JEE Advanced 2013 · 02 Jun 2013 · Paper 1

Q1.The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between $5.10cm$ and $5.15cm$ of the main scale. The Vernier scale has 50 divisions equivalent to $2.45cm$. The …

Q2.A ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3}\hat{j})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3}\hat{j})$. The angle of incidence is

Q3.In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$, the path difference (in terms of an integer $n$ ) corresponding to any point having half the peak intensity is

Q4.Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is $4:3$. The ratio of their densities is

Q5.Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity $\kappa$ and the other $2\kappa$. The temperature difference between the ends along the …

Q6.A pulse of light of duration $100ns$ is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is $3\times 10^{8}m{s}^{-1}$. The final momentum of the object is

Q7.A particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward …

Q8.The work done on a particle of mass $m$ by a force, $K\left[\frac{x}{{\left(x^2+y^2\right)}^{3/2}}\hat{i}+\frac{y}{{\left(x^2+y^2\right)}^{3/2}}\hat{j}\right]$ ( $K$ being a constant of appropriate dimensions), when the particle is taken from the point $(a,0)$ …

Q9.One end of a horizontal thick copper wire of length $2L$ and radius $2R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wi …

Q10.The image of an object, formed by a plano-convex lens at a distance of $8m$ behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the …

Q11.A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, $y(x,t)=(0.01m)\sin \left[\left(62.8m^{-1}\right)x\right]\cos \left[\left(628s^{-1}\right)t\right]$. Assuming $\pi =3.14$, the correct statement(s) is (are) …

Q12.A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete arrangement is placed in a liquid of den …

Q13.A particle of mass $M$ and positive charge $Q$, moving with a constant velocity ${\vec{u}}_1=4\hat{i}m{s}^{-1}$, enters a region of uniform static magnetic field normal to the $x-y$ plane. The region of the magnetic field extends from $x=0$ to $x=L$ for all values of …

Q14.Two non-conducting solid spheres of radii $R$ and $2R$, having uniform volume charge densities ${\rho }_1$ and ${\rho }_2$ respectively, touch each other. The net electric field at a distance $2R$ from the centre of the smaller sphere, along the line joining the centres …

Q15.In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S_1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C_2$. After so …

Q16.The work functions of Silver and Sodium are 4.6 and $2.3eV$, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is

Q17.A freshly prepared sample of a radioisotope of half-life $1386s$ has activity $10^3$ disintegrations per second. Given that $\ln 2=0.693$, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first $80s$ after p …

Q18.A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in $m{s}^{-1}$ ) of the particle is zero, the speed (in $m{s}^{-1}$ ) after $5s$ is

Q19.A uniform circular disc of mass $50kg$ and radius $0.4m$ is rotating with an angular velocity of $10rad{s}^{-1}$ about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius $0.2m$, are gently placed symmetrically on the disc …

Q20.A bob of mass $m$, suspended by a string of length $l_1$, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass $m$ suspended by a string of length $l_2$, which is i …

Q1.The compound that does NOT liberate $C{O}_2$, on treatment with aqueous sodium bicarbonate solution, is

Q2.Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of

Q3.Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25 °C. For this process, the correct statement is

Q4.Sulfide ores are common for the metals

Q5.The arrangement of $X^{-}$ ions around $A^{+}$ ion in solid AX is given in the figure (not drawn to scale). If the radius of $X^{-}$ is $250pm$, the radius of $A^{+}$ is

Q6.Upon treatment with ammoniacal $H_{2}S$, the metal ion that precipitates as a sulfide is

Q7.The standard enthalpies of formation of $C{O}_2(g),H_{2}O(l)$ and glucose $(s)$ at 25 °C are $-400kJ/mol,-300kJ/mol$ and $-1300kJ/mol$, respectively. The standard enthalpy of combustion per gram of glucose at 25 °C is

Q8.Consider the following complex ions, $P,Q$ and $R$.

