IIT-JEE 1980

Which of the following compounds are covalent?

The total number of electrons that take part in forming the bond in N2 is

Which of the following is soluble in water?

Element X is strongly electropositive and element Y is strongly electronegative. Both are univalent. The compound formed would be

M is molecular weight of KMnO4. The equivalent wight of KMnO4 when it is converted into K2MnO4 is

Calcium is obtained by

HCL is added to the following oxides. Which one would give H2O2?

Anhydrous MgCl2 is obtained by hydrated salt with ______.

Explain the following in not more than two sentenses.
A solution of FeCl3
in water gives a brown precipitate on
standing.

Compound A is a light green crystalline solid. It gives
the following tests :
(i) It dissolves in dilute sulphuric acid. No gas is
produced.
(ii) A drop of KMnO4
is added to the above solution. The
pink colour disappears.
(iii) Compound A ...

A hydrocarbon contains 10.5 g of carbon per gram of hydrogen. 1 litre of the hydrocarbon at 127oC and 1 atmosphere weighs 2.8 g. Find the molecular formula.

The total no of electron present in 18 ml of water is ______.

(a) One litre of a sample of hard water contains 1 mg of CaCl2 and 1 mg of MgCl2. Find the total hardness in terms of parts of CaCO3 per 106 parts of water by weight.
(b) A sample of hard water contains 20 mg of Ca++ ions per litre. How man...

A mixture contains NaCl and unknown chloride MCl.
(i) 1g of this is dissolved in water. Excess of acidified AgNO3 solution is added to it. 2.567 g of white ppt is formed.
(ii) 1 g of original mixture is heated to 300oC. Some vapours come ou...

Find
(i) The total number of neutrons and
(ii) The total mass of neutron in 7 mg of 14C
(Assume that mass of neutron = mass of hydrogen atom)

(a) 1 litre of a mixture of CO and CO2
is taken. This
mixture is passed through a tube containing red hot
charcoal. The volume now becomes 1.6 litre. The
volumes are measured under the same conditions.
Find the composition of the mixture b...

The modern atomic unit is based on the mass of ______.

(i). A sample of MnSO4.4H2O is strongly heated in air. The residue is Mn3O4.
(ii). The residue is dissolved in 100 ml of 0.1N FeSO4 containing dilute H2SO4.
(iii). The solution reacts completely with 50 ml of KMnO4 solution.
(iv). 25 ml of ...

Two circles \({x^2} + {y^2} = 6\) and \({x^2} + {y^2} - 6x + 8 = 0\) are given. Then the equation of the circle through their points of intersection and the point (1, 1) is

A square is inscribed in the circle \({x^2} + {y^2} - 2x + 4y + 3 = 0\). Its sides are parallel to the coordinate axes. The one vertex of the square is

The smallest positive integer n for which \({\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1\) is

Find the real values of x and y for which the following equation is satisfied \(\,{{(1 + i)x - 2i} \over {3 + i}} + {{(2 + 3i)y + i} \over {3 - i}} = i\)

Given \(y = {{5x} \over {3\sqrt {{{\left( {1 - x} \right)}^2}} }} + {\cos ^2}\left( {2x + 1} \right)\); Find \({{dy} \over {dx}}\).

Two events \(A\) and \(B\) have probabilities \(0.25\) and \(0.50\) respectively. The probability that both \(A\) and \(B\) occur simultaneously is \(0.14\). Then the probability that neither \(A\) nor \(B\) occurs is

The probability that an event \(A\) happens in one trial of an experiment is \(0.4.\) Three independent trials of the experiment are performed. The probability that the event \(A\) happens at least once is

(i) \(PQ\) is a vertical tower. \(P\) is the foot and \(Q\) is the top of the tower. \(A, B, C\) are three points in the horizontal plane through \(P\). The angles of elevation of \(Q\) from \(A\), \(B\), \(C\) are equal, and each is equal ...

