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1

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.
2

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
3

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.
4

IIT-JEE 1978

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

Answer

$${a^{{\raise0.5ex\hbox{$\scriptstyle { - 1}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}},\,\,{a^{{\raise0.5ex\hbox{$\scriptstyle { - 4}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}}}$$

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