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IIT JEE 1980
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52
Duration
180 mins
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IIT-JEE Advance - Previous Year Papers
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52questions
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PYP
IIT JEE 1980
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 out which are absorbed in acidified AgNO3 solution, 1.341 g of white precipitate was obtained.
Find the molecular weight of unknown chloride.
(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 out which are absorbed in acidified AgNO3 solution, 1.341 g of white precipitate was obtained.
Find the molecular weight of unknown chloride.
PYP
IIT JEE 1980
A rocket moves forward by pushing the surrounding air backwards.
PYP
IIT JEE 1980
(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 the KMnO4 solution used in step (iii) requires 30 ml of 0.1 N FeSO4 solution for complete reaction.
Find the amount of MnSO4.4H2O present in the sample.
(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 the KMnO4 solution used in step (iii) requires 30 ml of 0.1 N FeSO4 solution for complete reaction.
Find the amount of MnSO4.4H2O present in the sample.
PYP
IIT JEE 1980
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.
PYP
IIT JEE 1980
Given $$\alpha + \beta - \gamma = \pi ,$$ prove that
$$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$$
$$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$$
PYP
IIT JEE 1980
Find the real values of x and y for which the following equation is satisfied $$\,{{(1 + i)x - 2i} \over {3 + i}} + {{(2 + 3i)y + i} \over {3 - i}} = i$$
PYP
IIT JEE 1980
$$ABC$$ 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
$$$DF + FA + AE + ED = AB + AC$$$
PYP
IIT JEE 1980
For all $$\theta $$ in $$\left[ {0,\,\pi /2} \right]$$ show that, $$\cos \left( {\sin \theta } \right) \ge \,\sin \,\left( {\cos \theta } \right).$$
PYP
IIT JEE 1980
$$ABC$$ is a triangle. $$D$$ is the middle point of $$BC$$. If $$AD$$ is perpendicular to $$AC$$, then prove that
$$$\cos A\,\cos C = {{2\left( {{c^2} - {a^2}} \right)} \over {3ac}}$$$
PYP
IIT JEE 1980
Explain the following in not more than two sentenses.
A solution of FeCl3 in water gives a brown precipitate on standing.
PYP
IIT JEE 1980
$$ABC$$ is a triangle, $$P$$ is a point on $$AB$$, and $$Q$$ is point on $$AC$$ such that $$\angle AQP = \angle ABC$$. Complete the relation
$$${{area\,\,of\,\,\Delta APQ} \over {area\,\,of\,\,\Delta ABC}} = {{\left( {...} \right)} \over {A{C^2}}}$$$
PYP
IIT JEE 1980
Anhydrous MgCl2 is obtained by hydrated salt with ______.
PYP
IIT JEE 1980
The modern atomic unit is based on the mass of ______.
PYP
IIT JEE 1980
$$ABC$$ 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
$$$\angle DAE = {1 \over 2}\left[ {\left( {} \right) - \angle C} \right]$$$
PYP
IIT JEE 1980
In a $$\Delta ABC,\,\angle A = {90^ \circ }$$ and $$AD$$ is an altitude. Complete the relation $${{BD} \over {BA}} = {{AB} \over {\left( {....} \right)}}$$.
PYP
IIT JEE 1980
Two masses of 1gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is
PYP
IIT JEE 1980
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
PYP
IIT JEE 1980
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
PYP
IIT JEE 1980
If a machine is lubricated with oil
PYP
IIT JEE 1980
M is molecular weight of KMnO4. The equivalent wight of KMnO4 when it is converted into K2MnO4 is
PYP
IIT JEE 1980
Element X is strongly electropositive and element Y is strongly electronegative. Both are univalent. The compound formed would be
PYP
IIT JEE 1980
Which of the following is soluble in water?
PYP
IIT JEE 1980
The total number of electrons that take part in forming the bond in N2 is
PYP
IIT JEE 1980
Calcium is obtained by
PYP
IIT JEE 1980
HCL is added to the following oxides. Which one would give H2O2?
PYP
IIT JEE 1980
Which of the following compounds are covalent?
PYP
IIT JEE 1980
Both the roots of the equation (x - b) (x - c) + (x - a) (x - c) + (x - a) (x - b) = 0 are always
PYP
IIT JEE 1980
The least value of the expression $$2\,\,{\log _{10}}\,x\, - \,{\log _x}(0.01)$$ for x > 1, is
PYP
IIT JEE 1980
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
PYP
IIT JEE 1980
The smallest positive integer n for which $${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$$ is
PYP
IIT JEE 1980
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
PYP
IIT JEE 1980
If $$\,({x^2} + px + 1)\,$$ is a factor of $$(a{x^3} + bx + c)$$, then
PYP
IIT JEE 1980
The equation $$\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}$$ has
PYP
IIT JEE 1980
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 $$p/4$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.
