JEE Advanced 2016 Paper 1 Offline

The correct statements about of the following reaction sequence is (are)
Cumene (C9H12) \(\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{(ii)\,{H_3}{O^ + }}^{(i)\,{O_2}}}\) P $$\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{}^{CHC...

Positive Tollen’s test is observed for

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

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

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 ...

According to the Arrhenius equation,

The product(s) of the following reaction sequence is (are)

Among [Ni(CO)4], [NiCl4]2\(-\), [Co(NH3)4)Cl2]Cl, Na3[CoF6], Na2O2 and CsO2, the total number of paramagnetic compound is

The possible number of geometrical isomers for the complex [CoL2Cl2]-(L= H2NCH2CH2O-) is (are)...

The reagent(s) that can selectively precipitate S2- from a mixture of S2- and SO42- in aqueous solution is (are) :

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 t...

The increasing order of atomic radii of the following group 13 elements is

The crystalline form of borax has.

On complete hydrogenation, natural rubber produces

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....

The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its
molality. Density of this solution at 298 K is 2.0 g cm–3 . The ratio of the molecular weights of the solute and solvent, $$\left( {{...

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 ...

One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to
2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surrounding (\(\Delta\)Ssurr)in
JK–1 is (1L at...

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 s...

The least value of a \(\in R\) for which \(4a{x^2} + {1 \over x} \ge 1,\), for all \(x>0\). 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...

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

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

A solution curve of the differential equation
\(\left( {{x^2} + xy + 4x + 2y + 4} \right){{dy} \over {dx}} - {y^2} = 0,\) \(x>0,\) passes through the
point \((1,3)\). Then the solution curve

Let \(f:\mathbb{R} \to \mathbb{R},\,g:\mathbb{R} \to \mathbb{R}\) and \(h:\mathbb{R} \to \mathbb{R}\) be differentiable functions such that \(f\left( x \right)= {x^3} + 3x + 2,\) \(g\left( {f\left( x \right)} \right) = x\) and $$h\left( {g\...

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 _________.

Let \(m\) be the smallest positive integer such that the coefficient of \({x^2}\) in the expansion of $${\left( {1 + x} \right)^2} + {\left( {1 + x} \right)^3} + ........ + {\left( {1 + x} \right)^{49}} + {\left( {1 + mx} \right)^{50}}\,\,$...

Let \(P = \left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]\), where \(\alpha\) \(\in\) R. Suppose \(Q = [{q_{ij}}]\) is a matrix such that PQ = kl, where k \(\in\) R, k \(\ne\) 0 a...

The total number of distinct x \(\in\) R for which
\(\left| {\matrix{ x & {{x^2}} & {1 + {x^3}} \cr {2x} & {4{x^2}} & {1 + 8{x^3}} \cr {3x} & {9{x^2}} & {1 + 27{x^3}} \cr } } \right| = 10\) is ______________.

Let \(z = {{ - 1 + \sqrt 3 i} \over 2}\), where \(i = \sqrt { - 1}\), and r, s \(\in\) {1, 2, 3}. Let \(P = \left[ {\matrix{ {{{( - z)}^r}} & {{z^{2s}}} \cr {{z^{2s}}} & {{z^r}} \cr } } \right]\) and I be the identity matrix of...

The circle \({C_1}:{x^2} + {y^2} = 3,\) with centre at \(O\), intersects the parabola \({x^2} = 2y\) at the point \(P\) in the first quadrant, Let the tangent to the circle \({C_1}\), at \(P\) touches other two circles \({C_2}\) and $${C_3}...

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...

A computer producing factory has only two plants \({T_1}\) and \({T_2}.\) Plant \({T_1}\) produces \(20\)% and plant \({T_2}\) produces \(80\)% of the total computers produced. \(7\)% of computers produced in the factory turn out to be defe...

In a triangle \(\Delta\)\(XYZ\), let \(x, y, z\) be the lengths of sides opposite to the angles \(X, Y, Z\) respectively, and \(2s = x + y + z\).
If \({{s - x} \over 4} = {{s - y} \over 3} = {{s - z} \over 2}\) and area of incircle of the ...

Let \(- {\pi \over 6} < \theta < - {\pi \over {12}}.\) Suppose \({\alpha _1}\) and \({\beta_1}\) are the roots of the equation \({x^2} - 2x\sec \theta + 1 = 0\) and \({\alpha _2}\) and \({\beta _2}\) are the roots of the equation $${...

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 equa...

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n, where n >> 1. Which of the following statement(s) is(are) true?

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 m...

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...

An infinite line charge of uniform electric charge density l lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity e ...

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 sufficient...

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 th...

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 ...

Two inductors L1 (inductance 1mH, internal resistance 3\(\Omega\)) and L2 (inductance 2 mH, internal resistance 4\(\Omega\)), and a resistor R (resistance 12\(\Omega\)) are all connected in parallel across a 5V battery. The circuit is switc...

A plano-convex lens is made of material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex sur...

A parallel beam of light is incident from air at an anglea on the side PQ of a right angled triangular prism of refractive index n = \(\sqrt 2\). Light undergoes total internal reflection in the prism at the face PR when a has a mi...

A transparent slab of thickness d has a refractive index n (z) that increases with z. Here, z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (>...

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 genera...

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P)
by the metal. The sensor has a scale that displays \({\log _2}\left( {{P \over {{P_0}}}} \right)\), where P0 is a constant. When th...

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 \(\eta\) = 3 poiseulles. Sphere Q is dropped into a liquid of ...