IIT-JEE 1978

Paper was held on
Tue, Apr 11, 1978 9:00 AM

## Chemistry

27 g of Al will react completely with how many grams if oxygen?

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A compound was found to contain nitrogen and oxygen in the ratio 28 gm and 80 gm respectively. The formula of compound i

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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 Ag

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One gram of an alloy of aluminium and magnetism when treated with excess of dil. HCl forms magnesium chloride, aluminiu

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Igniting MnO2 converts it quantitatively to Mn3O4. A sample of pyrolusite is of the following composition : MnO2 80%, Si

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Naturally occurring boron consists of two isotopes whose atomic weighs are 10.01 and 11.01. The atomic weight of natural

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The substance absorbs CO2 and violently reacts with water. The substance is

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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 v

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## Mathematics

If x = a + b, y = a$$\gamma $$ + b$$\beta $$ and z = a$$\beta $$ +b$$\gamma $$ where $$\gamma $$ and $$\beta $$ are th

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Express $${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$$ in the form x + iy.

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If $$\tan \alpha = {m \over {m + 1}}\,$$ and $$\tan \beta = {2 \over {2m + 1}},$$ find the possible values of $$\left

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If $$\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - 1}}} \right).......\left( {1 - {x^{m - n

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Solve for $$x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - {2^{2x - 1}}$$

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Solve for $$x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.$$

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Solve the following equation for $$x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0$$

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Show that the square of $$\,{{\sqrt {26 - 15\sqrt 3 } } \over {5\sqrt 2 - \sqrt {38 + 5\sqrt 3 } }}$$ is a rational num

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Find all integers $$x$$ for which $$\left( {5x - 1} \right) < {\left( {x + 1} \right)^2} < \left( {7x - 3} \right)

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Sketch the solution set of the following system of inequalities:
$$${x^2} + {y^2} - 2x \ge 0;\,\,3x - y - 12 \le 0;\,\,

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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 ma

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The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)$$ and $$B\left( {3, - 2} \right)$$. The

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A straight line segment of length $$\ell $$ moves with its ends on two mutually perpendicular lines. Find the locus of t

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One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertices are $$(-3, 1)$$ and $$(1, 1).$$ Find

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Find the equation of the circle whose radius is 5 and which touches the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, -

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Find the derivative of $$\sin \left( {{x^2} + 1} \right)$$ with respect to $$x$$ first principle.

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A triangle $$ABC$$ has sides $$AB=AC=5$$ cm and $$BC=6$$ cm Triangle $$A'B'C'$$ is the reflection of the triangle $$ABC$

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Evaluate $$\int {{{\sin x} \over {\sin x - \cos x}}dx} $$

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Balls are drawn one-by-one without replacement from a box containing $$2$$ black, $$4$$ white and $$3$$ red balls till a

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From a point $$O$$ inside a triangle $$ABC,$$ perpendiculars $$OD$$, $$OE, OF$$ are drawn to the sides $$BC, CA, AB$$ re

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## Physics

A car accelerates from rest at a constant rate $$\alpha $$ for some time after which it decelerates at a constant rate $

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A horizontal uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by force F. Wh

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