JEE Advanced 2017 Question Paper with Solutions

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that $\overrightarrow{OP}$ . $\overrightarrow{OQ}$ + $\overrightarrow{OR}$ . $\overrightarrow{OS}$ = $\overrightarrow{OR}$ . $\overrightarrow{OP}$ + $\overrightarrow{OQ}$ . $\overrightarrow{OS}$ = $\overrightarrow{OQ}$ . $\overrightarrow{OR}$ + $\overrightarrow{OP}$ . $\overrightarrow{OS}$ Then the triangle PQR has S as its

| O X → × O Y → | = ?

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque τ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?

Consider regular polygons with number of sides $n=3,4,5....$ as shown in the figure. The center of mass of all the polygons is at height $h$ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is $\Delta$ . Then $\Delta$ depends on $n$ and $h$ as

The total kinetic energy of the ring is

The standard state Gibbs free energies of formation of $C$ (graphite) and $C$ (diamond) at $T=298$ $K$ are ${\Delta _f}{G^0}$ [ $C$ (graphite)] $= 0kJmo{l^{ - 1}}$ ${\Delta _f}{G^0}$ [ $C$ (diamond)] $= 2.9kJmo{l^{ - 1}}$ The standard state means that the pressure should be $1$ bar, and substance should be pure at a given temperature. The conversion of graphite [ $C$ (graphite)] to diamond [ $C$ (diamond)] reduces its volume by $2 \times {10^{ - 6}}\,{m^3}\,mo{l^{ - 1}}$ If $C$ (graphite) is converted to $C$ (diamond) isothermally at $T=298$ $K,$ the pressure at which $C$ (graphite) is in equilibrium with $C$ (diamond), is [Useful information : $1$ $J=1$ $kg\,{m^2}{s^{ - 2}};1\,Pa = 1\,kg\,{m^{ - 1}}{s^{ - 2}};$ $1$ bar $= {10^5}$ $Pa$ ]

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant K in terms of change in entropy is described by

The order of the oxidation state of the phosphorous atom in ${H_3}P{O_2},{H_3}P{O_4},{H_3}P{O_3}$ and ${H_4}{P_2}{O_6}$ is

For the following compounds, the correct statement(s) with respect to nucleophilic substitution reaction is (are)

If a 4 = 28, then p + 2q =

a 12 = ?

Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let N k be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N 1 + N 2 + N 3 + N 4 + N 5 =

Let $\alpha$ and $\beta$ be non zero real numbers such that $2(\cos \beta - \cos \alpha ) + \cos \alpha \cos \beta = 1$ . Then which of the following is/are true?

Two coherent monochromatic point sources ${S_1}$ and ${S_2}$ of wavelength $\lambda = 600\,nm$ are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance $d=1.8$ $mm.$ This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $\Delta \theta .$ Which of the following options is/are correct?

A symmetric star shaped conducting wire loop is carrying a steady state current I as shown in the figure. The distance between the diametrically opposite vertices of the star is 4 a . The magnitude of the magnetic field at the center of the loop is

The instantaneous voltages at three terminals marked $X,Y$ and $Z$ are given by ${V_x} = {V_0}\,\sin \,\omega t,$ ${V_Y} = {V_0}\,\sin$ $\left( {\omega t + {{2\pi } \over 3}} \right)$ and $Vz = {V_0}\sin \left( {\omega t + {{4\pi } \over 3}} \right)$ An ideal voltmeter is configured to read $rms$ value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z.$ The reading(s) of the voltmeter will be

A source of constant voltage V is connected to a resistance R and two ideal inductors L 1 and L 2 through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t = 0, the switch is closed and current begins to flow. Which of the following options is/are correct?

In Process 2, total energy dissipated across the resistance E D is

If y = y(x) satisfies the differential equation ${8\sqrt x \left( {\sqrt {9 + \sqrt x } } \right)dy = {{\left( {\sqrt {4 + \sqrt {9 + \sqrt x } } } \right)}^{ - 1}}}$ dx, x > 0 and y(0) = $\sqrt 7$ , then y(256) =

Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is

If f : R → R is a twice differentiable function such that f"(x) > 0 for all x ∈ R, and f ( 1 2 ) = 1 2 , f(1) = 1, then

Let $f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)$ for x $\ne$ 1. Then

If the line x = $\alpha$ divides the area of region R = {(x, y) $\in$ R 2 : x 3 $\le$ y $\le$ x, 0 $\le$ x $\le$ 1} into two equal parts, then

The major product of the following reaction is

The order of basicity among the following compounds is

The correct statement(s) about surface properties is (are)

The options(s) with only amphoteric oxides is (are)

Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 kg m o l − 1 . The figures shown below represent plots of vapor pressure ( V . P . ) versus temperature ( T ) . [molecular weight of ethanol is 46 g m o l − 1 . ] Among the following, the option representing change in the freezing point is