AIEEE 2010

From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous
ZnCl2, is

One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular
mass of 44 u. The alkene is

The correct order of increasing basicity of the given conjugate bases (R = CH3) is

Out of the following, the alkene that exhibits optical isomerism is

Biuret test is not given by

In aqueous solution the ionization constants for carbonic acid are
K1 = 4.2 x 10–7 and K2 = 4.8 x 10–11
Select the correct statement for a saturated 0.034 M solution of the carbonic acid.

The time for half life period of a certain reaction A \(\to\) products is 1 hour. When the initial
concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its concentration to
come from 0.50 to 0.25 mol L–1 if it i...

Consider the reaction :
Cl2(aq) + H2S(aq) → S(s) + 2H+ (aq) + 2Cl– (aq)
The rate equation for this reaction is rate = k [Cl2] [H2S]
Which of these mechanisms is/are consistent with this rate equation?
(A) Cl2 + H2S \(\to\) H+ + Cl– + Cl+ + ...

In the chemical reactions,

the compounds \('A'\) and \('B'\) respectively are

A solution containing 2.675g of CoCl3. 6NH3 (molar mass = 267.5 g mol–1) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of AgNO3 to give
4.78 g of AgCl (molar mass = 143.5 g mol–1). The...

Which one of the following has an optical isomer ?
(en = ethylenediamine)

The correct order of \(E_{{M^{2 + }}/M}^o\) values with negative sign for the four successive elements Cr, Mn, Fe
and Co is :

The Gibbs energy for the decomposition of Al2O3 at 500oC is as follows :
\({2 \over 3}A{l_2}{O_3}\) \(\to\) \({4 \over 3}Al + {O_2}\), \({\Delta _r}G\) = + 966 kJ mol–1
The potential difference needed for electrolytic reduction of Al2O3 at ...

If 10–4 dm3 of water is introduced into a 1.0 dm3 flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ?
(Given : Vapour pressure of H2O at 300 K is 3170 Pa ; R = 8.314 J K–1 mol–1)

Consider the following bromides :

The correct order of \({S_N}1\) reactive is

The main product of the following reaction is
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\) \({C_6}{H_5}C{H_2}CH\left( {OH} \right)CH{\left( {C{H_3}} \right)_2}\buildrel {conc.{H_2}S{O_4}} \over \longrightarrow \,?\)

Three reactions involving \(H_2PO_4^−\) are given below :
(i) H3PO4 + H2O \(\to\) H3O+ + \(H_2PO_4^−\)
(ii) \(H_2PO_4^−\) + H2O \(\to\) \(HPO_4^{2−}\) + H3O+
(iii) \(H_2PO_4^−\) + OH- \(\to\)H3PO4 + O2-
In which of the above does $$H_2PO_4^...

Solubility product of silver bromide is 5.0 \(\times\) 10–13. The quantity of potassium bromide (molar mass taken as 120g of mol–1) to be added to 1 litre of 0.05 M solution of silver nitrate to start the
precipitation of AgBr is :

At 25°C, the solubility product of Mg(OH)2 is 1.0 \(\times\) 10–11. At which pH, will Mg2+ ions start precipitating in the form of Mg(OH)2 from a solution of 0.001 M Mg2+ ions?

The correct sequence which shows decreasing order of the ionic radii of the elements is

The polymer containing strong intermolecular forces e.g. hydrogen bonding, is

29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method
and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl solution. The excess of the acid
required 15 mL of 0.1 M NaOH solution for complete ne...

Percentages of free space in cubic close packed structure and in body centred packed structure are
respectively :

The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the
cation is 110 pm, the radius of the anion is :

If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous
solution, the change in freezing point of water (∆Tf), when 0.01 mol of sodium sulphate is dissolved
in 1 kg of water, is (Kf = 1.86 K kg mol–1...

On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two
liquid components (heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of
the solution obtained by mixing 25.0g of heptane ...

