JEE Advanced 2018 Paper 2 Offline

LIST-I contains reactions and LIST-II contains major products.

Match the reaction in LIST-I with one or more products in LIST-II and choose the correct option.

In the following reaction sequence, the amount of \(D\) (in g) formed from \(10\) moles of acetophenone is ___________.
(Atomic weights in \(g\,mo{l^{ - 1}}:H = 1,C = 12,\) \(N = 14,O = 16,\) \(Br = 80.\). The yield (%) corresponding to th...

The desired product \(X\) can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II (given, order of migratory aptitude: aryl > alkyl > hydrogen)

The correct option is

For the given compound \(X,\) the total number of optically active stereoisomers is ____________.

The Fischer presentation of \(D\)-glucose is given below.

The correct structure(s) of \(\beta\)-\(L\)-glucopyranose is (are) :

For a first order reaction \(A\left( g \right) \to 2B\left( g \right) + C\left( g \right)\) at constant volume and \(300K,\) the total pressure at the beginning \((t=0)\) and at time \(t\) are \({P_0}\) and \({P_1},\) respectively. Initiall...

Consider the following reversible reaction, \(A\left( g \right) + B\left( g \right) \to AB\left( g \right).\)
The activation energy of the backward reaction exceeds that of the forward reaction by \(2RT\) (in \(J\,mo{l^{ - 1}}\)). If the ...

Aniline reacts with mixed acid (conc. \(HN{O_3}\) and conc. \({H_2}S{O_4}\)) at \(288\) \(K\) to give P \(\left( {51\% } \right),\) Q \(\left( {47\% } \right)\) and R \(\left( {2\% } \right).\) The major product(s) of the following reaction...

The correct option(s) regarding the complex
\({\left[ {Co\left( {en} \right){{\left( {N{H_3}} \right)}_3}\left( {{H_2}O} \right)} \right]^{3 + }}\,\,\) \(\left( {en = {H_2}NC{H_2}C{H_2}N{H_2}} \right)\) is (are)

Match each set of hybrid orbitals from LIST - A with complex(es) given in LIST - B

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The correct option(s) to distinguish nitrate salts of \(M{n^{2 + }}\) and \(C{u^{2 + }}\) taken separately is (are)

Consider an electrochemical cell :
\(A\left( s \right)\left| {{A^{n + }}\left( {aq,2M} \right)} \right|{B^{2n + }}\left( {aq,1M} \right)\left| {B\left( s \right).} \right.\)
The value of \(\Delta {H^ \circ }\) for the cell reaction is twi...

Dilution processes of different aqueous solutions, with water, are given in LIST - I. The effects of dilution of the solutions on \(\left[ {{H^ + }} \right]\) are given in LIST - II
(Note: Degree of dissociation (a) of weak acid and weak ...

Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight ...

The total number of compounds having at least one bridging oxo group among the molecules given below is _________.
\({N_2}{O_3},{N_2}{O_5},\) \({P_4}{O_6},{P_4}{O_7},\) \({H_4}{P_2}{O_5},{H_5}{P_3}{O_{10}},\) $${H_2}{S_2}{O_3},{H_2}{S_2}{O...

To measure the quantity of \(MnC{l_2}\) dissolved in an aqueous solution, it was completely converted to \(KMn{O_4}\) using the reaction,
\(MnC{l_2} + {K_2}{S_2}{O_8} + {H_2}O \to KMn{O_4} + {H_2}S{O_4} + HCl\) (equation not balanced).
...

For a reaction, \(A\,\,\rightleftharpoons\,\,P,\) the plots of \(\left[ A \right]\) and \(\left[ P \right]\) with time at temperature \({T_1}\) and \({T_2}\) are given below.

If \({T_2} > {T_1},\) the correct statement(s) is (are) (Assum...

The surface of copper gets tarnished by the formation of copper oxide. \({N_2}\) gas was passed to prevent the oxide formation during heating of copper at \(1250\) \(K.\) However, the \({N_2}\) gas contains \(1\) mole % of water vapor as i...

Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the X-axis, Y-axis and Z-axis, respectively, where O(0, 0, 0) is the origin. Let \(S\left( {{1 \over 2},{1 \over 2},{1 \over 2}} \right)\) be the centre of th...

Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicular to the plane x + y = 3 and the mid-point of PQ lies in the plane x + y = 3) lies on the Z-axis. Let the distance of P ...

Let s, t, r be non-zero complex numbers and L be the set of solutions \(z = x + iy(x,y \in R,\,i = \sqrt { - 1} )\) of the equation \(sz + t\overline z + r = 0\) where \(\overline z\) = x \(-\) iy. Then, which of the following statement(s...

The value of the integral\(\int_0^{1/2} {{{1 + \sqrt 3 } \over {{{({{(x + 1)}^2}{{(1 - x)}^6})}^{1/4}}}}dx}\) is ........

Let f : R \(\to\) R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation \({{dy} \over {dx}} = (2 + 5y)(5y - 2)\), then the value of \(\mathop {\lim }\limits_{n \to - \infty } f(x)\) is ...........

Consider two straight lines, each of which is tangent to both the circle x2 + y2 = (1/2) and the parabola y2 = 4x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0, 0) and whose semi-major axi...

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If \(\alpha\) is the number of one-one functions from X to Y and \(\beta\) is the number of onto functions from Y to X, then the value of $${1 \over {5!}}(\bet...

