IIT-JEE 1980

Paper was held on
Fri, Apr 11, 1980 9:00 AM

## Chemistry

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

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

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

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A hydrocarbon contains 10.5 g of carbon per gram of hydrogen. 1 litre of the hydrocarbon at 127oC and 1 atmosphere weigh

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

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A mixture contains NaCl and unknown chloride MCl.
(i) 1g of this is dissolved in water. Excess of acidified AgNO3 soluti

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(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 pa

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(i). A sample of MnSO4.4H2O is strongly heated in air. The residue is Mn3O4.
(ii). The residue is dissolved in 100 ml of

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(a) 1 litre of a mixture of CO and CO2
is taken. This
mixture is passed through a tube containing red hot
charcoal. The

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

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Which of the following compounds are covalent?

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

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Which of the following is soluble in water?

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Anhydrous MgCl2 is obtained by hydrated salt with ______.

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

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Calcium is obtained by

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

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Compound A is a light green crystalline solid. It gives
the following tests :
(i) It dissolves in dilute sulphuric acid.

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## Mathematics

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

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

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

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

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Given $$\alpha + \beta - \gamma = \pi ,$$ prove that
$$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\s

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Given $$A = \left\{ {x:{\pi \over 6} \le x \le {\pi \over 3}} \right\}$$ and
$$f\left( x \right) = \cos x - x\left( {

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

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

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Let $$y = \sqrt {{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)}}} $$
Find all the real

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For what values of $$m,$$ does the system of equations
$$$\matrix{
{3x + my = m} \cr
{2x - 5y = 20} \cr
} $

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

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

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

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

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The interior angles of a polygon are in arithmetic progression. The smallest angle is $${120^ \circ }$$, and the common

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The point $$\,\left( {4,\,1} \right)$$ undergoes the following three transformations successively.
Reflection about the

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A straight line $$L$$ is perpendicular to the line $$5x - y = 1.$$ The area of the triangle formed by the line $$L$$ and

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A square is inscribed in the circle $${x^2} + {y^2} - 2x + 4y + 3 = 0$$. Its sides are parallel to the coordinate axes.

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Two circles $${x^2} + {y^2} = 6$$ and $${x^2} + {y^2} - 6x + 8 = 0$$ are given. Then the equation of the circle through

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

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$$ABC$$ is a triangle with $$\angle B$$ greater than $$\angle C.\,D$$ and $$E$$ are points on $$BC$$ such that $$AD$$ is

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$$ABC$$ is a triangle, $$P$$ is a point on $$AB$$, and $$Q$$ is point on $$AC$$ such that $$\angle AQP = \angle ABC$$. C

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

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$$ABC$$ is a triangle. $$D$$ is the middle point of $$BC$$. If $$AD$$ is perpendicular to $$AC$$, then prove that
$$$\c

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$$ABC$$ is a triangle with $$AB=AC$$. $$D$$ is any point on the side $$BC$$. $$E$$ and $$F$$ are points on the side $$AB

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(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

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The probability that an event $$A$$ happens in one trial of an experiment is $$0.4.$$ Three independent trials of the ex

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Two events $$A$$ and $$B$$ have probabilities $$0.25$$ and $$0.50$$ respectively. The probability that both $$A$$ and $$

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## Physics

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

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A rocket moves forward by pushing the surrounding air backwards.

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A ship of mass 3 $$ \times $$ 107 kg initially at rest, is pulled by a force of 5 $$ \times $$ 104 N through a distance

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A block of mass 2 kg rests on a rough inclined plane making an angle of $$30^\circ $$ with the horizontal. The coefficie

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If a machine is lubricated with oil

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Two masses of 1gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum i

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