JEE Advanced 2018 Paper 1 Offline

In the following reaction sequence, the correct structure(s) of \(X\) is (are)

An organic acid P \(\left( {{C_{11}}{H_{12}}{O_2}} \right)\) can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P und...

An organic acid P \(\left( {{C_{11}}{H_{12}}{O_2}} \right)\) can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P und...

The compound \(Y\) is

The compound \(Z\) is

The reaction (s) leading to the formation of \(1,3,5\)-trimethylbenzene is (are)

A closed tank has two compartments \(A\) and \(B,\) both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure \(1.\)). If the old partition is replaced ...

The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by \(NiCl{}_2.6{H_2}O\) to form a stable coordination compound. Assume that both the reactions are \(100\%\) complete. If \(1584\) \(g\) of ammon...

The correct statement(s) regarding the binary transition metal carbonyl compounds is(are) (Atomic numbers : \(Fe = 26,Ni = 28\))

Among the species given below, the total number of diamagnetic species is _____________.
\(H\) atom, \(N{O_2}\) monomer, \({O_2}^ -\) (superoxide), dimeric sulphur in vapor phase, \(M{n_3}{O_4},\,\,\) $${\left( {N{H_4}} \right)_2}\left[ {F...

For the electrochemical cell,
\(\left. {Mg\left( s \right)} \right|M{g^{2 + }}\left( {aq,1\,M} \right)\left\| {C{u^{2 + }}} \right.\left( {aq,1M} \right)\left| {Cu\left( s \right)} \right.\)
the standard \(emf\) of the cell is \(2.70\) $$V...

The solubility of a salt of weak acid \((AB)\) at \(pH\,\) \(3\) is \(Y \times {10^{ - 3}}\) \(mol\,{L^{ - 1}}.\) The value of \(Y\) is ________________.
(Given that the value of solubility product of \(AB\) $$\left( {{K_{sp}}} \right) = 2...

Based on the compounds of group \(15\) elements, the correct statement(s) is (are)

The compounds(s) which generate(s) \({N_2}\) gas upon thermal decomposition below \({300^ \circ }C\) is (are)

Consider an ionic solid \(MX\) with \(NaCl\) structure. Construct a new structure \((Z)\) whose unit cell is constructed from the unit cell of \(MX\) following the sequential instructions given below. Neglect the charge balance.
$$(i)\,\,\...

The plot given below shows \(P-T\) curves (where \(P\) is the pressure and \(T\) is the temperature) for two solvents \(X\) and \(Y\) and isomolal solutions of \(NaCl\) in these solvents. \(NaCl\) completely dissociates in both the solvents...

Liquids A and B form ideal solution over the entire range of composition. At temperature \(T,\) equimolar binary solution of liquids \(A\) and \(B\) has vapor pressure \(45\) \(Torr.\) At the same temperature, a new solution of \(A\) and ...

A reversible cyclic process for an ideal gas is shown below. Here, \(P, V,\) and \(T\) are pressure, volume and temperature, respectively. The thermodynamic parameters \(q,w, H\) and \(U\) are heat, work, enthalpy and internal energy, respe...

Let P1 : 2x + y \(-\) z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE?

For each positive integer n, let \({y_n} = {1 \over n}(n + 1)(n + 2)...{(n + n)^{{1 \over n}}}\). For x\(\in\)R, let [x] be the greatest integer less than or equal to x. If \(\mathop {\lim }\limits_{n \to \infty } {y_n} = L\), then the va...

A farmer F1 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F2 takes away the region which lies between the sides PQ and a curve of the form y = xn (n > 1). If the a...

Let f : [0, \(\infty\)) \(\to\) R be a continuous function such that\(f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt}\) for all x \(\in\) [0, \(\infty\)). Then, which of the following statement(s) is (are) TRUE?

Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.Let E1E2 and F1F2 be the chords of S passing through the point P0 (1, 1) and parallel to the X-axis and the Y-axis, respectively. Let G1G2 be the chord of S passing throug...

For a non-zero complex number z, let arg(z) denote the principal argument with \(-\) \(\pi\) < arg(z) \(\le\) \(\pi\). Then, which of the following statement(s) is (are) FALSE?

Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point o...

The number of real solutions of the equation $$\eqalign{
& {\sin ^{ - 1}}\left( {\sum\limits_{i = 1}^\infty {} {x^{i + 1}} - x\sum\limits_{i = 1}^\infty {} {{\left( {{x \over 2}} \right)}^i}} \right) \cr
& = {\pi \over 2} - {\cos ...