The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is

Q9.In the reaction,

the time taken for 75% reaction of $P$ is twice the time taken for 50% reaction of $P$. The concentration of $Q$ varies with reaction time as shown in the figure. The overall order of the reaction is

Q10.$KI$ in acetone, undergoes $S_{N}2$ reaction with each of $\mathbf{P},\mathbf{Q},\mathbf{R}$ and $\mathbf{S}$. The rates of the reaction vary as

Q11.The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

Q12.Among $\mathbf{P},\mathbf{Q},\mathbf{R}$ and $\mathbf{S}$, the aromatic compound(s) is/are

Q13.The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

Q14.Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is(are)

Q15.The initial rate of hydrolysis of methyl acetate $(1M)$ by a weak acid $(HA,1M)$ is $1/100^{\text{th}}$ of that of a strong acid $(HX,1M)$, at 25 °C. The $K_a$ of $HA$ is

Q16.The total number of carboxylic acid groups in the product $\mathbf{P}$ is

Q17.A tetrapeptide has -COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with $-N{H}_2$ group attached to a chiral center is

Q18.EDTA ${}^{4-}$ is ethylenediaminetetraacetate ion. The total number of $N-Co-O$ bond angles in $[Co(EDTA){]}^{1-}$ complex ion is

Q19.The total number of lone-pairs of electrons in melamine is

Q20.The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of $He$ gas at $-73^{\circ }C$ is "$M$" times that of the de Broglie wavelength of Ne at $727^{\circ }C$. $M$ is

Q1.Let complex numbers $\alpha$ and $\frac{1}{\bar{\alpha }}$ lie on circles ${\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2=r^2$ and ${\left(x-x_0\right)}^2+{\left(y-y_0\right)}^2=4r^2$, respectively. If $z_0=x_0+i{y}_0$ satisfies the equation …

Q2.Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is

Q3.Let $f:\left[\frac{1}{2},1\right]\to \mathbb{R}$ (the set of all real numbers) be a positive, non-constant and differentiable function such that $f^{\prime }(x)<2f(x)$ and $f\left(\frac{1}{2}\right)=1$. Then the value of ${\int }_{1/2}^{1}f(x)dx$ lies in the i …

Q4.The number of points in $(-\infty ,\infty )$, for which $x^2-x\sin x-\cos x=0$, is

Q5.The area enclosed by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over the interval $\left[0,\frac{\pi }{2}\right]$ is

Q6.A curve passes through the point $\left(1,\frac{\pi }{6}\right)$. Let the slope of the curve at each point $(x,y)$ be $\frac{y}{x}+\sec \left(\frac{y}{x}\right),x>0$. Then the equation of the curve is

Q7.The value of $\cot \left({\sum }_{n=1}^{23}{\cot }^{-1}\left(1+{\sum }_{k=1}^{n}2k\right)\right)$ is

Q8.For $a>b>c>0$, the distance between $(1,1)$ and the point of intersection of the lines $ax+by+c=0$ and $bx+ay+c=0$ is less than $2\sqrt{2}$. Then

Q9.Perpendiculars are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}=\frac{z}{3}$ to the plane $x+y+z=3$. The feet of perpendiculars lie on the line

Q10.Let $\overrightarrow{PR}=3\hat{i}+\hat{j}-2\hat{k}$ and $\overrightarrow{SQ}=\hat{i}-3\hat{j}-4\hat{k}$ determine diagonals of a parallelogram $PQRS$ and $\overrightarrow{PT}=\hat{i}+2\hat{j}+3\hat{k}$ be another vector. Then the volume of the parallelepiped d …

Q11.Let $S_n={\sum }_{k=1}^{4n}(-1{)}^{\frac{k(k+1)}{2}}{k}^2$. Then $S_n$ can take value(s)

Q12.For $3\times 3$ matrices $M$ and $N$, which of the following statement(s) is (are) NOT correct ?

Q13.Let $f(x)=x\sin \pi x,x>0$. Then for all natural numbers $n,f^{\prime }(x)$ vanishes at

Q14.A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum v …

Q15.A line $l$ passing through the origin is perpendicular to the lines

Then, the coordinate(s) of t …

Q16.The coefficients of three consecutive terms of $(1+x{)}^{n+5}$ are in the ratio $5:10:14$. Then $n=$

Q17.A pack contains $n$ cards numbered from 1 to $n$. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is $k$, then $k-20=$

Q18.Of the three independent events $E_1,E_2$ and $E_3$, the probability that only $E_1$ occurs is $\alpha$, only $E_2$ occurs is $\beta$ and only $E_3$ occurs is $\gamma$. Let the probability $p$ that none of events $E_1,E_2$ or $E_3$ occurs …

Q19.A vertical line passing through the point $(h,0)$ intersects the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$ at the points $P$ and $Q$. Let the tangents to the ellipse at $P$ and $Q$ meet at the point $R$. If $\Delta (h)=$ area of the triangle …

Q20.Consider the set of eight vectors $V=\{\mathrm{a}\hat{i}+\mathrm{b}\hat{j}+\mathrm{c}\hat{k}:a,b,c\in \{-1,1\}\}$. Three noncoplanar vectors can be chosen from $V$ in $2^p$ ways. Then $p$ is