Reflection about the line $$y=x$$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $$p/4$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.
PYP
IIT JEE 1980
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
PYP
IIT JEE 1980
Given $${n^4} < {10^n}$$ for a fixed positive integer $$n \ge 2,$$ prove that $${\left( {n + 1} \right)^4} < {10^{n + 1}}.$$
PYP
IIT JEE 1980
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
PYP
IIT JEE 1980
Given $$A = {\sin ^2}\theta + {\cos ^4}\theta $$ then for all real values of $$\theta $$
PYP
IIT JEE 1980
Give the MKS units for each of the following quantities.
(i) Young's modulus
(ii) Magnetic Induction
(iii) Power of a lens
PYP
IIT JEE 1980
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.
PYP
IIT JEE 1980
(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 many milli-equivalent of Na2CO3 would be required to soften 1 litre of the sample?
(c) 1 gm of Mg is burnt in a closed vessel which contains 0.5gm of O2.
(i) Which reactant is left in excess?
(ii) Find the weight of the excess reactants.
(iii) How many milliliters of 0.5N H2SO4 will dissolve the residue in the vessel?
(b) A sample of hard water contains 20 mg of Ca++ ions per litre. How many milli-equivalent of Na2CO3 would be required to soften 1 litre of the sample?
(c) 1 gm of Mg is burnt in a closed vessel which contains 0.5gm of O2.
(i) Which reactant is left in excess?
(ii) Find the weight of the excess reactants.
(iii) How many milliliters of 0.5N H2SO4 will dissolve the residue in the vessel?
PYP
IIT JEE 1980
(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 by volume.
(b) A compound contains 28 percent of nitrogen and 72 percent of metal by weight. 3 atoms of metal combine with 2 atoms of N. Find the atomic weight of metal.
PYP
IIT JEE 1980
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)
(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)
PYP
IIT JEE 1980
The total no of electron present in 18 ml of water is ______.
PYP
IIT JEE 1980
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 is heated strongly. Gases B and C, with pungent smell, come out. A brown residue D is left behind.
(iv) The gas mixture (B and C) is passed into a dichromate solution. The solution turns green.
(v) The green solution from step (iv) gives a white precipitate E with a solution of barium nitrate.
(vi) Residue D from step (iii) is heated on charcoal in a reducing flame. It gives a magnetic substance E.
Name the compounds A, B, C, D and E.
PYP
IIT JEE 1980
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.
PYP
IIT JEE 1980
Find the solution set of the system
$$$\matrix{
{x + 2y + z = 1;} \cr
{2x - 3y - w = 2;} \cr
{x \ge 0;\,y \ge 0;\,z \ge 0;\,w \ge 0.} \cr
} $$$
PYP
IIT JEE 1980
For what values of $$m,$$ does the system of equations
$$$\matrix{
{3x + my = m} \cr
{2x - 5y = 20} \cr
} $$$
has solution satisfying the conditions $$x > 0,\,y > 0.$$
PYP
IIT JEE 1980
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 $$f\left( A \right).$$
$$f\left( x \right) = \cos x - x\left( {1 + x} \right);$$ find $$f\left( A \right).$$
PYP
IIT JEE 1980
(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 to $$\theta $$. The sides of the triangle $$ABC$$ are $$a, b, c$$; and the area of the triangle $$ABC$$ is $$\Delta $$. Show that the height of the tower is $${{abc\tan \theta } \over {4\Delta }}$$.
(ii) $$AB$$ is vertical pole. The end $$A$$ is on the level ground. $$C$$ is the middle point of $$AB$$. $$P$$ is a point on the level ground. The portion $$CB$$ subtends an angle $$\beta $$ at $$P$$. If $$AP = n\,AB,$$ then show that tan$$\beta $$ $$ = {n \over {2{n^2} + 1}}$$
PYP
IIT JEE 1980
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 $$L$$.
PYP
IIT JEE 1980
Given $$y = {{5x} \over {3\sqrt {{{\left( {1 - x} \right)}^2}} }} + {\cos ^2}\left( {2x + 1} \right)$$; Find $${{dy} \over {dx}}$$.
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