Exam Details
IIT JEE 1978
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Questions
30
Duration
180 mins
Package
IIT-JEE Advance - Previous Year Papers
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Subtopic distribution
Difficulty distribution
30questions
Medium
20
66.7%
Easy
8
26.7%
Hard
2
6.7%
Question type distribution
30questions
Subjective
27
90%
MCQ
3
10%
Syllabus
Full Syllabus
Practise paper questions
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PYP
IIT JEE 1978
Igniting MnO2 converts it quantitatively to Mn3O4. A sample of pyrolusite is of the following composition : MnO2 80%, SiO2 and other inert constituents 15%, rest being water. The sample is ignited in air to constant weight. What is the percentage of Mn in the ignited sample? [O = 16, Mn = 54.9]
PYP
IIT JEE 1978
What weight of AgCl will be precipitated when a solution containing 4.77 g of NaCl is added to a solution of 5.77g of AgNO3?
PYP
IIT JEE 1978
Naturally occurring boron consists of two isotopes whose atomic weighs are 10.01 and 11.01. The atomic weight of natural oron is 10.81. Calculate the percentage of each isotope in natural boron.
PYP
IIT JEE 1978
Solve for $$x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - {2^{2x - 1}}$$
PYP
IIT JEE 1978
Find all integers $$x$$ for which $$\left( {5x - 1} \right) < {\left( {x + 1} \right)^2} < \left( {7x - 3} \right).$$
PYP
IIT JEE 1978
Sketch the solution set of the following system of inequalities:
$$${x^2} + {y^2} - 2x \ge 0;\,\,3x - y - 12 \le 0;\,\,y - x \le 0;\,\,y \ge 0.$$$
PYP
IIT JEE 1978
Show that the square of $$\,{{\sqrt {26 - 15\sqrt 3 } } \over {5\sqrt 2 - \sqrt {38 + 5\sqrt 3 } }}$$ is a rational number.
PYP
IIT JEE 1978
From a point $$O$$ inside a triangle $$ABC,$$ perpendiculars $$OD$$, $$OE, OF$$ are drawn to the sides $$BC, CA, AB$$ respectively. Prove that the perpendiculars from $$A, B, C$$ to the sides $$EF, FD, DE$$ are concurrent.
PYP
IIT JEE 1978
Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done.
PYP
IIT JEE 1978
If x = a + b, y = a$$\gamma $$ + b$$\beta $$ and z = a$$\beta $$ +b$$\gamma $$ where $$\gamma $$ and $$\beta $$ are the complex cube roots of unity, show that xyz = $${a^3} + {b^3}$$.
PYP
IIT JEE 1978
Solve for $$x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.$$
PYP
IIT JEE 1978
The substance absorbs CO2 and violently reacts with water. The substance is
PYP
IIT JEE 1978
27 g of Al will react completely with how many grams if oxygen?
PYP
IIT JEE 1978
A compound was found to contain nitrogen and oxygen in the ratio 28 gm and 80 gm respectively. The formula of compound is
PYP
IIT JEE 1978
If $$\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - 1}}} \right).......\left( {1 - {x^{m - n + 1}}} \right)} \over {\left( {1 - x} \right)\left( {1 - {x^2}} \right).........\left( {1 - {x^n}} \right)}}$$
where $$m$$ and $$n$$ are positive integers $$\left( {n \le m} \right),$$ show that
$$\left( {m,n + 1} \right) = \left( {m - 1,\,n + 1} \right) + {x^{m - n - 1}}\left( {m - 1,n} \right).$$
PYP
IIT JEE 1978
A car accelerates from rest at a constant rate $$\alpha $$ for some time after which it decelerates at a constant rate $$\beta $$ to come to rest. If the total time lapse is t seconds, evaluate.
(i) maximum velocity reached, and
(ii) the total distance travelled.
PYP
IIT JEE 1978
A horizontal uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by force F. What is the tension in the rope at a distance $$l$$ from the end where the force is applied?
PYP
IIT JEE 1978
One gram of an alloy of aluminium and magnetism when treated with excess of dil. HCl forms magnesium chloride, aluminium chloride and hydrogen. The evolved hydrogen, collected over mercury at $${0^o}C$$ has a volume of 1.20 litres at 0.92 atm. pressure. Calculate the composition of the alloy. [H = 1, Mg = 24, Al = 27]
PYP
IIT JEE 1978
What is the molarity and molality of a 13% solution (by weight) of sulphuric acid with a density of 1.02 g/ml? To what volume should 100 ml of this acid be diluted in order to prepare a 1.5 N solution?
PYP
IIT JEE 1978
Solve the following equation for $$x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0$$
PYP
IIT JEE 1978
Balls are drawn one-by-one without replacement from a box containing $$2$$ black, $$4$$ white and $$3$$ red balls till all the balls are drawn. Find the probability that the balls drawn are in the order $$2$$ black, $$4$$ white and $$3$$ red.
PYP
IIT JEE 1978
Express $${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$$ in the form x + iy.
PYP
IIT JEE 1978
If $$\tan \alpha = {m \over {m + 1}}\,$$ and $$\tan \beta = {2 \over {2m + 1}},$$ find the possible values of $$\left( {\alpha + \beta } \right).$$
PYP
IIT JEE 1978
A triangle $$ABC$$ has sides $$AB=AC=5$$ cm and $$BC=6$$ cm Triangle $$A'B'C'$$ is the reflection of the triangle $$ABC$$ in a line parallel to $$AB$$ placed at a distance $$2$$ cm from $$AB$$, outside the triangle $$ABC$$. Triangle $$A''B''C''$$ is the reflection of the triangle $$A'B'C'$$ in a line parallel to $$BC$$ placed at a distance of $$2$$ cm from $$B'C'$$ outside the triangle $$A'B'C'$$. Find the distance between $$A$$ and $$A''$$.
PYP
IIT JEE 1978
One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find the equations of the other three sides.
PYP
IIT JEE 1978
The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)$$ and $$B\left( {3, - 2} \right)$$. The third vertex $$C$$ lies on $$y = x + 3$$. Find $$C$$.
PYP
IIT JEE 1978
A straight line segment of length $$\ell $$ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $$1 : 2$$
PYP
IIT JEE 1978
Find the equation of the circle whose radius is 5 and which touches the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$ at the point (5, 5).
PYP
IIT JEE 1978
Find the derivative of $$\sin \left( {{x^2} + 1} \right)$$ with respect to $$x$$ first principle.
PYP
IIT JEE 1978
Evaluate $$\int {{{\sin x} \over {\sin x - \cos x}}dx} $$
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