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1

IIT-JEE 1988

Subjective
Solve $$\left| {{x^2} + 4x + 3} \right| + 2x + 5 = 0$$

Answer

$$ - 4,\,\left( { - 1\, - \sqrt 3 } \right)$$
2

IIT-JEE 1987

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

Answer

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

IIT-JEE 1986

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

Answer

$$\left\{ {a \pm a\sqrt 2 ,\,\, - a \pm a\sqrt 6 } \right\}$$
4

IIT-JEE 1985

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

Answer

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

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