AIEEE 2004

Which one of the following ores is best concentrated by froth – floatation method?

The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey power. The transformation is related to :

Which among the following factors is the most important in making fluorine the strongest
oxidizing halogen?

Which one the following statement regarding helium is incorrect?

Aluminium chloride exists as dimer, Al2Cl6 in solid state as well as in solution of non-polar
solvents such as benzene. When dissolved in water, it gives :

Beryllium and aluminium exhibit many properties which are similar. But the two elements
differ in :

Among Al2O3, SiO2, P2O3 and SO2 the correct order of acid strength is

Which one of the following ions has the highest value of ionic radius?

The formation of the oxide ion O2-(g) requires first an exothermic and then an endothermic
step as shown below
O(g) + e- = \(O_{(g)}^{-}\) \(\Delta\)Ho = -142 kJmol-1
\(O_{(g)}^{-}\) + e- = \(O_{(g)}^{2-}\) \(\Delta\)Ho = 844 kJmol-1
T...

The compound formed in the positive test for nitrogen with the Lassaigne solution of an
organic compound is

One mole of magnesium nitride on the reaction with an excess of water gives :

What type of crystal defect is indicated in the diagram below?

For which of the following parameters the structural isomers C2H5OH and CH3OCH3 would
be expected to have the same values? (Assume ideal behaviour)

Which one of the following aqueous solutions will exhibit highest boiling point?

Which of the following liquid pairs shows a positive deviation from Raoult’s law?

Which one of the following statements is false?

To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H3PO3), the volume of 0.1 M aqueous KOH solution required is

6.02 \(\times\) 1020 molecules of urea are present in 100 ml of its solution. The concentration of urea solution is (Avogadro constant, NA = 6.02 \(\times\) 1023 mol-1)

The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100 mL of 0.1 M sulphuric acid. The excess of acid required 20 mL of 0.5 M sodium hydroxide solution for complete neutraliz...

Which of the following sets of quantum numbers is correct for an electron in 4f orbital?

Consider the ground state of Cr atom (Z = 24). The number of electrons with the azimuthal quantum numbers, l = 1 and 2 are respectively

The wavelength of the radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant = 1.097 \(\times\) 107 m-1)

Which one of the following sets of ions represents the collection of isoelectronic species? (Atomic nos. : F = 9, Cl = 17, Na = 11, Mg = 12, Al = 13, K = 19, Ca = 20, Sc = 21)

An ideal gas expands in volume from 1\(\times\)10-3 m3 to 1 \(\times\) 10-2 m3 at 300 K against a constant pressure of 1\(\times\)105 Nm-2. The work done is :

The enthalpies of combustion of carbon and carbon monoxide are -393.5 and -283 kJ mol-1
respectively. The enthalpy of formation of carbon monoxide per mole is :

If the straight lines
\(x=1+s,y=-3\)\(- \lambda s,\) \(z = 1 + \lambda s\) and \(x = {t \over 2},y = 1 + t,z = 2 - t,\) with parameters \(s\) and \(t\) respectively, are co-planar, then \(\lambda\) equals :

A line with direction cosines proportional to \(2,1,2\) meets each of the lines \(x=y+a=z\) and \(x+a=2y=2z\) . The co-ordinates of each of the points of intersection are given by :

A line makes the same angle \(\theta\), with each of the \(x\) and \(z\) axis.
If the angle \(\beta \,\), which it makes with y-axis, is such that \(\,{\sin ^2}\beta = 3{\sin ^2}\theta ,\) then \({\cos ^2}\theta\) equals :

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

The intersection of the spheres
\({x^2} + {y^2} + {z^2} + 7x - 2y - z = 13\) and
\({x^2} + {y^2} + {z^2} - 3x + 3y + 4z = 8\)
is the same as the intersection of one of the sphere and the plane

A point on the parabola \({y^2} = 18x\) at which the ordinate increases at twice the rate of the abscissa is

The normal to the curve x = a(1 + cos \(\theta\)), \(y = a\sin \theta\) at \('\theta '\) always passes through the fixed point

A function \(y=f(x)\) has a second order derivative \(f''\left( x \right) = 6\left( {x - 1} \right).\) If its graph passes through the point \((2, 1)\) and at that point the tangent to the graph is \(y = 3x - 5\), then the function is :

If \(2a+3b+6c=0\), then at least one root of the equation
\(a{x^2} + bx + c = 0\) lies in the interval

The area of the region bounded by the curves
\(y = \left| {x - 2} \right|,x = 1,x = 3\) and the \(x\)-axis is :

The coefficient of \({x^n}\) in expansion of \(\left( {1 + x} \right){\left( {1 - x} \right)^n}\) is

If \({S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}},\,}\)then \({{{t_{ n}}} \over {{S_n}}}\) is equal to

The coefficient of the middle term in the binomial expansion in powers of \(x\) of \({\left( {1 + \alpha x} \right)^4}\) and \({\left( {1 - \alpha x} \right)^6}\) is the same if \(\alpha\) equals

Intercept on the line y = x by the circle \({x^2}\, + \,{y^2} - 2x = 0\) is AB. Equation of the circle on AB as a diameter is :

If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference \(10\,\pi\), then the equation of the circle is :

If a circle passes through the point (a, b) and cuts the circle \({x^2}\, + \,{y^2} = 4\) orthogonally, then the locus of its centre is :

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is :

Let z and w be complex numbers such that \(\overline z + i\overline w = 0\) and arg zw = \(\pi\). Then arg z equals :

If \(\,\left| {{z^2} - 1} \right| = {\left| z \right|^2} + 1\), then z lies on :

If \(z = x - iy\) and \({z^{{1 \over 3}}} = p + iq\), then
\({{\left( {{x \over p} + {y \over q}} \right)} \over {\left( {{p^2} + {q^2}} \right)}}\) is equal to :

The value of \(I = \int\limits_0^{\pi /2} {{{{{\left( {\sin x + \cos x} \right)}^2}} \over {\sqrt {1 + \sin 2x} }}dx}\) is

If \(\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} }\) then \(A\) is

If \(f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {xg\left\{ {x\left( {1 - x} \right)} \right\}dx}\)
and $${I_2} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)...

The value of \(\int\limits_{ - 2}^3 {\left| {1 - {x^2}} \right|dx}\) is

\(\mathop {Lim}\limits_{n \to \infty } \sum\limits_{r = 1}^n {{1 \over n}{e^{{r \over n}}}}\) is