JEE Advanced 2018 · 20 May 2018 · Paper 2

Q1.A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK/dt=\gamma t$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the foll …

Q2.Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_0$. Which of the following statements is (are) …

Q3.An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ }$ at the centre …

Q4.A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are n …

Q5.In a radioactive decay chain, ${}_{90}^{232}\mathrm{Th}$ nucleus decays to ${}_{82}^{212}\mathrm{Pb}$ nucleus. Let $N_{\alpha }$ and $N_{\beta }$ be the number of $\alpha$ and ${\beta }^{-}$particles, respectively, emitted in this decay process. Which of the following sta …

Q6.In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500Hz$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length …

Q7.A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m=0.4kg$ is at rest on this surface. An impulse of $1.0Ns$ is applied to the block at time $t=0$ so that it starts moving along the $x$-axis with a velocity …

Q8.A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of $120m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of t …

Q9.A particle, of mass $10^{-3}kg$ and charge $1.0C$, is initially at rest. At time $t=0$, the particle comes under the influence of an electric field $\vec{E}(t)=E_0\sin \omega t\hat{ı}$, where $E_0=1.0N{C}^{-1}$ and $\omega =10^{3}rad{s}^{-1}$. Consider the …

Q10.A moving coil galvanometer has 50 turns and each turn has an area $2\times 10^{-4}{m}^2$. The magnetic field produced by the magnet inside the galvanometer is $0.02T$. The torsional constant of the suspension wire is $10^{-4}Nmra{d}^{-1}$. When a current flows through t …

Q11.A steel wire of diameter $0.5mm$ and Young's modulus $2\times 10^{11}N{m}^{-2}$ carries a load of mass $M$. The length of the wire with the load is $1.0m$. A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire …

Q12.One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100K$ and the universal gas constant $R=8.0Jmo{l}^{-1}{K}^{-1}$, the decrease in its internal energy, in Jou …

Q13.In a photoelectric experiment a parallel beam of monochromatic light with power of $200W$ is incident on a perfectly absorbing cathode of work function $6.25eV$. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligi …

Q14.Consider a hydrogen-like ionized atom with atomic number $Z$ with a single electron. In the emission spectrum of this atom, the photon emitted in the $n=2$ to $n=1$ transition has energy 74.8 eV higher than the photon emitted in the $n=3$ to $n=2$ transition. The ioniza …

Q15.The electric field $E$ is measured at a point $P(0,0,d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-I contains different relations between $E$ and $d$. List-II descr …

Q16.A planet of mass $M$, has two natural satellites with masses $m_1$ and $m_2$. The radii of their circular orbits are $R_1$ and $R_2$ respectively. Ignore the gravitational force between the satellites. Define $v_1,L_1,K_1$ and $T_1$ to be, respecti …

Q17.One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the cor …

Q18.In the List-I below, four different paths of a particle are given as functions of time. In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha \ne \beta$. In each case, the force acting on the particle is either zero or conser …

Q1.The correct option(s) regarding the complex ${\left[\mathrm{Co}(\mathrm{en})({\mathrm{NH}}_3{)}_3({\mathrm{H}}_2\mathrm{O})\right]}^{3+}$ (en $={\mathrm{H}}_2{\mathrm{NCH}}_2{\mathrm{CH}}_2{\mathrm{NH}}_2$) is (are)

Q2.The correct option(s) to distinguish nitrate salts of ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Cu}}^{2+}$ taken separately is (are)

Q3.Aniline reacts with mixed acid (conc. ${\mathrm{HNO}}_3$ and conc. ${\mathrm{H}}_2{\mathrm{SO}}_4$) at 288 K to give P (51%), Q (47%) and R (2%). The major product(s) of the following reaction sequence is (are) …

Q4.The Fischer presentation of D-glucose is given below.

