JEE Advanced 2019 · 27 May 2019 · Paper 2

Q1.A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure ${\mathrm{P}}_0$, volume ${\mathrm{V}}_0$ and temperature ${\mathrm{T}}_0$. If the gas mixture is adiabatically compressed to a volume ${\mathrm{V}}_0/4$ …

Q2.An electric dipole with dipole moment $\frac{{\mathrm{p}}_0}{\sqrt{2}}(\hat{\mathrm{i}}+\hat{\mathrm{j}})$ is held fixed at the origin O in the presence of an uniform electric field of magnitude ${\mathrm{E}}_0$. If the potential is constant on a circle of radius R centered a …

Q3.A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod make …

Q4.A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown i …

Q5.Three glass cylinders of equal height $\mathrm{H}=30\mathrm{cm}$ and same refractive index $\mathrm{n}=1.5$ are placed on a horizontal surfaces shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvatur …

Q6.In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $\alpha$ as shown in figure. On the screen, the point O is equidistant from the slits and distan …

Q7.A block of mass 2M is attached to a massless spring with spring-constant k . This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are ${\mathrm{a}}_1$, ${\mathrm{a}}_2$ and ${\mathrm{a}}_3$ as …

Q8.A free hydrogen atom after absorbing a photon of wavelength ${\lambda }_{\mathrm{a}}$ gets excited from the state $\mathrm{n}=1$ to the state $\mathrm{n}=4$. Immediately after that the electron jumps to $\mathrm{n}=\mathrm{m}$ state by emitting a photon of wavelength …

Q9.A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency $\Omega$ such that $\frac{4\pi \mathrm{M}\Omega }{\mathrm{h}}=10^{24}{\mathrm{m}}^{-2}$ with h as Planck's constant. N photons of wavelength …

Q10.A ball is thrown from ground at an angle $\theta$ with horizontal and with an initial speed ${\mathrm{u}}_0$. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is ${\mathrm{V}}_1$. A …

Q11.A 10 cm long perfectly conducting wire PQ is moving, with a velocity 1cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor $\mathrm{L}=1\mathrm{mH}$ and a resistance $\mathrm{R}=1\Omega$ as shown in figure. The horizontal …

Q12.A monochromatic light is incident from air on a refracting surface of a prism of angle 75° and refractive index ${\mathrm{n}}_0=\sqrt{3}$. The other refracting surface of a prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers to …

Q13.Suppose a ${}_{88}^{226}\mathrm{Ra}$ nucleus at rest and in ground state undergoes $\alpha$-decay to a ${}_{86}^{222}\mathrm{Rn}$ nucleus in its excited state. The kinetic energy of the emitted $\alpha$ particle is found to be 4.44 MeV. ${}_{86}^{222}\mathrm{Rn}$ nuc …

Q14.An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlap …

Q15.A musical instrument is made using four different metal strings, 1,2,3 and 4 with mass per unit length $\mu ,2\mu ,3\mu$ and $4\mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range ${\mathrm{L}}_0$ and …

Q16.A musical instrument is made using four different metal strings, 1,2,3 and 4 with mass per unit length $\mu ,2\mu ,3\mu$ and $4\mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range ${\mathrm{L}}_0$ and …

Q17.In a thermodynamics process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $\mathrm{T}\Delta \mathrm{X}$, where T is temperature of the system and $\Delta \mathrm{X}$ is the infinitesimal change in a thermodynamic quantity X of the system. …

Q18.In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $\mathrm{T}\Delta \mathrm{X}$, where T is temperature of the system and $\Delta \mathrm{X}$ is the infinitesimal change in a thermodynamic quantity X of the system. F …

Q1.The cyanide process of gold extraction involves leaching out gold from its ore with CN⁻ in the presence of Q in water to form R. Subsequently, R is treated with T to obtain Au and Z. Choose the correct option(s).

Q2.Which of the following reactions produce(s) propane as a major product?

