IIT-JEE 1979

The compound which contains both ionic and covalent bonds is

The octet rule is not valid for the molecule

A white amorphous powder (A) on heating yields a
colourless, non-combustible gas (B) and a solid (C).
The latter compound assumes a yellow colour on heating
and changes to white on cooling. (C) dissolves in dilute
acid and the resulting sol...

The precipitation of second group sulphides in qualitative
analysis is carried out with hydrogen sulphide in the presence
of hydrochloric acid but not in nitric acid. Explain.

4.215 g of a metallic carbonate was heated in a hard glass tube and the CO2 evolved was found to measure 1336 ml at 27oC and 700 mm pressure. What is the equivalent weight of metal?

The total number of electrons is one molecule of carbon dioxide is

5 ml of a gas containing only carbon and hydrogen were mixed with an excess of oxygen (30 ml) and the mixture exploded by means of an electric spark. After the explosion, the volume of the mixed gases remaining was 25 ml. On adding a concen...

The largest number of molecules is in

(a). 5.5 g of a mixture FeSO4.7H2O and Fe2(SO4)3.9H2O requires 5.4 ml of 0.1 N KMnO4 solution for complete oxidation. Calculate the number of gram mole of hydrated ferric sulphate in the mixture.
(b). The vapour density (hydrogen = 1) of a ...

Account for the following : Limit your answer to two
sentences.
"Atomic weights of most of the elements are fractional."

In the analysis of 0.5 g sample feldspar, a mixture of chlorides of sodium and potassium is obtained which weighs 0.1180g. Subsequent treatment of mixed chlorides with silver nitrate gives 0.2451 g of silver chloride. What is the percentage...

2.76 g of silver carbonate on being strongly heated yields a residue weighing

A gaseous mixture contains oxygen and nitrogen in the ratio of 1 : 4 by weight. Therefore the ratio of their no of molecules is

The number of neutrons in dipositive zinc ion with mass number 70 is

Prove that the minimum value of \({{\left( {a + x} \right)\left( {b + x} \right)} \over {\left( {c + x} \right)}},\)
\(a,b > c,x > - c\) is \({\left( {\sqrt {a - c} + \sqrt {b - c} } \right)^2}\).

If x + iy = \(\sqrt {{{a + ib} \over {c + id}}}\), prove that \({({x^2} + {y^2})^2} = {{{a^2} + {b^2}} \over {{c^2} + {d^2}}}\).

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

Find the derivative of
\($f\left( x \right) = \left\{ {\matrix{ {{{x - 1} \over {2{x^2} - 7x + 5}}} & {when\,\,x \ne 1} \cr { - {1 \over 3}} & {when\,\,x = 1} \cr } } \right.\)$
at \(x=1\)

Evaluate \(\int {{{{x^2}dx} \over {{{\left( {a + bx} \right)}^2}}}}\)

Given that \({C_1} + 2{C_2}x + 3{C_3}{x^2} + ......... + 2n{C_{2n}}{x^{2n - 1}} = 2n{\left( {1 + x} \right)^{2n - 1}}\)
where \({C_r} = {{\left( {2n} \right)\,!} \over {r!\left( {2n - r} \right)!}}\,\,\,\,\,r = 0,1,2,\,............,2n\)
P...

\({}^n{C_{r - 1}} = 36,{}^n{C_r} = 84\,\,and\,\,{}^n{C_{r + 1}} = 126\), then r is :

Two fair dice are tossed. Let \(x\) be the event that the first die shows an even number and \(y\) be the event that the second die shows an odd number. The two events \(x\) and \(y\) are:

Six boys and six girls sit in a row randomly. Find the probability that
(i) the six girls sit together
(ii) the boys and girls sit alternately.

(a) A balloon is observed simultaneously from three points \(A, B\) and \(C\) on a straight road directly beneath it. The angular elevation at \(B\) is twice that at \(A\) and the angular elevation at \(C\) is thrice that at \(A\). If the d...

(a) If a circle is inscribed in a right angled triangle \(ABC\) with the right angle at \(B\), show that the diameter of the circle is equal to \(AB+BC-AC\).
(b) If a triangle is inscribed in a circle, then the product of any two sides of ...

If the bisector of the angle \(P\) of a triangle \(PQR\) meets \(QR\) in \(S\), then

The equation x + 2y + 2z = 1 and 2x + 4y + 4z = 9 have

If \(\ell\), m, n are real, \(\ell \ne m\), then the roots by the equation :
\((\ell - m)\,{x^2} - 5\,(\ell + m)\,x - 2\,(\ell - m) = 0\) are

If x, y and z are real and different and \(\,u = {x^2} + 4{y^2} + 9{z^2} - 6yz - 3zx - 2xy\), then u is always.

Let a > 0, b > 0 and c > 0. Then the roots of the equation \(a{x^2} + bx + c = 0\)

If \(\alpha ,\,\beta\) are the roots of \({x^2} + px + q = 0\) and \(\gamma ,\,\delta\) are the roots of \({x^2} + rx + s = 0,\) evaluate $$\left( {\alpha - \gamma } \right)\left( {\alpha - \delta } \right)\left( {\beta - \gamma } \rig...

The harmonic mean of two numbers is 4.Their arithmetic mean \(A\) and the geometric mean \(G\) satisfy the relation. \(2A + {G^2} = 27\)

The points \(\left( { - a,\, - b} \right),\,\left( {0,\,0} \right),\,\left( {a,\,b} \right)\) and \(\left( {{a^2},\,ab} \right)\) are :

(a) Two vertices of a triangle are \((5, -1)\) and \((-2, 3).\) If the orthocentre of the triangle is the origin, find the coordinates of the third point.
(b) Find the equation of the line which bisects the obtuse angle between the lines $...

If \(\alpha + \beta + \gamma = 2\pi ,\) then

If \(\tan \theta = - {4 \over 3},then\sin \theta \,is\,\)

(a) Draw the graph of \(y = {1 \over {\sqrt 2 }}\left( {cinx + \cos x} \right)\) from \(x = - {\pi \over 2}\) to \(x = {\pi \over 2}\).
(b) If $$\cos \left( {\alpha + \beta } \right) = {4 \over 5},\,\,\sin \,\left( {\alpha - \beta } \r...

Answer the following giving reason in brief:
Is the time variation of position, shown in the figure observed in nature?

The dispalcement x of particle moving in one direction, under the action of a constant force is related to the time t by the equation \(t = \sqrt x + 3\)
where x is in meters and t in seconds. Find
(i) The displacement of the particle when...