1
IIT-JEE 1986
Subjective
+3
-0
Show that the area of the triangle on the Argand diagram formed by the complex numbers z, iz and z + iz is $${1 \over 2}\,{\left| z \right|^2}$$ .
2
IIT-JEE 1986
MCQ (More than One Correct Answer)
+2
-0.5
If $$S$$ is the set of all real $$x$$ such that $${{2x - 1} \over {2{x^3} + 3{x^2} + x}}$$ is positive, then $$S$$ contains
A
$$\left( { - \infty ,\, - {\textstyle{3 \over 2}}} \right)$$
B
$$\left( { - {3 \over 2},\, - {1 \over 4}} \right)$$
C
$$\left( { - {1 \over 4},\,{1 \over 2}} \right)$$
D
$$\left( {{1 \over 2},\,3} \right)\,\,\,\,$$
3
IIT-JEE 1986
MCQ (Single Correct Answer)
+2
-0.5
If $$a,\,b$$ and $$c$$ are distinct positive numbers, then the expression
$$\left( {b + c - a} \right)\left( {c + a - b} \right)\left( {a + b - c} \right) - abc$$ is
A
positive
B
negative
C
non-positive
D
non-negative
4
IIT-JEE 1986
Subjective
+5
-0
For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$
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