JEE Advanced 2019 · 27 May 2019 · Paper 1

Q1.A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as : …

Q2.A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is ${\mathrm{V}}_0$. A hole with a small area $\alpha 4\pi {\mathrm{R}}^2(\alpha \ll 1)$ is made on the shell without affecting the rest of the shell. Whic …

Q3.Consider a spherical gaseous cloud of mass density $\rho (\mathrm{r})$ in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force a …

Q4.In a radioactive sample, ${}_{19}^{40}\mathrm{K}$ nuclei either decay into stable ${}_{20}^{40}\mathrm{Ca}$ nuclei with decay constant $4.5\times 10^{-10}$ per year or into stable ${}_{18}^{40}\mathrm{Ar}$ nuclei with decay constant $0.5\times 10^{-10}$ per year. Given that in th …

Q5.One mole of a monoatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are :
[R is the gas constant]

Q6.In the circuit shown, initially there is no charge on capacitors and keys ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are open. The values of the capacitors are ${\mathrm{C}}_1=10\mu \mathrm{F},{\mathrm{C}}_2=30\mu \mathrm{F}$ and ${\mathrm{C}}_3={\mathrm{C}}_4=80\mu \mathrm{F}$ …

Q7.A thin convex lens is made of two materials with refractive indices ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when …

Q8.Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement (s) is/are correct ?

Q9.A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0° and 60°, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in f …

Q10.Two identical moving coil galvanometer have $10\Omega$ resistance and full scale deflection at $2\mu \mathrm{A}$ current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1 mA full scale current using appropriate resistors …

Q11.A charged shell of radius R carries a total charge Q. Given $\Phi$ as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is …

Q12.A conducting wire of parabolic shape, initially $y=x^2$, is moving with velocity $\vec{V}=V_0\hat{i}$ in a nonuniform magnetic field $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\left(1+{\left(\frac{\mathrm{y}}{\mathrm{L}}\right)}^{\beta }\right)\hat{\mathrm{k}}$, as shown in fi …

Q13.A block of weight 100 N is suspended by copper and steel wires of same cross sectional area $0.5{\mathrm{cm}}^2$ and, length $\sqrt{3}\mathrm{m}$ and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires …

Q14.A planar structure of length L and width W is made of two different optical media of refractive indices ${\mathrm{n}}_1=1.5$ and ${\mathrm{n}}_2=1.44$ as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition …

Q15.A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force $\overrightarrow{\mathrm{F}}=(\alpha \mathrm{y}\hat{\mathrm{i}}+2\alpha \mathrm{x}\hat{\mathrm{j}})$ N, where x and y are in meter and $\alpha =-1\mathrm{N}/{\mathrm{m}}^{-1}$. The …

Q16.A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness $\delta =\frac{\mathrm{d}}{\mathrm{N}}$. The dielectric constant of the …

Q17.A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away f …

Q18.A liquid at 30°C is poured very slowly into a Calorimeter that is at temperature of 110°C. The boiling temperature of the liquid is 80°C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is …

Q1.Molar conductivity (${\Lambda }_{\mathrm{m}}$) of aqueous solution of sodium stearate, which behaves as a strong electrolyte, is recorded at varying concentration(c) of sodium stearate. Which one of the following plots provides the correct representation of micelle formation in th …

Q2.The correct order of acid strength of the following carboxylic acids is -

Q3.Calamine, malachite, magnetite and cryolite, respectively are

Q4.The green colour produced in the borax bead test of a chromium(III) salt is due to -

Q5.Fusion of ${\mathrm{MnO}}_2$ with KOH in presence of ${\mathrm{O}}_2$ produces a salt $\mathbf{W}$. Alkaline solution of $\mathbf{W}$ upon eletrolytic oxidation yields another salt $\mathbf{X}$. The manganese containing ions present in $\mathbf{W}$ and $\mathbf{X}$, …

Q6.Which of the following statement(s) is (are) correct regarding the root mean square speed $\left({\mathrm{U}}_{\text{rms }}\right)$ and average translational kinetic energy ( ${\epsilon }_{\text{av }}$ ) of a molecule in a gas at equilibrium ?

Q7.In the decay sequence :
…

Q8.Which of the following statement(s) is(are) true ?

Q9.A tin chloride Q undergoes the following reactions (not balanced) …

Q10.Choose the correct option(s) for the following set of reactions

Q11.Each of the following options contains a set of four molecules. Identify the option(s) where all four molecules possess permanent dipole moment at room temperature.

Q12.Choose the reaction(s) from the following options, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation.

Q13.For the following reaction, the equilibrium constant ${\mathrm{K}}_{\mathrm{c}}$ at 298 K is $1.6\times 10^{17}$.

