JEE Advanced 2020 Paper 2 Offline

An organic compound (C8H10O2) rotates plane-porarised light. It produces pink color with neutral FeCl3 solution. What is the total number of all the possible isomers for this compound?

Consider the following four compounds, I, II, III, and IV. Choose the correct statement(s)

The structure of a peptide is given below. If the absolute values of the net charge of the peptide at $\mathrm{pH}$ $=2$, $\mathrm{pH}=6$, and $\mathrm{pH}=11$ are $\left|Z_1\right|,\left|Z_2\right|$, and $\left|Z_3\right|$, respectively, t...

Consider the following compounds in the liquid form :O2, HF, H2O, NH3, H2O2, CCl4, CHCl3, C6H6, C6H5ClWhen a charged comb is brought near their flowing stream, how many of them show deflection as per the following figure?

Which of the following plots is(are) correct for the given reaction?([P]0 is the initial concentration of P)

Consider the reaction sequence from P to Q shown below. The overall yield of the major product Q from P is 75%. What is the amount in grams of Q obtained from 9.3 mL of P? (Use density of P = 1.00 g mL-1; Molar mass of C = 12.0, H = 1.0, O ...

In an experiment, m grams of a compound X (gas/liquid/solid) taken in a container is loaded in a balance as shown in figure I below.In the presence of a magnetic field, the pan with X is either deflected upwards (figure II), or deflected do...

An acidified solution of potassium chromate was layered with an equal volume of amyl alcohol. When it was shaken after the addition of 1 mL of 3% H2O2, a blue alcohol layer was obtained. The blue colour is due to the formation of a chromium...

Consider the following transformations of a compound P. Choose the correct option(s).

An acidified solution of 0.05 M Zn2+ is saturated with 0.1 M H2S. What is the minimum molar concentration (M) of H+ required to prevent the precipitation of ZnS?Use Ksp(ZnS) = 1.25 \(\times\) 10\(-\)22 and overall dissociation constant of...

A solution of 0.1 M weak base (B) is titrated with 0.1 M of a strong acid (HA). The variation of pH of the solution with the volume of HA added is shown in the figure below. What is the pKb of the base? The neutralisation reaction is given ...

Which among the following statement(s) is/are true for the extraction of aluminium from bauxite?

The 1st, 2nd and 3rd ionisation enthalpies, I1, I2 and I3, of four atoms with atomic numbers n, n + 1, n + 2, and n + 3, where n < 10, are tabulated below. What is the value of n?

Choose the correct statement(s) among the following :

Liquids A and B form ideal solution for all compositions of A and B at 25\(^\circ\)C. Two such solutions with 0.25 and 0.50 mole fractions of A have the total vapour pressure of 0.3 and 0.4 bar, respectively. What is the vapour pressure of...

In the chemical reaction between stoichiometric quantities of KMnO4 and KI in weakly basic solution, what is the number of moles of I2 released for 4 moles of KMnO4 consumed?

The figure below is the plot of potential energy versus internuclear distance (d) of H2 molecule in the electronic ground state. What is the value of the net potential energy E0 (as indicated in the figure) in kJ mol-1, for d = d0 at which ...

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K) at which the reduction of cassiterite by coke would take place.At $$298K:{\Delta _f}H^\circ [Sn{O_2}(s)] = - 581....

Let \(\alpha\)2 + \(\beta\)2 + \(\gamma\)2 \(\ne\) 0 and \(\alpha\) + \(\gamma\) = 1. Suppose the point (3, 2, \(-\)1) is the mirror image of the point (1, 0, \(-\)1) with respect to the plane \(\alpha\)x + \(\beta\)y + \(\gamma\)...

Let O be the centre of the circle x2 + y2 = r2, where \(r > {{\sqrt 5 } \over 2}\). Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle ...

For a complex number z, let Re(z) denote that real part of z. Let S be the set of all complex numbers z satisfying \({z^4} - |z{|^4} = 4i{z^2}\), where i = \(\sqrt { - 1}\). Then the minimum possible value of |z1 \(-\) z2|2, where z1, z2$$...

Let \(f:R \to R\) be a differentiable function such that its derivative f' is continuous and f(\(\pi\)) = \(-\)6.If \(F:[0,\pi ] \to R\) is defined by \(F(x) = \int_0^x {f(t)dt}\), and if \(\int_0^\pi {(f'(x)} + F(x))\cos x\,dx\) = 2the...

