1
IIT-JEE 1981
Fill in the Blanks
+2
-0
Let $$a, b, c$$ be positive real numbers Let
$$\theta = {\tan ^{ - 1}}\sqrt {{{a\left( {a + b + c} \right)} \over {bc}}} + {\tan ^{ - 1}}\sqrt {{{b\left( {a + b + c} \right)} \over {ca}}} $$ $$ + {\,\,\tan ^{ - 1}}\sqrt {{{c\left( {a + b + c} \right)} \over {ab}}} $$

Then $$\tan \theta = $$ ____________

2
IIT-JEE 1981
Subjective
+2
-0
Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right)$$ at $$x = {1 \over 5}$$, where
$$0 \le {\cos ^{ - 1}}x \le \pi $$ and $$ - \pi /2 \le {\sin ^{ - 1}}x \le \pi /2$$.
3
IIT-JEE 1981
Subjective
+4
-0
Use the function $$f\left( x \right) = {x^{1/x}},x > 0$$. to determine the bigger of the two numbers $${e^\pi }$$ and $${\pi ^e}$$
4
IIT-JEE 1981
Subjective
+2
-0
Let $$x$$ and $$y$$ be two real variables such that $$x>0$$ and $$xy=1$$. Find the minimum value of $$x+y$$.
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