JEE Advanced 2013 Paper 1 Offline

The compound that does NOT liberate CO2, on treatment with aqueous sodium bicarbonate solution, is

The total number of carboxylic acid groups is the product P is _________.

The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

A tetrapeptide has \(-\)COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with $$-$...

The total number of lone-pairs of electrons in melamine is

In the reaction, P + Q \(\to\) R + S, the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

Consider the following complex ions : P, Q and R.
\(P = {[Fe{F_6}]^{3 - }}\), \(Q = {[V{({H_2}O)_6}]^{2 + }}\) and \(R = {[Fe{({H_2}O)_6}]^{2 + }}\)
The correct order of the complex ions, according to their spin-only magnetic moment values ...

The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

EDTA4\(-\) is ethylenediaminetetraacetate ion. The total number of N\(-\)Co\(-\)O bond angles in [Co(EDTA)]1\(-\) complex ion is ________.

Upon treatment with ammoniacal H2S, the metal ion that precipitates as a sulphide is

KI in acetone, undergoes SN2 reaction with each of P, Q, R and S. The rates of the reaction vary as

Among P, Q, R and S, the aromatic compound(s) is(are)

The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100th of that of a strong acid (HX, 1M), at 25oC. The Ka of HA is

Sulphide ores are common for the metals

Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of

The arrangement of X\(-\) ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the radius of X\(-\) is 250 pm, the radius of A+ is

The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength
of He gas at –73oC is “M” times that of the de Broglie wavelength of Ne at 727oC. M is

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25oC. For this process, the
correct statement is

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s)
is(are)

The standard enthalpies of formation of CO2(g), H2O(l) and glucose(s) at 25oC are –400 kJ/mol,
–300 kJ/mol and –1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at
25oC is

Perpendiculars are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}=\frac{z}{3}$ to the plane $x+y+$ $z=3$. The foot of perpendiculars lie on the line

A line \(l\) passing through the origin is perpendicular to the lines
\($\,{l_1}:\left( {3 + t} \right)\widehat i + \left( { - 1 + 2t} \right)\widehat j + \left( {4 + 2t} \right)\widehat k,\,\,\,\,\, - \infty < t < \infty\)$
$$${l_2}:\le...

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio \(8:15\) is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squar...

The area enclosed by the curves \(y = \sin x + {\mathop{\rm cosx}\nolimits}\) and \(y = \left| {\cos x - \sin x} \right|\) over the interval \(\left[ {0,{\pi \over 2}} \right]\) is

Let complex numbers \(\alpha \,and\,{1 \over {\overline \alpha }}\,\) lie on circles \({\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2} = {r^2}\) and $$\,{\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2...

Let \(f\) \(:\,\,\left[ {{1 \over 2},1} \right] \to R\) (the set of all real number) be a positive,
non-constant and differentiable function such that
\(f'\left( x \right) < 2f\left( x \right)\) and \(f\left( {{1 \over 2}} \right) = 1.\) ...

A curve passes through the point \(\left( {1,{\pi \over 6}} \right)\). Let the slope of
the curve at each point \((x,y)\) be \({y \over x} + \sec \left( {{y \over x}} \right),x > 0.\)
Then the equation of the curve is

A vertical line passing through the point \((h,0)\) intersects the ellipse \({{{x^2}} \over 4} + {{{y^2}} \over 3} = 1\) at the points \(P\) and \(Q\). Let the tangents to the ellipse at \(P\) and \(Q\) meet at the point \(R\). If $$\Delta...

The value of \(\cot \left( {\sum\limits_{n = 1}^{23} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{k = 1}^n {2k} } \right)} \right)\) is

The coefficient of three consecutive terms of \({\left( {1 + x} \right)^{n + 5}}\) are in the ratio \(5:10:14.\) Then \(n\) =

For 3 × 3 matrices M and N, which of the following statement(s)
is(are) NOT correct?

Consider the set of eight vectors \(V = \left\{ {a\,\hat i + b\,\hat j + c\hat k:a,\,b,\,c\, \in \left\{ { - 1,\,1} \right\}} \right\}\). Three non-coplanar vectors can be chosen from v in \({2^p}\) ways. Then p is

Of the three independent events \({E_1},{E_2}\) and \({E_3},\) the probability that only \({E_1}\) occurs is \(\alpha ,\) only \({E_2}\) occurs is \(\beta\) and only \({E_3}\) occurs is \(\gamma .\) Let the probability \(p\) that none of e...

Four persons independently solve a certain problem correctly with probabilities \({1 \over 2},{3 \over 4},{1 \over 4},{1 \over 8}.\) Then the probability that the problem is solved correctly by at least one of them is

Let \({S_n} = {\sum\limits_{k = 1}^{4n} {\left( { - 1} \right)} ^{{{k\left( {k + 1} \right)} \over 2}}}{k^2}.\) Then \({S_n}\)can take value(s)

A pack contains \(n\) cards numbered from \(1\) to \(n.\) Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is \(1224.\) If the smaller of the numbers on the removed cards is \(k,\) t...

For \(a > b > c > 0,\) the distance between \((1, 1)\) and the point of intersection of the lines \(ax + by + c = 0\) and \(bx + ay + c = 0\) is less than \(\left( {2\sqrt 2 } \right)\). Then

Let \(f\left( x \right) = x\sin \,\pi x,\,x > 0.\) Then for all natural numbers \(n,\,f'\left( x \right)\) vanishes at

The number of points in \(\left( { - \infty \,\infty } \right),\) for which \({x^2} - x\sin x - \cos x = 0,\) is

Let $\overrightarrow{\mathrm{PR}}=3 \hat{i}+\hat{j}-2 \hat{k}$ and $ \overrightarrow{\mathrm{SQ}}=\hat{i}-3 \hat{j}-4 \hat{k}$ determine diagonals of a parallelogram $P Q R S$ and $\overrightarrow{\mathrm{PT}}=\hat{i}+2 \hat{j}+3 \hat{k}$ b...

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in t...

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance \(C.\) The switch \({S_1}\) is pressed first to fully charge the capacitor \({C_1}\) and then released. The switch \({S_2}\) is then pressed to ...

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is ___________.

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 \(\times\) 108 ms\(-\)1. The final momentum of the object is

Two non-conducting solid spheres of radii \(R\) and \(2R,\) having uniform volume charge densities \({\rho _1}\) and \({\rho _2}\) respectively, touch each other. The net electric field at a distance \(2\) \(R\) from the center of the small...

A ray of light travelling in the direction \({1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} \right)\) is incident on a plane mirror. After reflection, it travels along the direction $${1 \over 2}\left( {\widehat i - \sqrt 3 \widehat j}...

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
one-third the size of the object. The wavelength of light inside the lens is \({2 \over 3}\) times the wavelength in free space. The ...

Two rectangular blocks, having identical dimensions, can be arranged in either configuration-I or configuration-II as shown in the figure. One of the blocks has thermal conductivity \(\kappa\) and the other 2\(\kappa\). The temperature di...

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their
partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their
densities is

A particle of mass m is projected from the ground with an initial speed u0 at an angle \(\alpha\) with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which...