1
IIT-JEE 1995
MCQ (Single Correct Answer)
+2
-0.5
The minimum value of the expression $$\sin \,\alpha + \sin \,\beta \, + \sin \,\gamma ,\,$$ where $$\alpha ,\,\beta ,\,\gamma $$ are real numbers satisfying $$\alpha + \beta + \gamma = \pi $$ is
A
positive
B
zero
C
negative
D
-3
2
IIT-JEE 1995
Subjective
+5
-0
If $$i{z^3} + {z^2} - z + i = 0$$ , then show that $$\left| z \right| = 1$$.
3
IIT-JEE 1995
Subjective
+5
-0
If $$\left| {Z - W} \right| \le 1,\left| W \right| \le 1$$, show that $${\left| {Z - W} \right|^2} \le {(\left| Z \right| - \left| W \right|)^2} + {(ArgZ - Arg\,W)^2}$$
4
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 $$x\, \in \,\left[ {0,2\pi } \right]$$.
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