When equal volumes of …

Q14.Among ${\mathrm{B}}_2{\mathrm{H}}_6,{\mathrm{B}}_3{\mathrm{N}}_3{\mathrm{H}}_6,{\mathrm{N}}_2\mathrm{O},{\mathrm{N}}_2{\mathrm{O}}_4,{\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_3$ and ${\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_8$, the total number of molecules c …

Q15.Consider the kinetic data given in the following table for the reaction $\mathrm{A}+\mathrm{B}+\mathrm{C}\to$ Product.

| Experiment No. | [A] $\left(\mathrm{mol}{\mathrm{dm}}^{-3}\right)$ | [B] $\left(\mathrm{mol}{\mathrm{dm}}^{-3}\right)$ | [C] …

Q16.On dissolving 0.5 g of a non-volatile non-ionic solute to 39 g of benzene, its vapor pressure decreases from 650 mm Hg to 640 mm Hg . The depression of freezing point of benzene (in K) upon addition of the solute is ____
(Given data : Molar mass and the molal freezing point depre …

Q17.Scheme 1 and 2 describe the conversion of $\mathbf{P}$ to $\mathbf{Q}$ and $\mathbf{R}$ to $\mathbf{S}$, respectively. Scheme 3 describes the synthesis of $\mathbf{T}$ from $\mathbf{Q}$ and $\mathbf{S}$. The total number of Br atoms in a molecule of $\mathbf{T}$ i …

Q18.At 143 K. the reaction of ${\mathrm{XeF}}_4$ with ${\mathrm{O}}_2{\mathrm{F}}_2$ produces a xenon compound $\mathbf{Y}$. The total number of lone pair(s) of electrons present on the whole molecule of $\mathbf{Y}$ is ____

Q1.Let $\mathrm{M}=\left[\begin{array}{cc}{\sin }^4\theta & -1-{\sin }^2\theta \\ 1+{\cos }^2\theta & {\cos }^4\theta \end{array}\right]=\alpha \mathrm{I}+\beta {\mathrm{M}}^{-1}$,
where $\alpha =\alpha (\theta )$ and $\beta =\beta (\theta )$ are real number, and I is the $2\times 2$ id …

Q2.A line $\mathrm{y}=\mathrm{mx}+1$ intersects the circle $(\mathrm{x}-3{)}^2+(\mathrm{y}+2{)}^2=25$ at the points P and Q. If the midpoint of the line segment PQ has x-coordinate $-\frac{3}{5}$, then which one of the following options is correct?

Q3.Let S be the set of all complex numbers z satisfying $|\mathrm{z}-2+\mathrm{i}|\ge \sqrt{5}$. If the complex number ${\mathrm{z}}_0$ is such that $\frac{1}{|z_0-1|}$ is the maximum of the set $\left\{\frac{1}{|z-1|}:z\in S\right\}$, then the principal argument of …

Q4.The area of the region $\left\{(\mathrm{x},\mathrm{y}):\mathrm{xy}\le 8,1\le \mathrm{y}\le {\mathrm{x}}^2\right\}$ is

Q5.There are three bags ${\mathrm{B}}_1,{\mathrm{B}}_2$ and ${\mathrm{B}}_3$. The bag ${\mathrm{B}}_1$ contains 5 red and 5 green balls, ${\mathrm{B}}_2$ contains 3 red and 5 green balls, and ${\mathrm{B}}_3$ contains 5 red and 3 green balls, Bags ${\mathrm{B}}_1,{\mathrm{B}}_2$ …

Q6.Define the collections $\left\{{\mathrm{E}}_1,{\mathrm{E}}_2,{\mathrm{E}}_3,\dots ..\right\}$ of ellipses and $\left\{{\mathrm{R}}_1,{\mathrm{R}}_2,{\mathrm{R}}_3,\dots ..\right\}$ of rectangles as follows : …

Q7.Let $\mathrm{M}=\left[\begin{array}{lll}0& 1& \mathrm{a}\\ 1& 2& 3\\ 3& \mathrm{b}& 1\end{array}\right]$ and $\mathrm{adj}\mathrm{M}=\left[\begin{array}{ccc}-1& 1& -1\\ 8& -6& 2\\ -5& 3& -1\end{array}\right]$ where a and b are real numbers. Which of the fo …

Q8.Let $f:\mathbb{R}\to \mathbb{R}$ be given by …

Q9.Let $\alpha$ and $\beta$ be the roots of $x^2-x-1=0$, with $\alpha >\beta$. For all positive integers n, define

Then which o …

Q10.Let $\Gamma$ denote a curve $\mathrm{y}=\mathrm{y}(\mathrm{x})$ which is in the first quadrant and let the point $(1,0)$ lie on it. Let the tangent to $\Gamma$ at a point P intersect the y-axis at ${\mathrm{Y}}_{\mathrm{P}}$. If ${\mathrm{PY}}_{\mathrm{P}}$ has length 1 for each poin …

Q11.In a non-right-angled triangle $\Delta \mathrm{PQR}$, let p, q, r denote the lengths of the sides opposite to the angles at P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E , and RS and PE intersect at O . If …

Q12.Let ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ denotes the lines

respectively. If …

Q13.If

then $27{\mathrm{I}}^2$ equals ____

Q14.Let the point B be the reflection of the point $\mathrm{A}(2,3)$ with respect to the line $8\mathrm{x}-6\mathrm{y}-23=0$. Let ${\Gamma }_{\mathrm{A}}$ and ${\Gamma }_{\mathrm{B}}$ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles …

Q15.Let AP (a; d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference $\mathrm{d}>0$. If $\mathrm{AP}(1;3)\cap \mathrm{AP}(2;5)\cap \mathrm{AP}(3;7)=\mathrm{AP}(\mathrm{a};\mathrm{d})$ then a + d equals ____

Q16.Let S be the sample space of all 3 × 3 matrices with entries from the set $\{0,1\}$. Let the events ${\mathrm{E}}_1$ and ${\mathrm{E}}_2$ be given by …

Q17.Three lines are given by

Let the lines cut the plane …

Q18.Let $\omega \ne 1$ be a cube root of unity. Then the minimum of the set

equals ____