The correct structure(s) of $\beta$-L-glucopyranose is (are)

Q5.For a first order reaction $\mathrm{A}(\mathrm{g})\to 2\mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ at constant volume and 300 K, the total pressure at the beginning $(t=0)$ and at time $t$ are $P_0$ and $P_t$, respectively. Initially, only A is present with conc …

Q6.For a reaction, $\mathrm{A}\rightleftharpoons \mathrm{P}$, the plots of $[\mathrm{A}]$ and $[\mathrm{P}]$ with time at temperatures $T_1$ and $T_2$ are given below.

If $T_2>T_1$, the correct statement(s) is (are)
(Assume $\Delta H^{\theta }$ and $\Delta S^{\theta }$ are i …

Q7.The total number of compounds having at least one bridging oxo group among the molecules given below is ____.

${\mathrm{N}}_2{\mathrm{O}}_3$, ${\mathrm{N}}_2{\mathrm{O}}_5$, ${\mathrm{P}}_4{\mathrm{O}}_6$, ${\mathrm{P}}_4{\mathrm{O}}_7$, …

Q8.Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight (in kg) of Pb produced per kg of …

Q9.To measure the quantity of ${\mathrm{MnCl}}_2$ dissolved in an aqueous solution, it was completely converted to ${\mathrm{KMnO}}_4$ using the reaction, …

Q10.For the given compound X, the total number of optically active stereoisomers is ____.

(In the structure of X: a bold wedge bond indicates that the configuration at the specific carbon and the geometry of the double bond is fixed; a wavy bond indicates that the co …

Q11.In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____.

(Atomic weights in $\mathrm{g}{\mathrm{mol}}^{-1}$: $\mathrm{H}=1$, $\mathrm{C}=12$, $\mathrm{N}=14$, $\mathrm{O}=16$, $\mathrm{Br}=80$. The yield (%) corresponding to the pro …

Q12.The surface of copper gets tarnished by the formation of copper oxide. ${\mathrm{N}}_2$ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the ${\mathrm{N}}_2$ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises cop …

Q13.Consider the following reversible reaction,

$\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g})\rightleftharpoons \mathrm{AB}(\mathrm{g})$

The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in $\mathrm{J}{\mathrm{mol}}^{-1}$). If the pre-exp …

Q14.Consider an electrochemical cell: $\mathrm{A}(\mathrm{s})|{\mathrm{A}}^{\mathrm{n}+}(\mathrm{aq},2\mathrm{M})||{\mathrm{B}}^{2\mathrm{n}+}(\mathrm{aq},1\mathrm{M})|\mathrm{B}(\mathrm{s})$. The value of $\Delta H^{\ominus }$ for the cell reaction is twice that of $\Delta G^{\ominus }$ …

Q15.Match each set of hybrid orbitals from LIST-I with complex(es) given in LIST-II.
| Q. ${\mathrm{sp}}^3$ | 2. …

Q16.The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.

(Given, order of migratory aptitude: aryl > alkyl > hydrogen)
| P. (see structure) | 1. …

Q17.LIST-I contains reactions and LIST-II contains major products.
| S. (see structure) | 4. (see structure) | …

Q18.Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on $\left[{\mathrm{H}}^{+}\right]$ are given in LIST-II.

(Note: Degree of dissociation $(\alpha )$ of weak acid and weak base is << 1; degree of hydrolysis o …

Q1.For any positive integer $n$, define $f_n:(0,\infty )\to \mathbb{R}$ as

(Here, the inverse trigonometric function ${\tan }^{-1}x$ assumes va …

Q2.Let $T$ be the line passing through the points $P(-2,7)$ and $Q(2,-5)$. Let $F_1$ be the set of all pairs of circles $(S_1,S_2)$ such that $T$ is tangent to $S_1$ at $P$ and tangent to $S_2$ at $Q$, and also such that $S_1$ and $S_2$ touch e …

Q3.Let $S$ be the set of all column matrices $\left[\begin{array}{l}{b}_1\\ b_2\\ b_3\end{array}\right]$ such that $b_1,b_2,b_3\in \mathbb{R}$ and the system of equations (in real variables) …

