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1

IIT-JEE 1985

Fill in the Blanks
The set of all real numbers $$a$$ such that $${a^2} + 2a,2a + 3$$ and $${a^2} + 3a + 8$$ are the sides of a triangle is ...........

Answer

$$\left( {5,x} \right)$$
2

IIT-JEE 1980

Fill in the Blanks
In a $$\Delta ABC,\,\angle A = {90^ \circ }$$ and $$AD$$ is an altitude. Complete the relation $${{BD} \over {BA}} = {{AB} \over {\left( {....} \right)}}$$.

Answer

$$B$$ $$C$$
3

IIT-JEE 1980

Fill in the Blanks
$$ABC$$ is a triangle, $$P$$ is a point on $$AB$$, and $$Q$$ is point on $$AC$$ such that $$\angle AQP = \angle ABC$$. Complete the relation $$${{area\,\,of\,\,\Delta APQ} \over {area\,\,of\,\,\Delta ABC}} = {{\left( {...} \right)} \over {A{C^2}}}$$$

Answer

$$A{P^2}$$
4

IIT-JEE 1980

Fill in the Blanks
$$ABC$$ is a triangle with $$\angle B$$ greater than $$\angle C.\,D$$ and $$E$$ are points on $$BC$$ such that $$AD$$ is perpendicular to $$BC$$ and $$AE$$ is the bisector of angle $$A$$. Complete the relation $$$\angle DAE = {1 \over 2}\left[ {\left( {} \right) - \angle C} \right]$$$

Answer

$${\angle B}$$

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