JEE Advanced 2018 · 20 May 2018 · Paper 1

Q1.The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r)=k{r}^2/2$, where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. If $v$ is the speed o …

Q2.Consider a body of mass $1.0kg$ at rest at the origin at time $t=0$. A force $\vec{F}=(\alpha t\hat{ı}+\beta \hat{ȷ})$ is applied on the body, where $\alpha =1.0N{s}^{-1}$ and $\beta =1.0N$. The torque acting on the body about the origin at time $t=1.0s$ is …

Q3.A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wal …

Q4.In the figure below, the switches $S_1$ and $S_2$ are closed simultaneously at $t=0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual induc …

Q5.Two infinitely long straight wires lie in the $xy$-plane along the lines $x=\pm R$. The wire located at $x=+R$ carries a constant current $I_1$ and the wire located at $x=-R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at …

Q6.One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?

Q7.Two vectors $\vec{A}$ and $\vec{B}$ are defined as $\vec{A}=a\hat{ı}$ and $\vec{B}=a(\cos \omega t\hat{ı}+\sin \omega t\hat{ȷ})$, where $a$ is a constant and $\omega =\pi /6rad{s}^{-1}$. If $|\vec{A}+\vec{B}|=\sqrt{3}|\vec{A}-\vec{B}|$ at time $t=\tau$ for the f …

Q8.Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0m{s}^{-1}$ and the man behind walks at a speed $2.0m{s}^{-1}$. A third man is standing at a height $12m$ above the same horizontal line such that all three men are i …

Q9.A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground i …

Q10.A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0\mathrm{N}{\mathrm{m}}^{-1}$ and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mas …

Q11.Three identical capacitors $C_1,C_2$ and $C_3$ have a capacitance of $1.0\mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity …

Q12.In the $xy$-plane, the region $y>0$ has a uniform magnetic field $B_1\hat{k}$ and the region $y<0$ has another uniform magnetic field $B_2\hat{k}$. A positively charged particle is projected from the origin along the positive $y$-axis with speed $v_0=\pi m{s}^{-1}$ …

Q13.Sunlight of intensity $1.3kW{m}^{-2}$ is incident normally on a thin convex lens of focal length $20cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in $kW{m}^{-2}$ …

Q14.Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1=300K$ and $T_2=100K$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivit …

Q15.In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fi …

Q16.In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fi …

Q17.If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relatio …

Q18.If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relatio …

Q1.The compound(s) which generate(s) ${\mathrm{N}}_2$ gas upon thermal decomposition below 300°C is (are)

Q2.The correct statement(s) regarding the binary transition metal carbonyl compounds is (are) (Atomic numbers: $\mathrm{Fe}=26,\mathrm{Ni}=28$)

Q3.Based on the compounds of group 15 elements, the correct statement(s) is (are)

Q4.In the following reaction sequence, the correct structure(s) of X is (are)

Q5.The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is (are)

Q6.A reversible cyclic process for an ideal gas is shown below. Here, $P,V$, and $T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q,w,H$ and $U$ are heat, work, enthalpy and internal energy, respectively.

The correct option(s) is (are …

Q7.Among the species given below, the total number of diamagnetic species is ____.

H atom, ${\mathrm{NO}}_2$ monomer, ${\mathrm{O}}_2{}^{-}$(superoxide), dimeric sulphur in vapour phase, …

Q8.The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by ${\mathrm{NiCl}}_2.6{\mathrm{H}}_2\mathrm{O}$ to form a stable coordination compound. Assume that both the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of …

Q9.Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance.

(i) Remove all the anions (X) except the central one
(ii) Replace …

Q10.For the electrochemical cell,

the standard emf of the cell is 2.70 V at 300K. When the concentration of …

Q11.A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat b …

Q12.Liquids A and B form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids A and B has vapour pressure 45 Torr. At the same temperature, a new solution of A and B having mole fractions $x_A$ and $x_B$, respectively, ha …

Q13.The solubility of a salt of weak acid (AB) at pH 3 is $\mathbf{Y}\times 10^{-3}\mathrm{mol}{\mathrm{L}}^{-1}$. The value of Y is ____. (Given that the value of solubility product of $\mathbf{AB}$ $(K_{sp})=2\times 10^{-10}$ and the value of ionization constant of HB …

Q14.The plot given below shows $P-T$ curves (where $P$ is the pressure and $T$ is the temperature) for two solvents $\mathbf{X}$ and $\mathbf{Y}$ and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents.

On addition of equal number …

Q15.Treatment of benzene with CO/HCl in the presence of anhydrous ${\mathrm{AlCl}}_3/\mathrm{CuCl}$ followed by reaction with ${\mathrm{Ac}}_2\mathrm{O}/\mathrm{NaOAc}$ gives compound $\mathbf{X}$ as the major product. Compound $\mathbf{X}$ upon reaction with …

Q16.Treatment of benzene with CO/HCl in the presence of anhydrous ${\mathrm{AlCl}}_3/\mathrm{CuCl}$ followed by reaction with ${\mathrm{Ac}}_2\mathrm{O}/\mathrm{NaOAc}$ gives compound $\mathbf{X}$ as the major product. Compound $\mathbf{X}$ upon reaction with …