Let b be a nonzero real number. Suppose f : R \(\to\) R is a differentiable function such that f(0) = 1. If the derivative f' of f satisfies the equation \(f'(x) = {{f(x)} \over {{b^2} + {x^2}}}\)for all x\(\in\)R, then which of the fol...

Let the function f : [0, 1] \(\to\) R be defined by\(f(x) = {{{4^x}} \over {{4^x} + 2}}\)Then the value of $$f\left( {{1 \over {40}}} \right) + f\left( {{2 \over {40}}} \right) + f\left( {{3 \over {40}}} \right) + ... + f\left( {{{39} \ov...

Let the function \(f:(0,\pi ) \to R\) be defined by \(f(\theta ) = {(\sin \theta + \cos \theta )^2} + {(\sin \theta - \cos \theta )^4}\)Suppose the function f has a local minimum at \(\theta\) precisely when $$\theta \in \{ {\lambda _...

Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\). Suppose the tangent to the hyperbola at P passes th...

Let f : R \(\to\) R and g : R \(\to\) R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) for all x, y\(\in\)R. If \(\mathop {\lim }\limits_{x \to 0} g(x) = 1\), then which of the following statements is/are T...

The value of the limit$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{4\sqrt 2 (\sin 3x + \sin x)} \over {\left( {2\sin 2x\sin {{3x} \over 2} + \cos {{5x} \over 2}} \right) - \left( {\sqrt 2 + \sqrt 2 \cos 2x + \cos {{3x} \over 2}} \righ...

Let the functions \(f:( - 1,1) \to R\) and \(g:( - 1,1) \to ( - 1,1)\) be defined by \(f(x) = |2x - 1| + |2x + 1|\) and \(g(x) = x - [x]\), where [x] denotes the greatest integer less than or equal to x. Let \(f\,o\,g:( - 1,1) \to R\) be th...

For non-negative integers s and r, let\(\left( {\matrix{ s \cr r \cr } } \right) = \left\{ {\matrix{ {{{s!} \over {r!(s - r)!}}} & {if\,r \le \,s,} \cr 0 & {if\,r\, > \,s} \cr } } \right.\)For positive integers m and...

The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 \(\times\) 2 matrix such that the trace of A is 3 and the trace of A3 is \(-\)18, then the value of the determinant of A is .............

An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the...

In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can...

The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of ...

Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns ...

Let a and b be positive real numbers. Suppose \(PQ = a\widehat i + b\widehat j\) and \(PS = a\widehat i - b\widehat j\) are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of \(w = \widehat i + \widehat j\) alo...

In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and char...

Two capacitors with capacitance values C1 = 2000 \(\pm\) 10 pF and C2 = 3000 \(\pm\) 15 pF are connected in series. The voltage applied across this combination is V = 5.00 \(\pm\) 0.02 V. The percentage error in the calculation of the...

In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance R3 has temperature coefficient 0.0004\(^\circ\)C-1. If the temperature of R3 is increased by 100$...

The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistors, mutual-inductance and applied voltages are specified in the given circuit. After both the...

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is \(\alpha\). The spheres are...

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as
shown in the figure. Charged oil drops of density 900 kg m−3
are released through a tiny hole at the
center of the top disc. Once some oil...

A point charge q of mass m is suspended vertically by a string of length l. A point dipole of dipole
moment \(\overrightarrow p\) is now brought towards q from infinity so that the charge moves away. The final
equilibrium position of the s...

A large square container with thin transparent vertical walls and filled with water
(refractive index \({4 \over 3}\)) is kept on a horizontal table. A student holds a thin straight wire vertically
inside the water 12 cm from one of its cor...

A beaker of radius r is filled with water (refractive index \({4 \over 3}\)) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed \(\omega\). This makes the water surface ...

A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two
equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the
partition is held initially at a...

A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm\(-\)2 and it is absorbed by the wate...

A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R \(-\) a). For a << R the magnitu...

Starting at time t = 0 from the origin with speed 1 ms-1, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation \(y = {{{x^2}} \over 2}\). The x and y components of its accelera...

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total
mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at
an equilibrium height of 100 m. When...