Let \({E_1} = \left\{ {x \in R:x \ne 1\,and\,{x \over {x - 1}} > 0} \right\}\) and $${E_2} = \left\{ \matrix{
x \in {E_1}:{\sin ^{ - 1}}\left( {{{\log }_e}\left( {{x \over {x - 1}}} \right)} \right) \hfill \cr
is\,a\,real\,number \hfil...

Let \(H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\), where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60\(^\circ\) at one of its vertices N. Let the area of the \(\Delta\)LMN be $$4\...

Let T be the line passing through the points P(\(-\)2, 7) and Q(2, \(-\)5). Let F1 be the set of al pairs of circles (S1, S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point...

For any positive integer n, define \({f_n}:(0,\infty ) \to R\) as\({f_n} = \sum\limits_{j = 1}^n {{{\tan }^{ - 1}}} \left( {{1 \over {1 + (x + j)(x + j - 1)}}} \right)\)for all x\(\in\)(0, \(\infty\)). (Here, the inverse trigonometric fu...

Let \({f_1}:R \to R,\,{f_2}:\left( { - {\pi \over 2},{\pi \over 2}} \right) \to R,\,{f_3}:( - 1,{e^{\pi /2}} - 2) \to R\) and \({f_4}:R \to R\) be functions defined by(i) \({f_1}(x) = \sin (\sqrt {1 - {e^{ - {x^2}}}} )\),(ii) $${f_2}(x) =...

Let f : (0, \(\pi\)) \(\to\) R be a twice differentiable function such that \(\mathop {\lim }\limits_{t \to x} {{f(x)\sin t - f(t)\sin x} \over {t - x}} = {\sin ^2}x\) for all x\(\in\) (0, \(\pi\)).If $$f\left( {{\pi \over 6}} \right...

Let \(X = {({}^{10}{C_1})^2} + 2{({}^{10}{C_2})^2} + 3{({}^{10}{C_3})^2} + ... + 10{({}^{10}{C_{10}})^2}\), where \({}^{10}{C_r}\), r \(\in\){1, 2, ..., 10} denote binomial coefficients. Then, the value of \({1 \over {1430}}X\) is ..........

Let S be the set of all column matrices \(\left[ {\matrix{ {{b_1}} \cr {{b_2}} \cr {{b_3}} \cr } } \right]\) such that \({b_1},{b_2},{b_3} \in R\) and the system of equations (in real variables)$$\eqalign{
& - x + 2y + 5...

Let P be a matrix of order 3 \(\times\) 3 such that all the entries in P are from the set {\(-\)1, 0, 1}. Then, the maximum possible value of the determinant of P is ............ .

In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5.(i) Let \(\alpha\)1 be the total number of ways in which the committee can be formed such that the committee has 5 ...

Let f : R \(\to\) R be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x) f'(y) + f'(x) f(y) for all x, y\(\in\) R.Then, the value of loge(f(4)) is ...........

In a radioactive decay chain, \({}_{90}^{232}Th\) nucleus decays to \({}_{82}^{212}Pb\) nucleus. Let \({N_\alpha }\) and \({N_\beta }\) be the number of \(\alpha\) and \({\beta ^ - }\) particles, respectively, emitted in this decay process...

Consider a hydrogen-like ionized atom with atomic number \(Z\) with a single electron. In the emission spectrum of this atom, the photon emitted in the \(n=2\) to \(n=1\) transition has energy \(74.8eV\) higher than the photon emitted in th...

In a photoelectric experiment a parallel beam of monochromatic light with power of \(200\) \(W\) is incident on a perfectly absorbing cathode of work function \(6.25\) \(ev.\) The frequency of light is just above the threshold frequency so ...

The electric field \(E\) is measured at a point \(P(0,0,d)\) generated due to various charge distributions and the dependence of \(E\) on \(d\) is found to be different for different charge distributions. List-\({\rm I}\) contains differen...

A particle, of mass \({10^{ - 3}}\) \(kg\) and charge \(1.0\) \(C,\) is initially at rest. At time \(t=0,\) the particle comes under the influence of an electric field \(\overrightarrow E \left( t \right) = {E_0}\sin \,\,\) $$\omega t\wideh...

An infinitely long thin non-conducting wire is parallel to the \(z\)-axis and carries a uniform line charge density \(\lambda .\) It pierces a thin non-conducting spherical shell of radius \(R\) in such a way that the arc \(PQ\) subtends an...

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length \(f,\) as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the ima...

A planet of mass \(M,\) has two natural satellites with masses \({m_1}\) and \({m_2}.\) The radii of their circular orbits are \({R_1}\) and \({R_2}\) respectively, Ignore the gravitational force between the satellites. Define $${v_1},{...

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is \(100\,K\) and the universal gas constant \(R=8.0\) $$J\,mo{l^{ - 1}}{K^{...

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the \(PV\)-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the pr...

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass \(m=0.4\) \(kg\) is at rest on this surface. An impulse of \(1.0\) \(Ns\) is applied to the block at time \(t=0\) so that it starts moving along the...

A moving coil galvanometer has \(50\) turns and each turn has an area \(2 \times {10^{ - 4}}\,{m^2}.\) The magnetic field produced by the magnet inside the galvanometer is \(0.02\) \(T.\) The torsional constant of the suspension wire is $${...

A ball is projected from the ground at an angle of \({45^o}\) with the horizontal surface. It reaches a maximum height of \(120\) \(m\) and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic ener...

Consider a thin square plate floating on a viscous liquid in a large tank. The height \(h\) of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity $${\mu _{0.}}$...