IIT-JEE 1992

The cyanide ion, CN- and N2 are isoelectronic, But in contrast to CN-, N2 is chemically inert, because of

The maximum number of hydrogen bonds a water molecule can form is

The molecules that will have dipole moment are

The type of hybrid orbitals used by the chlorine atom in \(ClO_2^-\) is

Which of the following have identical bond order?

For the galvanic cell
Ag | AgCl(s), KCl (0.2M) || KBr (0.001M), AgBr(s) | Ag
Calculate the EMF generated and assign correct polarity to each electrode for a spontaneous process after taking into account the cell reaction at 25oC.
[Ksp(AgCl)...

An aqueous solution of NaCl on electrolysis gives H2(g), Cl2(g) and NaOH according to the reaction:
2Cl- (aq) + 2H2O = 2OH- (aq) + H2 (g) + Cl2 (g)
A direct current of 25 amperes with a current efficiency of 62 % is passed through 20 litres...

At 27oC, hydrogen is leaked through a tiny hole into a vessel for 20 minutes. Another unknown gas at the same temperature and pressure as that of H2 is leaked through the same hole for 20 minutes After the effusion of the gases the mixture ...

At room temperature the following reacton is procedd nearly to completion:
2NO + O2 \(\to\) 2NO2 \(\to\) N2O4
The dimer, N2O4, solidifies at 262 K. A 250 ml flask and a 100 ml flask are separated by a stop-cock. At 300 K, the nitric oxid...

Give reasons of the following:
Hydrogen peroxide acts as an oxidising as well as a reducing agent.

The statement that is not correct for the periodic classification of element is

For the redox reaction:
\(MnO_4^ - + {C_2}O_4^{ - 2} + {H^ + }\) \(\to M{n^{2 + }} + C{O_2} + {H_2}O\)
The correct coefficients of the reactants for the balanced
reaction are

The species that do not contain peroxide ions are

A 2.0 g sample of a mixture containing sodium carbonate, sodium bicarbonate and sodium suplphate is gently heated till the evolution of CO2 ceases. The volume of CO2 at 750 mm Hg pressure and at 298K is measured to be 123.9 ml. A 1.5g of th...

One gram of commercial AgNO3 is dissolved in 50 ml. of water. It is treated with 50 ml. of a KI solution. The silver iodide thus precipitated is filtered off. Excess of KI in the filterate is titrated with (M/10) KIO3 solution in presence o...

Which of the following does not characterise X-rays?

Which of the following relates to photons both as wave motion and as a stream of particles?

What normal to the curve \(y = {x^2}\) forms the shortest chord?

A cubic \(f(x)\) vanishes at \(x=2\) and has relative minimum / maximum at \(x=-1\) and \(x = {1 \over 3}\) if \(\int\limits_{ - 1}^1 {f\,\,dx = {{14} \over 3}}\), find the cubic \(f(x)\).

In this questions there are entries in columns \(I\) and \(II\). Each entry in column \(I\) is related to exactly one entry in column \(II\). Write the correct letter from column \(II\) against the entry number in column \(I\) in your answe...

Sketch the region bounded by the curves \(y = {x^2}\) and
\(y = {2 \over {1 + {x^2}}}.\) Find the area.

The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle \({x^2} + {y^2} = 9\)is

Let a circle be given by 2x (x - a) + y (2y - b) = 0, \((a\, \ne \,0,\,\,b\, \ne 0)\). Find the condition on a abd b if two chords, each bisected by the x-axis, can be drawn to the circle from \(\left( {a,\,\,{b \over 2}} \right)\).

\({\rm{z }} \ne {\rm{0}}\) is a complex number
Column I
(A) Re z = 0
(B) Arg \(z = {\pi \over 4}\)
Column II
(p) Re\({z^2}\) = 0
(q) Im\({z^2}\) = 0
(r) Re\({z^2}\) = Im\({z^2}\)

Determine a positive integer \(n \le 5,\) such that
\($\int\limits_0^1 {{e^x}{{\left( {x - 1} \right)}^n}dx = 16 - 6e}\)$

Find the indefinite integral \(\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x } \right)} \over {\root 3 \of x + \root \, \of x }}} \right)} dx\)

Let \(p \ge 3\) be an integer and \(\alpha\), \(\beta\) be the roots of \({x^2} - \left( {p + 1} \right)x + 1 = 0\) using mathematical induction show that \({\alpha ^n} + {\beta ^n}.\)
(i) is an integer and (ii) is no...

The expansion \({\left( {x + {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5}\) is a polynomial of degree

If \(\sum\limits_{r = 0}^{2n} {{a_r}{{\left( {x - 2} \right)}^r}\,\, = \sum\limits_{r = 0}^{2n} {{b_r}{{\left( {x - 3} \right)}^r}} }\) and \({a_k} = 1\) for all \(k \ge n,\) then show that \({b_n} = {}^{2n + 1}{C_{n + 1}}\)

Three faces of a fair die are yellow, two faces red and one blue. The die is tossed three times. The probability that the colours, yellow, red and blue, appear in the first, second and the third tosses respectively is ...............

A lot contains \(50\) defective and \(50\) non defective bulbs. Two bulbs are drawn at random, one at a time, with replacement. The events \(A, B, C\) are defined as
\(A=\) (the first bulbs is defective)
\(B=\) (the second bulbs is non-def...

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting, points \(0,\) \(1\) and \(2\) are \(0.45, 0.05\) and \(0.50\) respectively. Assuming that the outcomes are independent, the proba...

Three circles touch the one another externally. The tangent at their point of contact meet at a point whose distance from a point of contact is \(4\). Find the ratio of the product of the radii to the sum of the radii of the circles.

Let \(\alpha \,,\,\beta\) be the roots of the equation (x - a) (x - b) = c, \(c \ne 0\). Then the roots of the equation \((x - \alpha \,)\,(x - \beta ) + c = 0\) are

Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio .........

Determine all values of \(\alpha\) for which the point \(\left( {\alpha ,\,{\alpha ^2}} \right)\) lies insides the triangle formed by the lines
$$$\matrix{
{2x + 3y - 1 = 0} \cr
{x + 2y - 3 = 0} \cr
{5x - 6y - 1 = 0} \cr

...

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

In this questions there are entries in columns 1 and 2. Each entry in column 1 is related to exactly one entry in column 2. Write the correct letter from column 2 against the entry number in column 1 in your answer book.
$${{\sin \,3\alpha ...

Show that the value of \({{\tan x} \over {\tan 3x}},\) wherever defined never lies between \({1 \over 3}\) and 3.

A unit vector coplanar with \(\overrightarrow i + \overrightarrow j + 2\overrightarrow k\) and \(\overrightarrow i + 2\overrightarrow j + \overrightarrow k\) and perpendicular to $$\overrightarrow i + \overrightarrow j + \overrighta...