The value of \({({({\log _2}9)^2})^{{1 \over {{{\log }_2}({{\log }_2}9)}}}} \times {(\sqrt 7 )^{{1 \over {{{\log }_4}7}}}}\) is ....................

For every twice differentiable function \(f:R \to [ - 2,2]\) with \({(f(0))^2} + {(f'(0))^2} = 85\), which of the following statement(s) is(are) TRUE?

Let f : R \(\to\) R and g : R \(\to\) R be two non-constant differentiable functions. If f'(x) = (e(f(x) \(-\) g(x))) g'(x) for all x \(\in\) R and f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?

The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is .................

There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination ...

There are five students S1, S2, S3, S4 and S5 in a music class and for them there are five seats R1, R2, R3, R4 and R5 arranged in a row, where initially the seat Ri is allotted to the student Si, i = 1, 2, 3, 4, 5. But, on the examination ...

Let a, b, c three non-zero real numbers such that the equation \(\sqrt 3 a\cos x + 2b\sin x = c,x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]\), has two distinct real roots \(\alpha\) and \(\beta\) with $$\alpha + \beta = {\pi...

Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ...., and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, .... . Then, the number of elements in the set X ...

In a \(\Delta\)PQR = 30\(^\circ\) and the sides PQ and QR have lengths 10\(\sqrt 3\) and 10, respectively. Then, which of the following statement(s) is(are) TRUE?

Let a and b be two unit vectors such that a . b = 0. For some x, y\(\in\)R, let \(\overrightarrow c = x\overrightarrow a + y\overrightarrow b + \overrightarrow a \times \overrightarrow b\). If | \(\overrightarrow c\)| = 2 and the ve...

Three identical capacitors \({C_1},{C_2}\) and \({C_3}\) have a capacitance of \(1.0\,\mu F\) each and they are unchanged initially. They are connected in a circuit as shown in the figure and \({C_1}\) is then filled completely with a diele...

In the figure below, the switches \({S_1}\) and \({S_2}\) are closed simultaneously at \(t=0\) and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are a...

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, \([E]\) and \([B]\) stand fo...

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, \([E]\) and \([B]\) stand fo...

Sunlight of intensity \(1.3\) \(kW\,{m^{ - 2}}\) is incident normally on a thin convex lens of focal length \(20\) cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal len...

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where \(V\) is the volume and \(T\) is the temperature). Which of the statements below is (are) true?

In the \(xy\)-plane, the region \(y > 0\) has a uniform magnetic field \({B_1}\widehat k\) and the region \(y < 0\) has another uniform magnetic field \({B_2}\widehat k.\) A positively charged particle is projected from the origin along the...

Two infinitely long straight wires lie in the \(xy\)-plane along the lines \(x = \pm R.\) The wire located at \(x = + R\) carries a constant current \({I_1}\) and the wire located at \(x=-R\) carries a constant current \({I_2}.\) A circul...

A uniform capillary tube of inner radius \(r\) is dipped vertically into a beaker filled with water. The water rises to a height \(h\) in the capillary tube above the water surface in the beaker. The surface tension of water is \(\sigma .\)...

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures \({T_1} = 300\,K\) and \({T_2} = 100\,K\), as shown in the figure. The radius of the bigger cylinder is twice t...

Consider a body of mass \(1.0\) \(kg\) at rest at the origin at time \(t=0.\) A force \(\overrightarrow F = \left( {\alpha t \widehat i + \beta \widehat j} \right)\) is applied on the body, where \(\alpha = 1.0N{s^{ - 1}}\) and $$\beta =...

Two vectors \(\overrightarrow A\) and \(\overrightarrow B\) are defined as \(\overrightarrow A\) \(=\) \(a\widehat i\) and \(\overrightarrow B = a\) \(\left( {\cos \,\omega T\widehat i + \sin \,\omega t\,\widehat j} \right),\) where $$...

The potential energy of a particle of mass \(m\) at a distance \(r\) from a fixed point \(O\) is given by \(V\left( r \right) = k{r^2}/2,\) where \(k\) is a positive constant of appropriate dimensions. This particle is moving in a circular ...

A ring and disc are initially at rest, side by side, at the top of an inclined plane which makes an angle \({60^ \circ }\) with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the...