1
IIT-JEE 1979
Subjective
+5
-0
(a) If a circle is inscribed in a right angled triangle $$ABC$$ with the right angle at $$B$$, show that the diameter of the circle is equal to $$AB+BC-AC$$.

(b) If a triangle is inscribed in a circle, then the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the third side from the opposite vertex. Prove the above statement.

2
IIT-JEE 1979
Subjective
+2
-0
Prove that the minimum value of $${{\left( {a + x} \right)\left( {b + x} \right)} \over {\left( {c + x} \right)}},$$
$$a,b > c,x > - c$$ is $${\left( {\sqrt {a - c} + \sqrt {b - c} } \right)^2}$$.
3
IIT-JEE 1979
Subjective
+3
-0
Evaluate $$\int {{{{x^2}dx} \over {{{\left( {a + bx} \right)}^2}}}} $$
4
IIT-JEE 1979
MCQ (Single Correct Answer)
+1
-0.25
Two fair dice are tossed. Let $$x$$ be the event that the first die shows an even number and $$y$$ be the event that the second die shows an odd number. The two events $$x$$ and $$y$$ are:
A
Mutually exclusive
B
Independent and mutually exclusive
C
Dependent
D
None of these.
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