JEE Advanced 2020 Paper 1 Offline

In the reaction scheme shown below Q, R and S are the major products.The correct structure of

In the following reaction, compound Q is obtained from compound P via an ionic intermediateWhat is the degree of unsaturation of Q?

Which of the following structures has the IUPAC name3-ethynyl-2-hydroxy-4-methylhex-3-en-5-ynoic acid?

Newman projections P, Q, R and S are shown below :Which one of the following options represents identical molecules?

With respect to the compounds I-V, choose the correct statement(s).

The Fischer projection of D-erythrose is shown below : D-erythrose and its isomers are listed as P, Q, R, and S in Column - I. Choose the correct relationship of P, Q, R, and S with D-erythrose from Column - II.

Consider the reaction,A \(\rightleftharpoons\) Bat 1000 K. At time t', the temperature of the system was increased to 2000 K and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintai...

\(_{92}^{238}U\) is known to undergo radioactive decay to form \(_{82}^{206}Pb\) by emitting alpha and beta particles. A rock initially contained 68 \(\times\) 10\(-\)6 g of \(_{92}^{238}U\). If the number of alpha particles that it would...

Choose the correct statement(s) among the following :

Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K. Its cell reaction is \({H_2}(g) + {1 \over 2}{O_2}(g)\buildrel {} \over \longrightarrow {H_2}O(l)\)The work derived from the cell on t...

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is

Aluminium reacts with sulphuric acid to form aluminium sulphate and hydrogen. What is the volume of hydrogen gas in litre (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulphuric acid are combined f...

Which of the following liberates O2 upon hydrolysis?

With respect to hypochlorite, chlorate and perchlorate ions, choose the correct statement(s).

A colourless aqueous solution contains nitrates of two metals, X and Y. When it was added to an aqueous solution of NaCl, a white precipitate was formed. This precipitate was found to be partly soluble in hot water to give a residue P and a...

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

5.00 mL of 0.10 M oxalic acid solution taken in a conical flask is titrated against NaOH from a burette using phenolphthalein indicator. The volume of NaOH required for the appearance of permanent faint pink color is tabulated below for fiv...

In thermodynamics, the p-V work done is given by\(w = - \int {dV{p_{ext}}}\)For a system undergoing a particular process, the work done is \(w = - \int {dV\left( {{{RT} \over {V - b}} - {a \over {{V^2}}}} \right)}\)This equation is appl...

Let L1 and L2 be the following straight lines.\({L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}\) and \({L_2}:{{x - 1} \over { - 3}} = {y \over { - 1}} = {{z - 1} \over 1}\).Suppose the straight line $$L:{{x - \alpha } \over ...

Consider the rectangles lying the region \(\left\{ {(x,y) \in R \times R:0\, \le \,x\, \le \,{\pi \over 2}} \right.\) and \(\left. {0\, \le \,y\, \le \,2\sin (2x)} \right\}\)and having one side on the X-axis. The area of the rectangle whic...

Let the functions f : R \(\to\) R and g : R \(\to\) R be defined byf(x) = ex \(-\) 1 \(-\) e\(-\)|x \(-\) 1|and g(x) = \({1 \over 2}\)(ex \(-\) 1 + e1 \(-\) x).The the area of the region in the first quadrant bounded by the curves y = f...

Let S be the set of all complex numbers z satisfying |z2 + z + 1| = 1. Then which of the following statements is/are TRUE?

Which of the following inequalities is/are TRUE?

If the function f : R \(\to\) R is defined by f(x) = |x| (x \(-\) sin x), then which of the following statements is TRUE?

Let f : [0, 2] \(\to\) R be the function defined by\(f(x) = (3 - \sin (2\pi x))\sin \left( {\pi x - {\pi \over 4}} \right) - \sin \left( {3\pi x + {\pi \over 4}} \right)\)If \(\alpha ,\,\beta \in [0,2]\) are such that $$\{ x \in [0,2]:...

For a polynomial g(x) with real coefficients, let mg denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by $$S = \{ {({x^2} - 1)^2}({a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}):...

let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit\(\mathop {\lim }\limits_{x \to {0^ + }} {{{{(1 - x)}^{1/x}} - {e^{ - 1}}} \over {{x^a}}}\)is equal to a non-zero real number, is ....

