1
IIT-JEE 1982
Subjective
+3
-0
For any real $$t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t}}} \over 2}$$ is a point on the
hyperbola $${x^2} - {y^2} = 1$$. Show that the area bounded by this hyperbola and the lines joining its centre to the points corresponding to $${t_1}$$ and $$-{t_1}$$ is $${t_1}$$.
2
IIT-JEE 1981
Subjective
+4
-0
Find the area bounded by the curve $${x^2} = 4y$$ and the straight
3
IIT-JEE 1981
Subjective
+2
-0
Show that : $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + .... + {1 \over {6n}}} \right) = \log 6$$
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