1
IIT-JEE 1986
Fill in the Blanks
+2
-0
From the point A(0, 3) on the circle $${x^2} + 4x + {(y - 3)^2} = 0$$, a chord AB is drawn and extended to a point M such that AM = 2AB. The equation of the locus of M is..........................
2
IIT-JEE 1986
MCQ (Single Correct Answer)
+2
-0.5
The expression $$2\left[ {{{\sin }^6}\left( {{\pi \over 2} + \alpha } \right) + {{\sin }^6}\left( {5\pi - \alpha } \right)} \right]$$ is equal to
A
0
B
1
C
3
D
$$\sin \,4\,\alpha + \cos \,6\,\alpha \,\,\,\,$$
3
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 $${1 \over 2}\,{\left| z \right|^2}$$ .
4
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
$$\left( {{1 \over 2},\,3} \right)\,\,\,\,$$
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