Q4.Consider two straight lines, each of which is tangent to both the circle $x^2+y^2=\frac{1}{2}$ and the parabola $y^2=4x$. Let these lines intersect at the point $Q$. Consider the ellipse whose center is at the origin $O(0,0)$ and whose semi-major axis is $OQ$. If …

Q5.Let $s,t,r$ be non-zero complex numbers and $L$ be the set of solutions $z=x+iy$ $(x,y\in \mathbb{R},i=\sqrt{-1})$ of the equation $sz+t\bar{z}+r=0$, where $\bar{z}=x-iy$. Then, which of the following statement(s) is (are) TRUE?

Q6.Let $f:(0,\pi )\to \mathbb{R}$ be a twice differentiable function such that

If $f\left(\frac{\pi }{6}\right)=-\frac{\pi }{12}$, then which of the following s …

Q7.The value of the integral

is ____.

Q8.Let $P$ be a matrix of order $3\times 3$ such that all the entries in $P$ are from the set $\{-1,0,1\}$. Then, the maximum possible value of the determinant of $P$ is ____.

Q9.Let $X$ be a set with exactly 5 elements and $Y$ be a set with exactly 7 elements. If $\alpha$ is the number of one-one functions from $X$ to $Y$ and $\beta$ is the number of onto functions from $Y$ to $X$, then the value of $\frac{1}{5!}(\beta -\alpha )$ is ____.

Q10.Let $f:\mathbb{R}\to \mathbb{R}$ be a differentiable function with $f(0)=0$. If $y=f(x)$ satisfies the differential equation

then the value of ${\lim }_{x\to -\infty }f(x)$ is ____.

Q11.Let $f:\mathbb{R}\to \mathbb{R}$ be a differentiable function with $f(0)=1$ and satisfying the equation

Then, the value of ${\log }_e(f(4))$ is ____.

Q12.Let $P$ be a point in the first octant, whose image $Q$ in the plane $x+y=3$ (that is, the line segment $PQ$ is perpendicular to the plane $x+y=3$ and the mid-point of $PQ$ lies in the plane $x+y=3$) lies on the $z$-axis. Let the distance of $P$ from the $x$-a …

Q13.Consider the cube in the first octant with sides $OP,OQ$ and $OR$ of length 1, along the $x$-axis, $y$-axis and $z$-axis, respectively, where $O(0,0,0)$ is the origin. Let $S\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ be the centre of the cube and $T$ be …

Q14.Let

where ${}^{10}{C}_r,r\in \{1,2,\cdots ,10\}$ denote binomial coefficients. Then, the value of $\frac{1}{1430}X$ is ___ …

Q15.Let $E_1=\{x\in \mathbb{R}:x\ne 1$ and $\frac{x}{x-1}>0\}$
and $E_2=\{x\in E_1:{\sin }^{-1}\left({\log }_e\left(\frac{x}{x-1}\right)\right)$ is a real number $\}$.
(Here, the inverse trigonometric function ${\sin }^{-1}x$ ass …

Q16.In a high school, a committee has to be formed from a group of 6 boys $M_1,M_2,M_3,M_4,M_5,M_6$ and 5 girls $G_1,G_2,G_3,G_4,G_5$.
(i) Let ${\alpha }_1$ be the total number of ways in which the committee can be formed such that the committee ha …

Q17.Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $a>b>0$, be a hyperbola in the $xy$-plane whose conjugate axis $LM$ subtends an angle of $60^0$ at one of its vertices $N$. Let the area of the triangle $LMN$ be $4\sqrt{3}$.
| LIST-I | | LIST-II | || …

Q18.Let $f_1:\mathbb{R}\to \mathbb{R},f_2:\left(-\frac{\pi }{2},\frac{\pi }{2}\right)\to \mathbb{R},f_3:\left(-1,e^{\frac{\pi }{2}}-2\right)\to \mathbb{R}$ and $f_4:\mathbb{R}\to \mathbb{R}$ be functions defined by
(i) …