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1

IIT-JEE 1979

Subjective
If $$\alpha ,\,\beta $$ are the roots of $${x^2} + px + q = 0$$ and $$\gamma ,\,\delta $$ are the roots of $${x^2} + rx + s = 0,$$ evaluate $$\left( {\alpha - \gamma } \right)\left( {\alpha - \delta } \right)\left( {\beta - \gamma } \right)$$ $$\left( {\beta - \delta } \right)$$ in terms of $$p,\,q,\,r$$ and $$s$$.

deduce the condition that the equations have a common root.

Answer

$$q{\left( {r - p} \right)^2} - p\left( {r - p} \right)\left( {s - q} \right) + {\left( {s - q} \right)^2};\,\,{\left( {q - s} \right)^2} = \left( {r - p} \right)\left( {ps - qr} \right)$$
2

IIT-JEE 1978

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

Answer

Solve it.
3

IIT-JEE 1978

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

Answer

3
4

IIT-JEE 1978

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

Answer

Solve it.

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