Let the function f : R \(\to\) R be defined by f(x) = x3 \(-\) x2 + (x \(-\) 1)sin x and let g : R \(\to\) R be an arbitrary function. Let fg : R \(\to\) R be the product function defined by (fg)(x) = f(x)g(x). Then which of the follo...

Let M be a 3 \(\times\) 3 invertible matrix with real entries and let I denote the 3 \(\times\) 3 identity matrix. If M\(-\)1 = adj(adj M), then which of the following statements is/are ALWAYS TRUE?

Let a, b and \(\lambda\) be positive real numbers. Suppose P is an end point of the latus return of the parabola y2 = 4\(\lambda\)x, and suppose the ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\) passes through the poin...

Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are \({{2 \over 3}}\) and \({{1 \over 3}}\), respectively. Suppose \(\alpha\) is the number of heads that appear when C1 is tossed twice, indepe...

In a triangle PQR, let a = QR, b = RP, and c = PQ. If |a| = 3, |b| = 4 and \({{a\,.(\,c - \,b)} \over {c\,.\,(a - \,b)}} = {{|a|} \over {|a| + |b|}}\), then the value of |a \(\times\) b|2 is ......

Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides of a triangle opposite to its angles X, Y, and Z, respectively. If\(\tan {X \over 2} + \tan {Z \over 2} = {{2y} \over {x + y + z}}\), then which of the...

Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x \(-\) 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2 \(-\) 20x + 2020. Then the value of ac(a \(-\) c) + ad(a \(-\) d) ...

Let a1, a2, a3, .... be a sequence of positive integers in arithmetic progression with common difference 2. Also, let b1, b2, b3, .... be a sequence of positive integers in geometric progression with common ratio 2. If a1 = b1 = c, then the...

Let m be the minimum possible value of \({\log _3}({3^{{y_1}}} + {3^{{y_2}}} + {3^{{y_3}}})\), where \({y_1},{y_2},{y_3}\) are real numbers for which \({{y_1} + {y_2} + {y_3}}\) = 9. Let M be the maximum possible value of $$({\log _3}{x_1} ...

A particle of mass m moves in circular orbits with potential energy V(r) = Fr, where F is a positive
constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the
radius of the particle’s orbit is ...

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity \(\rho\). Its inner
radius is R1 and outer radius is R2. If a voltage V0 is applied between its two ends, a current I flows
in it. In addition, it is...

A uniform electric field, \(\overrightarrow E = - 400\sqrt 3 \widehat y\) NC−1
is applied in a region. A charged particle of mass m
carrying positive charge q is projected in this region with an initial speed of 2\(\sqrt {10}\) $$ \times...

One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0, 0).
A point particle of mass m carrying a positive charge q is attached at its other end. The entire system
is kept on a smooth horizontal...

A circular disc of radius R carries surface charge density
\(\sigma \left( r \right) = {\sigma _0}\left( {1 - {r \over R}} \right)\), where \(\sigma\)0 is a constant
and r is the distance from the center of the disc. Electric flux through ...

Consider one mole of helium gas enclosed in a container at initial pressure P1 and volume V1. It
expands isothermally to volume 4V1. After this, the gas expands adiabatically and its volume becomes
32V1. The work done by the gas during isot...

The filament of a light bulb has surface area 64 mm2
. The filament can be considered as a black
body at temperature 2500 K emitting radiation like a point source when viewed from far. At night
the light bulb is observed from a distance of ...

Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm
and the right one at 90.00 cm. When you attempt to move both the fingers slowly towards the center,
initially only the left finger slips with...

A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One
end of the plank is now lifted so that it gets tilted making an angle \(\theta\) from the horizontal as shown in
the figure below. The maxi...

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate
about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away
from its axis. On revolving the magn...

A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure,
its two ends are connected to two wires and it is hanging by those wires with its plane being vertical.
The wires are connected to a capaci...

When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to
the surface tension of water. To calculate h just before water starts flowing, model the shape of the
water above the rim as a disc o...

An open-ended U-tube of uniform cross-sectional area contains water (density 103 kg m−3
). Initially the
water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of
density 800 kg m−3
is added to th...

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of
potassium permanganate (KMnO4) of different concentrations n1 and n2 (n1 > n2) molecules per
unit volume with \(\Delta\)n = (n1 − n2) << n1. Wh...