JEE Main 2013 (Offline)

Arrange the following compounds in order of decreasing acidity :

An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary,
secondary or tertiary. Which alcohol reacts fastest and by what mechanism:

The order of stability of the following carbocations :

Synthesis of each molecule of glucose in photosynthesis involves:

Stability of the species Li2, \(Li_2^−\) and \(Li_2^+\) increases in the order of:

Which one of the following molecules is expected to exhibit diamagnetic behaviour?

In which of the following pairs of molecules/ions, both the species are not likely to exist?

The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such
a reaction will be:(R = 8.314 JK–1 mol–1 and log 2 = 0.301)

A compound with molecular mass 180 is acylated with CH3COCl to get a compound with molecular mass
390. The number of amino groups present per molecule of the former compound is:

An organic compound A upon reacting with \(N{H_3}\) gives \(B.\) On heating \(B\) gives \(C.\) \(C\) in presence of \(KOH\) reacts with \(B{r_2}\) to given \(C{H_3}C{H_2}N{H_2}2.\) \(A\) is :

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

Which of the following complex species is not expected to exhibit optical isomerism?

Which of the following arrangements does not represent the correct order of the property stated against it?

Four successive members of the first row transition elements are listed below with atomic numbers. Which
one of them is expected to have the highest \(E_{{M^{3 + }}/{M^{2 + }}}^0\) value?

Given
\(E_{C{r^{2 + }}/Cr}^o\) = -0.74 V; \(E_{MnO_4^ - /M{n^{2 + }}}^o\) = 1.51 V
\(E_{C{r_2}O_7^{2 - }/C{r^{3 + }}}^o\) = 1.33 V; \(E_{Cl/C{l^ - }}^o\) = 1.36 V
Based on the data given above, strongest oxidising agent will be :

For gaseous state, if most probable speed is denoted by C*, average speed by \(\mathop C\limits^{\_\_}\) and mean square speed by
C, then for a large number of molecules the ratios of these speeds are:

Compound \(\left( A \right),\,{C_8}{H_9}Br,\,\,\,\) gives a white precipitate when warmed with alcoholic \(AgN{O_3}.\) Oxidation of \((A)\) gives an acid \(\left( B \right),\) \({C_8}{H_6}{O_4}.\,\,\left( B \right)\) easily forms anhydride...

A solution of (–\(l\)) – chloro –1 – phenylethane in toluene racemises slowly in the presence of a small
amount of SbCl5, due to the formation of :

How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an
aqueous solution with pH of 2?

Which of the following is the wrong statement?

Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se
and Ar?

The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+
will be:

Consider the following reaction:
\(xMnO_4^- + yC_2O_4^{2-}\) + zH+ \(\to\) xMn2+ + 2yCO2 + \({z \over 2}{H_2}O\)
The value's of x, y and z in the reaction are, respectively :

Which of the following exists as covalent crystals in the solid state?

The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:

A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO2. The empirical formula of the hydrocarbon is

Experimentally it was found that a metal oxide has formula M0.98O. Metal M, present as M2+ and M3+ in its oxide. Fraction of the metal which exists as M3+ would be

Energy of an electron is given by \(E = - 2.178 \times {10^{ - 18}}J\left( {{{{Z^2}} \over {{n^2}}}} \right)\). Wavelength of light required to excite an
electron in an hydrogen atom from level n = 1 to n = 2 will be
(h = 6.62 × 10−34 Js ...

The coagulating power of electrolytes having ions Na+, Al3+ and Ba2+ for arsenic sulphide sol increases in the order:

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant
temperature of 37.0oC. As it does so, it absorbs 208J of heat. The values of q and w for the process will be :
(R = 8.314 J/mol K) ( l n 7...

Distance between two parallel planes \(2x+y+2z=8\) and \(4x+2y+4z+5=0\) is :

If the lines \({{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}\) and \({{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}\) are coplanar, then \(k\) can have :

The real number \(k\) for which the equation, \(2{x^3} + 3x + k = 0\) has two distinct real roots in \(\left[ {0,\,1} \right]\)

The intercepts on \(x\)-axis made by tangents to the curve,
\(y = \int\limits_0^x {\left| t \right|dt,x \in R,}\) which are parallel to the line \(y=2x\), are equal to :

The area (in square units) bounded by the curves \(y = \sqrt {x,}\) \(2y - x + 3 = 0,\) \(x\)-axis, and lying in the first quadrant is :

The term independent of \(x\) in expansion of
\({\left( {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over {x - {x^{1/2}}}}} \right)^{10}}\) is

The circle passing through \((1, -2)\) and touching the axis of \(x\) at \((3, 0)\) also passes through the point :

If z is a complex number of unit modulus and argument \(\theta\), then arg \(\left( {{{1 + z} \over {1 + \overline z }}} \right)\) equals :

Statement-1 : The value of the integral
\(\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}}\) is equal to \(\pi /6\)
Statement-2 : $$\int\limits_a^b {f\left( x \right)} dx = \int\limits_a^b {f\left( {a + b - x} \right)}...

At present, a firm is manufacturing \(2000\) items. It is estimated that the rate of change of production P w.r.t. additional number of workers \(x\) is given by \({{dp} \over {dx}} = 100 - 12\sqrt x .\) If the firm employs \(25\) more wo...

If \(y = \sec \left( {{{\tan }^{ - 1}}x} \right),\) then \({{{dy} \over {dx}}}\) at \(x=1\) is equal to :

The equation of the circle passing through the foci of the ellipse \({{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1\), and having centre at \((0,3)\) is :

\(ABCD\) is a trapezium such that \(AB\) and \(CD\) are parallel and \(BC \bot CD.\) If \(\angle ADB = \theta ,\,BC = p\) and \(CD = q,\) then AB is equal to:

If \(\int {f\left( x \right)dx = \psi \left( x \right),}\) then \(\int {{x^5}f\left( {{x^3}} \right)dx}\) is equal to

If \(x, y, z\) are in A.P. and \({\tan ^{ - 1}}x,{\tan ^{ - 1}}y\) and \({\tan ^{ - 1}}z\) are also in A.P., then :

\(\mathop {\lim }\limits_{x \to 0} {{\left( {1 - \cos 2x} \right)\left( {3 + \cos x} \right)} \over {x\tan 4x}}\) is equal to

Consider :
Statement − I : \(\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)\) is a fallacy.
Statement − II :\(\left( {p \to q} \right) \leftrightarrow \left( { \sim q \to \sim p} \right)\) is a tautology.

The number of values of \(k\), for which the system of equations : \($\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr }\)$
has no solution, is

If \(P = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]\) is the adjoint of a \(3 \times 3\) matrix \(A\) and
\(\left| A \right| = 4,\) then \(\alpha\) is equal to :

Given : A circle, \(2{x^2} + 2{y^2} = 5\) and a parabola, \({y^2} = 4\sqrt 5 x\).
Statement-1 : An equation of a common tangent to these curves is \(y = x + \sqrt 5\).
Statement-2 : If the line, $$y = mx + {{\sqrt 5 } \over m}\left( {m \n...