Q17.An organic acid $\mathbf{P}$ $\left({\mathrm{C}}_{11}{\mathrm{H}}_{12}{\mathrm{O}}_2\right)$ can easily be oxidized to a dibasic acid which reacts with ethyleneglycol to produce a polymer dacron. Upon ozonolysis, $\mathbf{P}$ gives an aliphatic ketone as one of the products. …

Q18.An organic acid $\mathbf{P}$ $\left({\mathrm{C}}_{11}{\mathrm{H}}_{12}{\mathrm{O}}_2\right)$ can easily be oxidized to a dibasic acid which reacts with ethyleneglycol to produce a polymer dacron. Upon ozonolysis, $\mathbf{P}$ gives an aliphatic ketone as one of the products. …

Q1.For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument with $-\pi <\arg (z)\le \pi$. Then, which of the following statement(s) is (are) FALSE?

Q2.In a triangle $PQR$, let $\angle PQR=30^{\circ }$ and the sides $PQ$ and $QR$ have lengths $10\sqrt{3}$ and 10, respectively. Then, which of the following statement(s) is (are) TRUE?

Q3.Let $P_1:2x+y-z=3$ and $P_2:x+2y+z=2$ be two planes. Then, which of the following statement(s) is (are) TRUE?

Q4.For every twice differentiable function $f:\mathbb{R}\to [-2,2]$ with $(f(0){)}^2+{\left(f^{\prime }(0)\right)}^2=85$, which of the following statement(s) is (are) TRUE?

Q5.Let $f:\mathbb{R}\to \mathbb{R}$ and $g:\mathbb{R}\to \mathbb{R}$ be two non-constant differentiable functions. If $f^{\prime }(x)=\left(e^{(f(x)-g(x))}\right)g^{\prime }(x)$ for all $x\in \mathbb{R}$, and $f(1)=g(2)=1$, then which of the following s …

Q6.Let $f:[0,\infty )\to \mathbb{R}$ be a continuous function such that $f(x)=1-2x+{\int }_0^x{e}^{x-t}f(t)dt$ for all $x\in [0,\infty )$. Then, which of the following statement(s) is (are) TRUE?

Q7.The value of ${\left({\left({\log }_{2}9\right)}^2\right)}^{\frac{1}{{\log }_2\left({\log }_{2}9\right)}}\times (\sqrt{7}{)}^{\frac{1}{{\log }_{4}7}}$ is ____.

Q8.The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is ____.

Q9.Let $X$ be the set consisting of the first 2018 terms of the arithmetic progression $1,6,11,\dots$, and $Y$ be the set consisting of the first 2018 terms of the arithmetic progression $9,16,23,\dots$. Then, the number of elements in the set $X\cup Y$ is ____.

Q10.The number of real solutions of the equation ${\sin }^{-1}\left({\sum }_{i=1}^{\infty }{x}^{i+1}-x{\sum }_{i=1}^{\infty }{\left(\frac{x}{2}\right)}^i\right)=\frac{\pi }{2}-{\cos }^{-1}\left({\sum }_{i=1}^{\infty }{\left(-\frac{x}{2}\right)}^i-{\sum }_{i=1}^{\infty }(-x{)}^i\right)$ lying in the int …

Q11.For each positive integer $n$, let $y_n=\frac{1}{n}((n+1)(n+2)\cdots (n+n){)}^{\frac{1}{n}}$. For $x\in \mathbb{R}$, let $[x]$ be the greatest integer less than or equal to $x$. If ${\lim }_{n\to \infty }{y}_n=L$, then the value of $[L]$ is ____.

Q12.Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that $\vec{a}\cdot \vec{b}=0$. For some $x,y\in \mathbb{R}$, let $\vec{c}=x\vec{a}+y\vec{b}+(\vec{a}\times \vec{b})$. If $|\vec{c}|=2$ and the vector $\vec{c}$ is inclined at the same angle $\alpha$ to bot …

Q13.Let $a,b,c$ be three non-zero real numbers such that the equation $\sqrt{3}a\cos x+2b\sin x=c$, $x\in \left[-\frac{\pi }{2},\frac{\pi }{2}\right]$, has two distinct real roots $\alpha$ and $\beta$ with $\alpha +\beta =\frac{\pi }{3}$. Then, the value of …

Q14.A farmer $F_1$ has a land in the shape of a triangle with vertices at $P(0,0),Q(1,1)$ and $R(2,0)$. From this land, a neighbouring farmer $F_2$ takes away the region which lies between the side $PQ$ and a curve of the form $y=x^n(n>1)$. If the area of the regi …

Q15.Let $S$ be the circle in the $xy$-plane defined by the equation $x^2+y^2=4$.

Let $E_1{E}_2$ and $F_1{F}_2$ be the chords of $S$ passing through the point $P_0(1,1)$ and parallel to the $x$-axis and the $y$-axis, respectively. Let $G_1{G}_2$ be …

Q16.Let $S$ be the circle in the $xy$-plane defined by the equation $x^2+y^2=4$.

Let $P$ be a point on the circle $S$ with both coordinates being positive. Let the tangent to $S$ at $P$ intersect the coordinate axes at the points $M$ and $N$. Then, the mid-poin …

Q17.There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,i=1,2,3,4,5$. But, on th …

Q18.There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,i=1,2,3,4,5$. But, on th …