1
IIT-JEE 1984
Subjective
+4
-0
With usual notation, if in a triangle $$ABC$$;
$${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$ then prove that $${{\cos A} \over 7} = {{\cos B} \over {19}} = {{\cos C} \over {25}}$$.
2
IIT-JEE 1984
Fill in the Blanks
+2
-0
The numerical value of $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 5}} \right) - {\pi \over 4}} \right\}$$ is equal to __________
3
IIT-JEE 1984
True or False
+1
-0
For $$0 < a < x,$$ the minimum value of the function $$lo{g_a}x + {\log _x}a$$ is $$2$$.
A
TRUE
B
FALSE
4
IIT-JEE 1984
Subjective
+2
-0
Evaluate the following $$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} $$
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