AIEEE 2003

Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The
explanation for it is that :

What may be expected to happen when phosphine gas is mixed with chlorine gas?

Which one of the following is an amphoteric oxide?

The reduction in atomic size with increase in atomic number is a characteristic of elements of

The atomic numbers of Vanadium (V), Chromium (cr), Manganese (Mn) and Iron (Fe), respectively, \(23,24,25\) and \(26\). Which one of these may be expected to have the higher second ionization enthalpy?

According to the Periodic Law of elements, the variation in properties of elements is related to their

Nylon threads are made of

In curing cement plasters water is sprinkled from time to time. This helps in :

The solubilities of carbonates decrease down the magnesium group due to a decrease in :

The substance not likely to contain CaCO3 is :

How many unit cells are present in a cubeshaped ideal crystal of NaCl of mass 1.00 g?
[Atomic masses: Na = 23, Cl = 35.5]

If liquids A and B form an ideal solution

In a 0.2 molal aqueous solution of a weak acid HX the degree of ionization is 0.3. Taking kf for water as 1.85, the freezing point of the solution will be nearest to

A pressure cooker reduces cooking time for food because

What volume of hydrogen gas at 273 K and 1 atm pressure will be consumed in obtaining 21.6 g of elemental boron (atomic mass = 10.8) from the reduction of boron trichloride by hydrogen?

25 ml of a solution of barium hydroxide on titration with a 0.1 molar solution of hydrochloric acid gave a litre value of 35 ml. The molarity of barium hydroxide solution was

The de Broglie wavelength of a tennis ball of mass 60 g moving with a velocity of 10 meters per second is approximately

Which one of the following groupings represents a collection of isoelectronic species? (At. nos. : Cs : 55, Br : 35)

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen

The orbital angular momentum for an electron revolving in an orbit is given by \(\sqrt {l(l + 1)} {h \over {2\pi }}\). This momentum for an s-electron will be given by

Which one of the following characteristics is not correct for physical adsorption?

If at 298 K the bond energies of C - H, C - C, C = C and H - H bonds are respectively 414, 347, 615 and 435 kJ/mol, the value of enthalpy change for the reaction
H2C = CH2(g) + H2(g) \(\to\) H3C - CH3(g) at 298 K will be :

The internal energy change when a system goes from state A to B is 40 kJ/mole. If the system goes from A to B by a reversible path and returns to state A by an irreversible path what would be the net change in internal energy?

The enthalpy change for a reaction does not depend upon :

The correct relationship between free energy change in a reaction and the corresponding equilibrium constant Kc is :

In an irreversible process taking place at constant T and P and in which only pressure-volume work is being done, the change in Gibbs free energy (dG) and change in entropy (dS), satisfy the criteria :

Two systems of rectangular axes have the same origin. If a plane cuts then at distances \(a,b,c\) and \(a', b', c'\) from the origin then

The radius of the circle in which the sphere
\({x^2} + {y^2} + {z^2} + 2x - 2y - 4z - 19 = 0\) is cut by the plane
\(x+2y+2z+7=0\) is

The two lines \(x=ay+b,z=cy+d\) and \(x = a'y + b',z = c'y + d'\) will be perpendicular, if and only 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 if :

The shortest distance from the plane \(12x+4y+3z=327\) to the sphere \({x^2} + {y^2} + {z^2} + 4x - 2y - 6z = 155\) is

The real number \(x\) when added to its inverse gives the minimum sum at \(x\) equal :

If the function \(f\left( x \right) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1,\) where \(a>0,\) attains its maximum and minimum at \(p\) and \(q\) respectively such that \({p^2} = q\) , then \(a\) equals

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

If \(x\) is positive, the first negative term in the expansion of \({\left( {1 + x} \right)^{27/5}}\) is

The number of integral terms in the expansion of \({\left( {\sqrt 3 + \root 8 \of 5 } \right)^{256}}\) is

If the two circles \({(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}\) and \(\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, = 0\) intersect in two distinct point, then :

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is :

Let \({Z_1}\) and \({Z_2}\) be two roots of the equation \({Z^2} + aZ + b = 0\), Z being complex. Further , assume that the origin, \({Z_1}\) and \({Z_2}\) form an equilateral triangle. Then :

If \(z\) and \(\omega\) are two non-zero complex numbers such that \(\left| {z\omega } \right| = 1\) and \(Arg(z) - Arg(\omega ) = {\pi \over 2},\) then \(\,\overline {z\,} \omega\) is equal to

If \({\left( {{{1 + i} \over {1 - i}}} \right)^x} = 1\) then :

Let \(f(x)\) be a function satisfying \(f'(x)=f(x)\) with \(f(0)=1\) and \(g(x)\) be a function that satisfies \(f\left( x \right) + g\left( x \right) = {x^2}\). Then the value of the integral $$\int\limits_0^1 {f\left( x \right)g\left( x \...

The value of the integral \(I = \int\limits_0^1 {x{{\left( {1 - x} \right)}^n}dx}\) is

The value of \(\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec }^2}tdt} } \over xsinx}\) is

If \(f\left( {a + b - x} \right) = f\left( x \right)\) then \(\int\limits_a^b {xf\left( x \right)dx}\) is equal to

If \(f\left( y \right) = {e^y},\) \(g\left( y \right) = y;y > 0\) and
\(F\left( t \right) = \int\limits_0^t {f\left( {t - y} \right)g\left( y \right)dy,}\) then :

\(\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \over {{n^5}}}\) - \(\mathop {\lim }\limits_{n \to \infty } {{1 + {2^3} + {3^3} + .... + {n^3}} \over {{n^5}}}\)

The solution of the differential equation
\(\left( {1 + {y^2}} \right) + \left( {x - {e^{{{\tan }^{ - 1}}y}}} \right){{dy} \over {dx}} = 0,\) is :

The degree and order of the differential equation of the family of all parabolas whose axis is \(x\)-axis, are respectively.

Let \(f\left( x \right)\) be a polynomial function of second degree. If \(f\left( 1 \right) = f\left( { - 1} \right)\) and \(a,b,c\) are in \(A.P,\) then \(f'\left( a \right),f'\left( b \right),f'\left( c \right)\) are in