JEE Advanced 2016 Question Paper with Solutions

Consider two solid spheres P and Q each of density 8 gm cm –3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm –3 and viscosity η = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm –3 and viscosity η = 2 poiseulles. The ratio of the terminal velocities of P and Q is

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is : (Specific heat of water is 4.2 kJ kg −1 K −1 and the density of water is 1000 kg m −3 )

A length-scale (l) depends on the permittivity ( $\varepsilon$ ) of a dielectric material, Boltzmann constant (k B ), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for I is(are) dimensionally correct?

A uniform wooden stick of mass 1.6 kg and length $l$ rests in an inclined manner on a smooth, vertical wall of height h ( < $l$ ) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^\circ$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio ${h \over l}$ and the frictional force f at the bottom of the stick are ( g =10 ms -2 )

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure P i = 10 5 Pa and volume V i = 10 -3 m 3 changes to a final state at P f = $\left( {{1 \over {32}}} \right) \times {10^5}\,Pa$ and V f = 8 $\times$ 10 -3 m 3 in an adiabatic quasi-static process, such that P 3 V 5 = constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at P i followed by an isochoric (isovolumetric) process at volume V f . The amount of heat supplied to the system in the two-step process is approximately

The compound(s) with TWO lone pairs of electrons on the central atom is(are)

In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitative oxidise thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is....

In the following mono-bromination reaction, the number of possible chiral product(s) is (are)...

P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is $4\pi r^2dr$ . The quantitative ketch of the dependence of P on r is

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is ___________:

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection of a captain (from among these 4 members ) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

Let RS be the diameter of the circle ${x^2}\, + \,{y^2} = 1$ , where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point (s)

Let $S = \left\{ {x \in \left( { - \pi ,\pi } \right):x \ne 0, \pm {\pi \over 2}} \right\}.$ The sum of all distinct solutions of the equation $\sqrt 3 \,\sec x + \cos ec\,x + 2\left( {\tan x - \cot x} \right) = 0$ in the set S is equal to

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

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

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90 $^\circ$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 As $-$ 1 . Which of the following statement(s) is (are) true?

A hydrogen atom in its ground state is irradiated by light of wavelength 970 $\mathop A\limits^o$ . Taking hc = 1.237 $\times$ 10 $-$ 6 eVm and the ground state energy of hydrogen atom as $-$ 13.6 eV, the number of lines present in the emission spectrum is

The isotope $_5^{12}B$ having a mass 12.014 u undergoes $\beta$ -decay to $_6^{12}C$ . $_6^{12}C$ has an excited state of the nucleus ( $_6^{12}C$ *) at 4.041 MeV above its ground state. If $_5^{12}B$ decays to $_6^{12}C$ *, the maximum kinetic energy of the $\beta$ -particle in units of MeV is (1u = 931.5 MeV/c 2 , where c is the speed of light in vacuum).

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength ( $\lambda$ ) of incident light and the corresponding stopping potential (V 0 ) are given below: .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} $\lambda \left( {\mu m} \right)$ V 0 (Volt) 0.3 2.0 0.4 1.0 0.5 0.4 Given that c = 3 $\times$ 10 8 ms -1 and e = 1.6 $\times$ 10 -19 C, Planck's constant (in units of J-s) found from such an experiment is) :

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is (are) true?

Let $\alpha$ , $\beta$ $\in$ R be such that $\mathop {\lim }\limits_{x \to 0} {{{x^2}\sin (\beta x)} \over {\alpha x - \sin x}} = 1$ . Then 6( $\alpha$ + $\beta$ ) equals _________.

Consider a pyramid $OPQRS$ located in the first octant $\left( {x \ge 0,y \ge 0,z \ge 0} \right)$ with $O$ as origin, and $OP$ and $OR$ along the $x$ -axis and the $y$ -axis, respectively. The base $OPQR$ of the pyramid is a square with $OP=3.$ The point $S$ is directly above the mid-point, $T$ of diagonal $OQ$ such that $TS=3.$ Then

The least value of a ∈ R for which 4 a x 2 + 1 x ≥ 1 , , for all x > 0 . is

Let $f:(0,\infty ) \to R$ be a differentiable function such that $f'(x) = 2 - {{f(x)} \over x}$ for all $x \in (0,\infty )$ and $f(1) \ne 1$ . Then

The total number of distinct $x \in \left[ {0,1} \right]$ for which $\int\limits_0^x {{{{t^2}} \over {1 + {t^4}}}} dt = 2x - 1$

The crystalline form of borax has.

According to the Arrhenius equation,

Positive Tollen’s test is observed for

A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of decay is(are)

The correct statements about of the following reaction sequence is (are) Cumene (C 9 H 12 ) ⟶ ( i i ) H 3 O + ( i ) O 2 P ⟶ C H C l 3 / N a O H Q (major) + R (minor) Q ⟶ P h C H 2 B r N a O H S