AIEEE 2005

Heating an aqueous solution of aluminium chloride to dryness will give :

The number of hydrogen atom(s) attached to phosphorus atom in hypophosphorous
acid is :

In silicon dioxide :

The structure of diborane (B2H6) contains :

The correct order of the thermal stability of hydrogen halides (H – X) is :

In which of the following arrangements the order is NOT according to the property
indicated against it?

Which of the following oxides is amphoteric in character?

Which of the following is fully fluorinated polymer?

Which of the following is a polyamide?

Based on lattice energy and other considerations which one of the following alkali
metal chlorides is expected to have the highest melting point :

An ionic compound has a unit cell consisting of A ions at the corners of a cube and B
ions on the centres of the faces of the cube. The empirical formula for this compound
would be :

Benzene and toluene form nearly ideal solutions. At 20 oC, the vapour pressure of
benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of
benzene at 20 oC for a solution containing 78 g of benzene and 46 g of tolue...

If \(\alpha\) is the degree of dissociation of Na2SO4, the vant Hoff’s factor (i) used for
calculating the molecular mass is :

Equimolar solutions in the same solvent have

Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first solution + 520 ml of 1.2 M second solution. What is the molarity of the final mixture?

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of the substance will

In a multi-electron atom, which of the following orbitals described by the three quantum members will have the same energy in the absence of magnetic and electric fields?
(A) n = 1, l = 0, m = 0
(B) n = 2, l = 0, m = 0
(C) n = 2, l = 1, m =...

Of the following sets which one does NOT contain isoelectronic species?

Pick out the isoelectronic structure from the following :
$$\eqalign{
& \left( i \right)\,\,\,\,\,\,C{H_3}^ + \cr
& \left( {ii} \right)\,\,\,\,{H_3}{O^ + } \cr
& \left( {iii} \right)\,\,\,N{H_3} \cr
& \left( {iv} \right)\,\,...

The disperse phase in colloidal iron (III) hydroxide and colloidal gold is positively and
negatively charged, respectively, which of the following statements is NOT correct?

The volume of a colloidal particle, VC as compared to the volume of a solute particle
in a true solution VS, could be

Consider the reaction: N2 + 3H2 \(\to\) 2NH3 carried out at constant temperature and
pressure. If \(\Delta H\) and \(\Delta U\) are the enthalpy and internal energy changes for the
reaction, which of the following expressions is true?

Consider an endothermic reaction, X \(\to\) Y with the activation energies Eb and Ef
for the backward and forward reactions, respectively. In general :

If the bond dissociation energies of XY, X2 and Y2 (all diatomic molecules) are in the ratio of 1:1:0.5 and \(\Delta H_f\) for the formation of XY is -200 kJ mole-1. The bond
dissociation energy of X2 will be :

If the angel \(\theta\) between the line \({{x + 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 2}\) and
the plane \(2x - y + \sqrt \lambda \,\,z + 4 = 0\) is such that \(\sin \,\,\theta = {1 \over 3}\) then value of \(\lambda\) is :

The distance between the line
\(\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),\) and the plane
\(\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5\) is

The plane \(x+2y-z=4\) cuts the sphere \({x^2} + {y^2} + {z^2} - x + z - 2 = 0\) in a circle of radius

If the plane \(2ax-3ay+4az+6=0\) passes through the midpoint of the line joining the centres of the spheres
\({x^2} + {y^2} + {z^2} + 6x - 8y - 2z = 13\) and
\({x^2} + {y^2} + {z^2} - 10x + 4y - 2z = 8\) then a equals :

The angle between the lines \(2x=3y=-z\) and \(6x=-y=-4z\) is :

A function is matched below against an interval where it is supposed to be
increasing. Which of the following pairs is incorrectly matched?

Area of the greatest rectangle that can be inscribed in the
ellipse \({{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1\)

If the equation \({a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + ........... + {a_1}x = 0\)
\({a_1} \ne 0,n \ge 2,\) has a positive root \(x = \alpha\), then the equation
$$n{a_n}{x^{n - 1}} + \left( {n - 1} \right){a_{n - 1}}{x^{n - 2}} + ..........

Let f be differentiable for all x. If f(1) = -2 and f'(x) \(\ge\) 2 for
x \(\in \left[ {1,6} \right]\), then

A spherical iron ball \(10\) cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of \(50\) cm\(^3\) /min. When the thickness of ice is \(5\) cm, then the rate at which the thickness of ice decreases is

A lizard, at an initial distance of 21 cm behind an insect moves from rest with an acceleration of $2 \mathrm{~cm} / \mathrm{s}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20 \mathrm{~cm} / \ma...

The normal to the curve
\(x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)\) at any point
\(\theta\, '\) is such that

The parabolas \({y^2} = 4x\) and \({x^2} = 4y\) divide the square region bounded by the lines \(x=4,\) \(y=4\) and the coordinate axes. If \({S_1},{S_2},{S_3}\) are respectively the areas of these parts numbered from top to bottom ; then $$...

Let \(f(x)\) be a non - negative continuous function such that the area bounded by the curve \(y=f(x),\) \(x\)-axis and the ordinates \(x = {\pi \over 4}\) and \(x = \beta > {\pi \over 4}\) is $$\left( {\beta \sin \beta + {\pi \over 4...

The area enclosed between the curve \(y = {\log _e}\left( {x + e} \right)\) and the coordinate axes is :

The value of \(\,{}^{50}{C_4} + \sum\limits_{r = 1}^6 {^{56 - r}} {C_3}\) is

If \(x\) is so small that \({x^3}\) and higher powers of \(x\) may be neglected, then \({{{{\left( {1 + x} \right)}^{{3 \over 2}}} - {{\left( {1 + {1 \over 2}x} \right)}^3}} \over {{{\left( {1 - x} \right)}^{{1 \over 2}}}}}\) may be approxi...

If the coefficients of rth, (r+1)th, and (r + 2)th terms in the binomial expansion of \({{\rm{(1 + y )}}^m}\) are in A.P., then m and r satisfy the equation

If the coefficient of \({x^7}\) in \({\left[ {a{x^2} + \left( {{1 \over {bx}}} \right)} \right]^{11}}\) equals the coefficient of \({x^{ - 7}}\) in \({\left[ {ax - \left( {{1 \over {b{x^2}}}} \right)} \right]^{11}}\), then \(a\) and \(b\)...

If a circle passes through the point (a, b) and cuts the circle \({x^2}\, + \,{y^2} = {p^2}\) orthogonally, then the equation of the locus of its centre is :

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is :

If the pair of lines \(a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0\) lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then :

If the circles \({x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0\) and \({x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0\) intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :

If \({z_1}\) and \({z_2}\) are two non-zero complex numbers such that \(\,\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|\), then arg \({z_1}\) - arg \({z_2}\) is equal to :

If the cube roots of unity are 1, \(\omega \,,\,{\omega ^2}\) then the roots of the equation \({(x - 1)^3}\) + 8 = 0, are :

If \(\,\omega = {z \over {z - {1 \over 3}i}}\,\) and \(\left| \omega \right| = 1\), then \(z\) lies on :