Q3.The ground state energy of hydrogen atom is -13.6 eV. Consider an electronic state $\Psi$ of ${\mathrm{He}}^{+}$ whose energy, azimuthal quantum number and magnetic quantum number are -3.4 eV, 2 and 0 respectively. Which of the following statement(s) is(are) true for the state …

Q4.Choose the correct option(s) that give(s) an aromatic compound as the major product.

Q5.Consider the following reactions (unbalanced) …

Q6.With reference to aqua regia, choose the correct option(s).

Q7.Choose the correct option(s) from the following

Q8.Choose the correct option(s) for the following reaction sequence

Consider Q, R and S as major products

Q9.The decomposition reaction $2{\mathrm{N}}_2{\mathrm{O}}_5(\mathrm{g})\stackrel{\Delta }{\to }2{\mathrm{N}}_2{\mathrm{O}}_4(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After …

Q10.Total number of isomers, considering both structural and stereoisomers, of cyclic ethers with the molecular formula ${\mathrm{C}}_4{\mathrm{H}}_8\mathrm{O}$ is ____

Q11.The amount of water produced (in g) in the oxidation of 1 mole of rhombic sulphur by conc. ${\mathrm{HNO}}_3$ to a compound with the highest oxidation state of sulphur is ____

(Given data : Molar mass of water $=18\mathrm{g}{\mathrm{mol}}^{-1}$)

Q12.Total number of cis N-Mn-Cl bond angles (that is, Mn-N and Mn-Cl bonds in cis positions) present in a molecule of cis-$\left[\mathrm{Mn}(\text{en}{)}_2{\mathrm{Cl}}_2\right]$ complex is ____

(en $={\mathrm{NH}}_2{\mathrm{CH}}_2{\mathrm{CH}}_2{\mathrm{NH}}_2$)

Q13.Total number of hydroxyl groups present in a molecule of the major product P is ____

Q14.The mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the solution is $1.2\mathrm{g}{\mathrm{cm}}^{-3}$, the molarity of urea solution is ____

(Given data : Molar masses of urea and water are $60\mathrm{g}{\mathrm{mol}}^{-1}$ …

Q15.Answer the following by appropriately matching the lists based on the information given in the paragraph

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the $n^{\text{th}}$ orbit …

Q17.Answer the following by appropriately matching the lists based on the information given in the paragraph

List-I includes starting materials and reagents of selected chemical reactions. List-II gives structures of compounds that may be formed as intermediate products and/or final …

Q1.Let $\mathrm{f}:\mathbb{R}\to \mathbb{R}$ be given by $\mathrm{f}(\mathrm{x})=(\mathrm{x}-1)(\mathrm{x}-2)(\mathrm{x}-5)$. Define $\mathrm{F}(\mathrm{x})={\int }_0^{\mathrm{x}}\mathrm{f}(\mathrm{t})\mathrm{dt},\mathrm{x}>0$. Then which of the following options i …

Q2.For $\mathrm{a}\in \mathbb{R},|\mathrm{a}|>1$, let …

Q3.Three lines
$L_1:\vec{r}=\lambda \hat{i},\lambda \in \mathbb{R}$,
$L_2:\vec{r}=\vec{k}+\mu \hat{j},\mu \in \mathbb{R}$ and
$L_3:\vec{r}=\hat{i}+\hat{j}+v\hat{k},v\in \mathbb{R}$
are given. For which point(s) Q on $L_2$ can we find a point P on $L_1$ an …

Q4.Let $\mathrm{F}:\mathbb{R}\to \mathbb{R}$ be a function. We say that f has
PROPERTY 1 if ${\lim }_{\mathrm{h}\to 0}\frac{\mathrm{f}(\mathrm{h})-\mathrm{f}(0)}{\sqrt{|\mathrm{h}|}}$ exists and is finite, and
PROPERTY 2 if …

Q5.For non-negative integers n, let

Assuming ${\cos }^{-1}\mathrm{x}$ takes values in $[0,\pi ]$, which of the foll …

Q6.Let $P_1=I=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$, $P_2=\left[\begin{array}{lll}1& 0& 0\\ 0& 0& 1\\ 0& 1& 0\end{array}\right]$, $P_3=\left[\begin{array}{lll}0& 1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right]$, …

Q7.Let $\mathrm{x}\in \mathbb{R}$ and let $\mathrm{P}=\left[\begin{array}{lll}1& 1& 1\\ 0& 2& 2\\ 0& 0& 3\end{array}\right]$, $\mathrm{Q}=\left[\begin{array}{ccc}2& \mathrm{x}& \mathrm{x}\\ 0& 4& 0\\ \mathrm{x}& \mathrm{x}& 6\end{array}\right]$ and …

Q8.Let $\mathrm{f}(\mathrm{x})=\frac{\sin \pi \mathrm{x}}{{\mathrm{x}}^2},\mathrm{x}>0$
Let ${\mathrm{x}}_1<{\mathrm{x}}_2<{\mathrm{x}}_3<\dots <{\mathrm{x}}_{\mathrm{n}}<\dots$ be all the points of local maximum of f and …

Q9.The value of ${\sec }^{-1}\left(\frac{1}{4}{\sum }_{\mathrm{k}=0}^{10}\sec \left(\frac{7\pi }{12}+\frac{\mathrm{k}\pi }{2}\right)\sec \left(\frac{7\pi }{12}+\frac{(\mathrm{k}+1)\pi }{2}\right)\right)$ in the interval $\left[-\frac{\pi }{4},\frac{3\pi }{4}\right]$ equals

Q10.Let |X| denote the number of elements in set X. Let $\mathrm{S}=\{1,2,3,4,5,6\}$ be a sample space, where each element is equally likely to occur. If A and B are indepenent events associated with S, then the number of ordered pairs (A,B) such that …

Q11.Five person A,B,C,D and E are seated in a ciruclar arrangement. If each of them is given a hat of one of the three colours red, blue and green ,then the number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is

Q12.Suppose $\det \left[\begin{array}{cc}{\sum }_{k=0}^{n}k& {\sum }_{k=0}^n{}^n{C}_k{k}^2\\ {\sum }_{k=0}^n{}^n{C}_{k}k& {\sum }_{k=0}^n{}^n{C}_k{3}^k\end{array}\right]=0$, holds for some positive integer $n$. Then …

Q13.The value of the integral ${\int }_0^{\pi /2}\frac{3\sqrt{\cos \theta }}{(\sqrt{\cos \theta }+\sqrt{\sin \theta }{)}^5}\mathrm{d}\theta$ equals

Q14.Let $\vec{a}=2\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}+\hat{k}$ be two vectors. Consider a vector $\vec{c}=\alpha \vec{a}+\beta \vec{b},\alpha ,\beta \in \mathbb{R}$. If the projection of $\vec{c}$ on the vector $(\vec{a}+\vec{b})$ is $3\sqrt{2}$, th …

Q15.Answer the following by appropriately matching the lists based on the information given in the paragraph
Let $f(x)=\sin (\pi \cos x)$ and $g(x)=\cos (2\pi \sin x)$ be two functions defined for $x>0$. Define the following sets whose elements are written in the increasing or …

Q17.Answer the following by appropriately matching the lists based on the information given in the paragraph
Let the circles ${\mathrm{C}}_1:{\mathrm{x}}^2+{\mathrm{y}}^2=9$ and ${\mathrm{C}}_2:(\mathrm{x}-3{)}^2+(\mathrm{y}-4{)}^2=16$, intersect at the points X and Y. Suppose t …

Q18.Answer the following by appropriately matching the lists based on the information given in the paragraph
Let the circles ${\mathrm{C}}_1:{\mathrm{x}}^2+{\mathrm{y}}^2=9$ and ${\mathrm{C}}_2:(\mathrm{x}-3{)}^2+(\mathrm{y}-4{)}^2=16$, intersect at the points X and Y. Suppose t …