Ionisation energy of He+ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n = 1) of Li2+ is

The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol–1. The longest
wavelength of light capable of breaking a single Cl – Cl bond is
(c = 3 x 108 ms–1 and NA = 6.02 x 1023 mol–1)

For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If Te is
the temperature at equilibrium, the reaction would be spontaneous when :

The standard enthalpy of formation of NH3 is –46.0 kJ mol–1. If the enthalpy of formation of H2 from its atoms is –436 kJ mol–1 and that of N2 is –712 kJ mol–1, the average bond enthalpy of N–H bond in NH3 is :

A line \(AB\) in three-dimensional space makes angles \({45^ \circ }\) and \({120^ \circ }\) with the positive \(x\)-axis and the positive \(y\)-axis respectively. If \(AB\) makes an acute angle \(\theta\) with the positive \(z\)-axis, th...

Statement-1 : The point \(A(3, 1, 6)\) is the mirror image of the point \(B(1, 3, 4)\) in the plane \(x-y+z=5.\)
Statement-2 : The plane \(x-y+z=5\) bisects the line segment joining \(A(3, 1, 6)\) and \(B(1, 3, 4).\)

Let \(f:R \to R\) be defined by
\($f\left( x \right) = \left\{ {\matrix{ {k - 2x,\,\,if} & {x \le - 1} \cr {2x + 3,\,\,if} & {x > - 1} \cr } } \right.\)$
If \(f\)has a local minimum at \(x=-1\), then a possible value of \(k\)...

The equation of the tangent to the curve \(y = x + {4 \over {{x^2}}}\), that
is parallel to the \(x\)-axis, is

Let \(f:R \to R\) be a continuous function defined by
\($f\left( x \right) = {1 \over {{e^x} + 2{e^{ - x}}}}\)$
Statement - 1 : \(f\left( c \right) = {1 \over 3},\) for some \(c \in R\).
Statement - 2 : $$0 < f\left( x \right) \le {1 \over...

The area bounded by the curves \(y = \cos x\) and \(y = \sin x\) between the ordinates \(x=0\) and \(x = {{3\pi } \over 2}\) is

Let \({s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}\),
\({{s_2} = \sum\limits_{j = 1}^{10} {} } j.{}^{10}{C_j}\) and \({{s_3} = \sum\limits_{j = 1}^{10} {{j^2}.{}^{10}{C_j}.} }\)
Statement-1 : $${{S_3} = 55 \times...

The circle \({x^2} + {y^2} = 4x + 8y + 5\) intersects the line \(3x - 4y = m\) at two distinct points if :

The number of complex numbers z such that \(\left| {z - 1} \right| = \left| {z + 1} \right| = \left| {z - i} \right|\) equals :

Let \(p(x)\) be a function defined on \(R\) such that \(p'(x)=p'(1-x),\) for all \(x \in \left[ {0,1} \right],p\left( 0 \right) = 1\) and \(p(1)=41.\) Then \(\int\limits_0^1 {p\left( x \right)dx}\) equals :

Solution of the differential equation
\(\cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x <{\pi \over 2}\) is :

Let \(f:\left( { - 1,1} \right) \to R\) be a differentiable function with \(f\left( 0 \right) = - 1\) and \(f'\left( 0 \right) = 1\). Let \(g\left( x \right) = {\left[ {f\left( {2f\left( x \right) + 2} \right)} \right]^2}\). Then $$g'\lef...

Let \(f:R \to R\) be a positive increasing function with
\(\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1\). Then \(\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} =\)

Let S be a non-empty subset of R. Consider the following statement:
P : There is a rational number x ∈ S such that x > 0.
Which of the following statements is the negation of the statement P?

Let \(A\) be a \(\,2 \times 2\) matrix with non-zero entries and let \({A^2} = I,\)
where \(I\) is \(2 \times 2\) identity matrix. Define
\(Tr\)\((A)=\) sum of diagonal elements of \(A\) and \(\left| A \right| =\) determinant of matrix $...

The number of \(3 \times 3\) non-singular matrices, with four entries as \(1\) and all other entries as \(0\), is :

Consider the system of linear equations;
\($\matrix{ {{x_1} + 2{x_2} + {x_3} = 3} \cr {2{x_1} + 3{x_2} + {x_3} = 3} \cr {3{x_1} + 5{x_2} + 2{x_3} = 1} \cr }\)$
The system has :

If two tangents drawn from a point \(P\) to the parabola \({y^2} = 4x\) are at right angles, then the locus of \(P\) is

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :