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1

IIT-JEE 1987

Subjective
Find the set of all $$x$$ for which $${{2x} \over {\left( {2{x^2} + 5x + 2} \right)}}\, > \,{1 \over {\left( {x + 1} \right)}}$$

$$\left( { - 2,\, - 1} \right) \cup \left( {{{ - 2} \over 3},\,{{ - 1} \over 2}} \right)$$
2

IIT-JEE 1986

Subjective
For $$a \le 0,$$ determine all real roots of the equation $${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$\$

$$\left\{ {a \pm a\sqrt 2 ,\,\, - a \pm a\sqrt 6 } \right\}$$
3

IIT-JEE 1985

Subjective
Solve for $$x$$ ; $${\left( {5 + 2\sqrt 6 } \right)^{{x^2} - 3}} + {\left( {5 - 2\sqrt 6 } \right)^{{x^2} - 3}} = 10$$

$$\pm 2,\, \pm \sqrt 2$$
4

IIT-JEE 1983

Subjective
Find all real values of $$x$$ which satisfy $${x^2} - 3x + 2 > 0$$ and $${x^2} - 2x - 4 \le 0$$

$$\left[ { - 1,1} \right) \cup \left( {2,4} \right]$$

Joint Entrance Examination

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