JEE Advanced 2016 · 22 May 2016 · Paper 2

Q1.The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by

The measured masses of the neutron, ${}_1^1\mathrm{H},{}_7^{15}\mathrm{N}$ and …

Q2.An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is …

Q3.A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i=10^5\mathrm{Pa}$ and volume $V_i=10^{-3}{\mathrm{m}}^3$ changes to a final state at $P_f=(1/32)\times 10^5\mathrm{Pa}$ and …

Q4.The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10 °C. Now the end P is maintained at 10 °C, while the end S is heated and maintained at 400 °C. The system is thermally insulated from its surroundin …

Q5.A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle …

Q6.There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers ( $C_1$ ) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper …

Q7.Two thin circular discs of mass $m$ and $4m$, having radii of $a$ and $2a$, respectively, are rigidly fixed by a massless, rigid rod of length $l=\sqrt{24}a$ through their centers. This assembly is laid on a firm and flat surface, and set rolling without slipping on …

Q8.light of wavelength ${\lambda }_{\text{ph }}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $\varphi$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. A potential diff …

Q9.In an experiment to determine the acceleration due to gravity $g$, the formula used for the time period of a periodic motion is $T=2\pi \sqrt{\frac{7(R-r)}{5g}}$. The values of $R$ and $r$ are measured to be $(60\pm 1)\mathrm{mm}$ and $(10\pm 1)\mathrm{mm}$, res …

Q10.Consider two identical galvanometers and two identical resistors with resistance $R$. If the internal resistance of the galvanometers $R_{\mathrm{C}}<R/2$, which of the following statement(s) about any one of the galvanometers is(are) true?

Q11.In the circuit shown below, the key is pressed at time $t=0$. Which of the following statement(s) is(are) true?

Q12.A block with mass $M$ is connected by a massless spring with stiffness constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: (i) when the bl …

Q13.While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the $x-y$ plane containing two small holes that act as two coherent point sources ( $S_1,S_2$ ) emitting light of wavelength 600 nm . The student mistakenly …

Q14.A rigid wire loop of square shape having side of length $L$ and resistance $R$ is moving along the $x$-axis with a constant velocity ${\mathrm{v}}_0$ in the plane of the paper. At $t=0$, the right edge of the loop enters a region of length $3L$ where there is a unifo …

Q15.PARAGRAPH 1

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $\omega$ is an example of …

Q16.PARAGRAPH 1

A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $\omega$ is an example of …

Q17.PARAGRAPH 2

Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material ar …

Q18.PARAGRAPH 2

Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material ar …

Q1.For the following electrochemical cell at 298 K, …

Q2.The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of $\mathrm{KCl}$, ${\mathrm{CH}}_3\mathrm{OH}$ and …

Q3.In the following reaction sequence in aqueous solution, the species $\mathbf{X},\mathbf{Y}$ and $\mathbf{Z}$, respectively, are

Q4.The geometries of the ammonia complexes of ${\mathrm{Ni}}^{2+},{\mathrm{Pt}}^{2+}$ and ${\mathrm{Zn}}^{2+}$, respectively, are

Q5.The correct order of acidity for the following compounds is

Q6.The major product of the following reaction sequence is

Q7.According to Molecular Orbital Theory,

Q8.Mixture(s) showing positive deviation from Raoult's law at 35 °C is(are)

Q9.The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are)

Q10.Extraction of copper from copper pyrite $\left({\mathrm{CuFeS}}_2\right)$ involves

Q11.The nitrogen containing compound produced in the reaction of ${\mathrm{HNO}}_3$ with ${\mathrm{P}}_4{\mathrm{O}}_{10}$

Q12.For 'invert sugar', the correct statement(s) is(are)
(Given: specific rotations of (+)-sucrose, (+)-maltose, L-(-)-glucose and L-(+)-fructose in aqueous solution are $+66^{\circ },+140^{\circ },-52^{\circ }$ and $+92^{\circ }$, respectively)

Q13.Reagent(s) which can be used to bring about the following transformation is(are)

Q14.Among the following, reaction(s) which gives(give) tert-butyl benzene as the major product is(are)

Q15.Thermal decomposition of gaseous ${\mathrm{X}}_2$ to gaseous X at 298 K takes place according to the following equation:

The standard reaction Gibbs energy, ${\Delta }_r{G}^{\circ }$, of this reaction is po …

Q16.Thermal decomposition of gaseous ${\mathrm{X}}_2$ to gaseous X at 298 K takes place according to the following equation:

The standard reaction Gibbs energy, ${\Delta }_r{G}^{\circ }$, of this reaction is po …

Q17.Treatment of compound O with ${\mathrm{KMnO}}_4/{\mathrm{H}}^{+}$ gave P, which on heating with ammonia gave Q. The compound Q on treatment with ${\mathrm{Br}}_2/\mathrm{NaOH}$ produced R. On strong heating, Q gave S, which on further treatment with ethyl 2-bromopropanoate in t …

Q18.Treatment of compound O with ${\mathrm{KMnO}}_4/{\mathrm{H}}^{+}$ gave P, which on heating with ammonia gave Q. The compound Q on treatment with ${\mathrm{Br}}_2/\mathrm{NaOH}$ produced R. On strong heating, Q gave S, which on further treatment with ethyl 2-bromopropanoate in t …

Q1.Let $P=\left[\begin{array}{ccc}1& 0& 0\\ 4& 1& 0\\ 16& 4& 1\end{array}\right]$ and $I$ be the identity matrix of order 3. If $Q=\left[q_{ij}\right]$ is a matrix such that $P^{50}-Q=I$, then $\frac{q_{31}+q_{32}}{q_{21}}$ equals

Q2.Let $b_i>1$ for $i=1,2,\dots ,101$. Suppose ${\log }_e{b}_1,{\log }_e{b}_2,\dots ,{\log }_e{b}_{101}$ are in Arithmetic Progression (A.P.) with the common difference ${\log }_{e}2$. Suppose $a_1,a_2,\dots ,a_{101}$ are in A.P. such that $a_1=b_1$ and …

Q3.The value of ${\sum }_{k=1}^{13}\frac{1}{\sin \left(\frac{\pi }{4}+\frac{(k-1)\pi }{6}\right)\sin \left(\frac{\pi }{4}+\frac{k\pi }{6}\right)}$ is equal to

Q4.The value of ${\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\frac{x^2\cos x}{1+e^x}dx$ is equal to

Q5.Area of the region $\left\{(x,y)\in {\mathbb{R}}^2:y\ge \sqrt{|x+3|},5y\le x+9\le 15\right\}$ is equal to

Q6.Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the plane passing through $P$ and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is

Q7.Let $f(x)={\lim }_{n\to \infty }{\left(\frac{n^n(x+n)\left(x+\frac{n}{2}\right)\cdots \left(x+\frac{n}{n}\right)}{n!\left(x^2+n^2\right)\left(x^2+\frac{n^2}{4}\right)\cdots \left(x^2+\frac{n^2}{n^2}\right)}\right)}^{\frac{x}{n}}$, for all $x>0$. Then

Q8.Let $a,b\in \mathbb{R}$ and $f:\mathbb{R}\to \mathbb{R}$ be defined by $f(x)=a\cos \left(\left|x^3-x\right|\right)+b|x|\sin \left(\left|x^3+x\right|\right)$. Then $f$ is

Q9.Let $f:\mathbb{R}\to (0,\infty )$ and $g:\mathbb{R}\to \mathbb{R}$ be twice differentiable functions such that $f^{\prime \prime }$ and $g^{\prime \prime }$ are continuous functions on $\mathbb{R}$. Suppose …

Q10.Let $f:\left[-\frac{1}{2},2\right]\to \mathbb{R}$ and $g:\left[-\frac{1}{2},2\right]\to \mathbb{R}$ be functions defined by $f(x)=\left[x^2-3\right]$ and $g(x)=|x|f(x)+|4x-7|f(x)$, where $[y]$ denotes the greatest integer less than or equal to …

Q11.Let $a,b\in \mathbb{R}$ and $a^2+b^2\ne 0$. Suppose $S=\left\{z\in \mathbb{C}:z=\frac{1}{a+ibt},t\in \mathbb{R},t\ne 0\right\}$, where $i=\sqrt{-1}$. If $z=x+iy$ and $z\in S$, then $(x,y)$ lies on

Q12.Let $P$ be the point on the parabola $y^2=4x$ which is at the shortest distance from the center $S$ of the circle $x^2+y^2-4x-16y+64=0$. Let $Q$ be the point on the circle dividing the line segment $SP$ internally. Then

Q13.Let $a,\lambda ,\mu \in \mathbb{R}$. Consider the system of linear equations

Which of the following statement(s) is(are) correct?

Q14.Let $\hat{u}=u_1\hat{i}+u_2\hat{j}+u_3\hat{k}$ be a unit vector in ${\mathbb{R}}^3$ and $\hat{w}=\frac{1}{\sqrt{6}}(\hat{i}+\hat{j}+2\hat{k})$. Given that there exists a vector $\vec{v}$ in ${\mathbb{R}}^3$ such that $|\hat{u}\times \vec{v}|=1$ and …

Q15.Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and …

Q17.Let $F_1\left(x_1,0\right)$ and $F_2\left(x_2,0\right)$, for $x_1<0$ and $x_2>0$, be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1$. Suppose a parabola having vertex at the origin and focus at $F_2$ intersects the ellipse at point $M$ in …

Q18.Let $F_1\left(x_1,0\right)$ and $F_2\left(x_2,0\right)$, for $x_1<0$ and $x_2>0$, be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1$. Suppose a parabola having vertex at the origin and focus at $F_2$ intersects the ellipse at point $M$ in …