1
IIT-JEE 1995
MCQ (Single Correct Answer)
+2
-0.5
The orthocentre of the triangle formed by the lines $$xy=0$$ and $$x+y=1$$ is
A
$$\left( {{1 \over 2},\,{1 \over 2}} \right)$$
B
$$\left( {{1 \over 3},\,{1 \over 3}} \right)$$
C
$$\left( {0,\,0} \right)$$
D
$$\left( {{1 \over 4},\,{1 \over 4}} \right)$$
2
IIT-JEE 1995
Subjective
+5
-0
Let $$a,\,b,\,c$$ be real. If $$a{x^2} + bx + c = 0$$ has two real roots $$\alpha $$ and $$\beta ,$$ where $$\alpha < - 1$$ and $$\beta > 1,$$ then show that $$1 + {c \over a} + \left| {{b \over a}} \right| < 0.$$
3
IIT-JEE 1995
Subjective
+5
-0
Find the smallest positive number $$p$$ for which the equation $$\cos \left( {p\,\sin x} \right) = \sin \left( {p\cos x} \right)$$ has a solution $$x\, \in \,\left[ {0,2\pi } \right]$$.
4
IIT-JEE 1995
Subjective
+5
-0
If $$\left| {Z - W} \right| \le 1,\left| W \right| \le 1$$, show that $${\left| {Z - W} \right|^2} \le {(\left| Z \right| - \left| W \right|)^2} + {(ArgZ - Arg\,W)^2}$$
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