm{d}}_{\mathrm{B}}$ are connected by a string. They are fully immersed in a fluid of density ${\mathrm{d}}_{\mathrm{F}}$. They get arranged into an equilibrium state as s …

Q10.A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4 . The current $I_R$ through the resistor and voltage $V_C$ across the capacitor are compared in the …

Q11.Which of the following statement(s) is/are correct?
(A) If the electric field due to a point charge varies as $r^{-25}$ instead of $r^{-2}$, then the Gauss law will still be valid.
(B) The Gauss law can be used to calculate the field distribution around an electric dipole.
(C …

Q13.A train is moving along a straight line with a constant acceleration ' $a$ '. A boy standing in the train throws a ball forward with a speed of $10\mathrm{m}/\mathrm{s}$, at an angle of $60^{\circ }$ to the horizontal. The boy has to move forward by 1.15 m inside the tra …

Q14.A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a …

Q15.Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is

Q16.Water (with refractive index $=\frac{4}{3}$ ) in a tank is 18 cm deep. Oil of refractive index $\frac{7}{4}$ lies on water making a convex surface of radius of curvature ' $\mathrm{R}=6\mathrm{cm}$ ' as shown. Consider oil to act as a thin lens. An object ' S ' is placed …

Q17.A series R-C combination is connected to an AC voltage of angular frequency $\omega =500\mathrm{radian}/\mathrm{s}$. If the impedance of the R-C circuit is R $\sqrt{1.25}$, the time constant (in millisecond) of the circuit is

Q18.A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of pho …

Q19.One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.

Column I
(A) Process A → B
(B) Process B → C
(C) Process C → D
(D) Pr …

Q20.Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as ${\lambda }_{\mathrm{f}}$. Match each system with statements given in Column …

Q1.Oxidation states of the metal in the minerals haematite and magnetite, respectively, are

Q2.Among the following complexes (K-P), ${\mathrm{K}}_3\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$ ($\mathbf{K}$), $\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]{\mathrm{Cl}}_3$ ($\mathbf{L}$), ${\mathrm{Na}}_3\left[\mathrm{Co}(\text{oxalate}{)}_3\right]$ ( …

Q3.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

Q4.Consider the following cell reaction:
$2{\mathrm{Fe}}_{(\mathrm{s})}+{\mathrm{O}}_{2(\mathrm{g})}+4{\mathrm{H}}_{(\mathrm{aq})}^{+}\to 2{\mathrm{Fe}}_{(\mathrm{aq})}^{2+}+2{\mathrm{H}}_2{\mathrm{O}}_{(\mathrm{l})}{\mathrm{E}}^{\circ }=1.67\mathrm{V}$
At …

Q5.The freezing point (in °C) of a solution containing 0.1 g of ${\mathrm{K}}_3\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$ (Mol. Wt. 329) in 100 g of water $({\mathrm{K}}_{\mathrm{f}}=1.86\mathrm{K}\mathrm{kg}{\mathrm{mol}}^{-1})$ is

Q6.Amongst the compounds given, the one that would form a brilliant colored dye on treatment with ${\mathrm{NaNO}}_2$ in dil. HCl followed by addition to an alkaline solution of $\beta$-naphthol is

Q8.The following carbohydrate is

Q10.The equilibrium

in aqueous medium at 25 °C shifts towards the left in the presence of

Q11.For the first order reaction

(A) the concentration of the reactant decreases exponentially with time.
(B) the half-life of the reaction decreases with increasin …

Q12.The correct functional group X and the reagent/reaction conditions Y in the following scheme are

Q14.The volume (in mL) of 0.1 $\mathrm{M}$ ${\mathrm{AgNO}}_3$ required for complete precipitation of chloride ions present in 30 mL of 0.01 M solution of $\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5\mathrm{Cl}\right]{\mathrm{Cl}}_2$, as silver chloride is close …

Q16.The number of hexagonal faces that are present in a truncated octahedron is

Q18.The total number of contributing structures showing hyperconjugation (involving C-H bonds) for the following carbocation is

Q19.Match the transformations in column I with appropriate options in column II
| (B) …

Q20.Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column II
| (B) (see structure) | (q) Electrophilic substi …

Q1.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 $(9,0)$, then the eccentricity of the hyperbola is

Q3.Let $\omega \ne 1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form

where each of $a$, $b$, and $c$ is either $\omega$ or …

Q4.The circle passing through the point $(-1,0)$ and touching the $y$-axis at $(0,2)$ also passes through the point

Q5.If

then the value of $\theta$ is

Q6.Let $f:[-1,2]\to [0,\infty )$ be a continuous function such that $f(x)=f(1-x)$ for all $x\in [-1,2]$. Let $R_1={\int }_{-1}^{2}xf(x)dx$, and $R_2$ be the area of the region bounded by $y=f(x),x=-1,x=2$, and the $x$-axis. Then

Q7.Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x\in \mathbb{R}$. Then the set of all $x$ satisfying $(f\circ g\circ g\circ f)(x)=(g\circ g\circ f)(x)$, where $(f\circ g)(x)=f(g(x))$, is

Q8.Let $(x,y)$ be any point on the parabola $y^2=4x$. Let $P$ be the point that divides the line segment from $(0,0)$ to $(x,y)$ in the ratio $1:3$. Then the locus of $P$ is

Q9.If

then

Q10.Let $E$ and $F$ be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$. If $P(T)$ denotes the probability of occurrence of the event $T$, then

Q11.Let $L$ be a normal to the parabola $y^2=4x$. If $L$ passes through the point (9, 6), then $L$ is given by

Q14.The number of distinct real roots of $x^4-4x^3+12x^2+x-1=0$ is

Q15.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 $\frac{df(x)}{dx}$ and $g(x)$ is a given non-constant differentiable function on $\mathbb{R}$ with $g(0)=g(2)=0$. Then the value of …

Q16.Let $M$ be a $3\times 3$ matrix satisfying …

Q17.Let $\vec{a}=-\hat{i}-\hat{k},\vec{b}=-\hat{i}+\hat{j}$ and $\vec{c}=\hat{i}+2\hat{j}+3\hat{k}$ be three given vectors. If $\vec{r}$ is a vector such that $\vec{r}\times \vec{b}=\vec{c}\times \vec{b}$ and $\vec{r}.\vec{a}=0$, then the value of …

Q18.The straight line $2x-3y=1$ divides the circular region $x^2+y^2\le 6$ into two parts. If

then the num …