In a \(\Delta ABC,\,\angle A = {90^ \circ }\) and \(AD\) is an altitude. Complete the relation \({{BD} \over {BA}} = {{AB} \over {\left( {....} \right)}}\).

\(ABC\) is a triangle with \(\angle B\) greater than \(\angle C.\,D\) and \(E\) are points on \(BC\) such that \(AD\) is perpendicular to \(BC\) and \(AE\) is the bisector of angle \(A\). Complete the relation
$$$\angle DAE = {1 \over 2}\l...

\(ABC\) is a triangle. \(D\) is the middle point of \(BC\). If \(AD\) is perpendicular to \(AC\), then prove that
\($\cos A\,\cos C = {{2\left( {{c^2} - {a^2}} \right)} \over {3ac}}\)$

\(ABC\) is a triangle, \(P\) is a point on \(AB\), and \(Q\) is point on \(AC\) such that \(\angle AQP = \angle ABC\). Complete the relation
$$${{area\,\,of\,\,\Delta APQ} \over {area\,\,of\,\,\Delta ABC}} = {{\left( {...} \right)} \over {...

\(ABC\) is a triangle with \(AB=AC\). \(D\) is any point on the side \(BC\). \(E\) and \(F\) are points on the side \(AB\) and \(AC\), respectively, such that \(DE\) is parallel to \(AC\), and \(DF\) is parallel to \(AB\). Prove that
$$$DF...

Find the solution set of the system
\($\matrix{ {x + 2y + z = 1;} \cr {2x - 3y - w = 2;} \cr {x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr }\)$

Both the roots of the equation (x - b) (x - c) + (x - a) (x - c) + (x - a) (x - b) = 0 are always

For what values of \(m,\) does the system of equations
\($\matrix{ {3x + my = m} \cr {2x - 5y = 20} \cr }\)$
has solution satisfying the conditions \(x > 0,\,y > 0.\)

Let \(y = \sqrt {{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)}}}\)
Find all the real values of \(x,\) for which \(y\) takes real values.

Given \({n^4} < {10^n}\) for a fixed positive integer \(n \ge 2,\) prove that \({\left( {n + 1} \right)^4} < {10^{n + 1}}.\)

The least value of the expression \(2\,\,{\log _{10}}\,x\, - \,{\log _x}(0.01)\) for x > 1, is

If \(\,({x^2} + px + 1)\,\) is a factor of \((a{x^3} + bx + c)\), then

The interior angles of a polygon are in arithmetic progression. The smallest angle is \({120^ \circ }\), and the common difference is \({5^ \circ }\), Find the number of sides of the polygon.

The point \(\,\left( {4,\,1} \right)\) undergoes the following three transformations successively.
Reflection about the line \(y=x\).
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle ...

A straight line \(L\) is perpendicular to the line \(5x - y = 1.\) The area of the triangle formed by the line \(L\) and the coordinate axes is \(5\). Find the equation of the Line \(L\).

Given \(\alpha + \beta - \gamma = \pi ,\) prove that
\(\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y\)

The equation \(\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}\) has

Given \(A = {\sin ^2}\theta + {\cos ^4}\theta\) then for all real values of \(\theta\)

Given \(A = \left\{ {x:{\pi \over 6} \le x \le {\pi \over 3}} \right\}\) and
\(f\left( x \right) = \cos x - x\left( {1 + x} \right);\) find \(f\left( A \right).\)

For all \(\theta\) in \(\left[ {0,\,\pi /2} \right]\) show that, \(\cos \left( {\sin \theta } \right) \ge \,\sin \,\left( {\cos \theta } \right).\)

A ship of mass 3 \(\times\) 107 kg initially at rest, is pulled by a force of 5 \(\times\) 104 N through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is

A rocket moves forward by pushing the surrounding air backwards.

A block of mass 2 kg rests on a rough inclined plane making an angle of \(30^\circ\) with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is

Give the MKS units for each of the following quantities.
(i) Young's modulus
(ii) Magnetic Induction
(iii) Power of a lens