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IIT-JEE 1978

Exam Held on Tue Apr 11 1978 09:00:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

27 g of Al will react completely with how many grams if oxygen?
A compound was found to contain nitrogen and oxygen in the ratio 28 gm and 80 gm...
What weight of AgCl will be precipitated when a solution containing 4.77 g of Na...
One gram of an alloy of aluminium and magnetism when treated with excess of dil...
Igniting MnO<sub>2</sub> converts it quantitatively to Mn<sub>3</sub>O<sub>4</su...
Naturally occurring boron consists of two isotopes whose atomic weighs are 10.01...
The substance absorbs CO<sub>2</sub> and violently reacts with water. The substa...
What is the molarity and molality of a 13% solution (by weight) of sulphuric aci...

Mathematics

If x = a + b, y = a$$\gamma $$ + b$$\beta $$ and z = a$$\beta $$ +b$$\gamma $$ ...
Express $${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$$ in the form x + iy.
If $$\tan \alpha = {m \over {m + 1}}\,$$ and $$\tan \beta = {2 \over {2m + 1}}...
If $$\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - ...
Solve for $$x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - ...
Solve for $$x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.$$
Solve the following equation for $$x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\...
Show that the square of $$\,{{\sqrt {26 - 15\sqrt 3 } } \over {5\sqrt 2 - \sqrt...
Find all integers $$x$$ for which $$\left( {5x - 1} \right) &lt; {\left( {x + 1}...
Sketch the solution set of the following system of inequalities: $$${x^2} + {y^...
Six X' s have to be placed in the squares of figure below in such a way that eac...
A straight line segment of length $$\ell $$ moves with its ends on two mutually ...
The area of a triangle is $$5$$. Two of its vertices are $$A\left( {2,1} \right)...
One side of rectangle lies along the line $$4x + 7y + 5 = 0.$$ Two of its vertic...
Find the equation of the circle whose radius is 5 and which touches the circle $...
Find the derivative of $$\sin \left( {{x^2} + 1} \right)$$ with respect to $$x$$...
A triangle $$ABC$$ has sides $$AB=AC=5$$ cm and $$BC=6$$ cm Triangle $$A'B'C'$$ ...
Evaluate $$\int {{{\sin x} \over {\sin x - \cos x}}dx} $$
Balls are drawn one-by-one without replacement from a box containing $$2$$ black...
From a point $$O$$ inside a triangle $$ABC,$$ perpendiculars $$OD$$, $$OE, OF$$ ...

Physics

A car accelerates from rest at a constant rate $$\alpha $$ for some time after w...
A horizontal uniform rope of length L, resting on a frictionless horizontal surf...

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