1
IIT-JEE 1983
Subjective
+3
-0
The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta $$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.
2
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is $${15^ \circ }$$. The distance of the boat from the foot of the light house is
A
$$\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right)60$$ metres
B
$$\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right)60$$ metres
C
$${\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right)^2}$$ metres
D
none of these
3
IIT-JEE 1983
True or False
+1
-0
The derivative of an even function is always an odd function.
A
TRUE
B
FALSE
4
IIT-JEE 1983
Subjective
+5
-0
Through a fixed point (h, k) secants are drawn to the circle $$\,{x^2}\, + \,{y^2} = \,{r^2}$$. Show that the locus of the mid-points of the secants intercepted by the circle is $$\,{x^2}\, + \,{y^2} $$ = $$hx + ky$$.
JEE Advanced Papers
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