1
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
If $$z = x + iy$$ and $$\omega = \left( {1 - iz} \right)/\left( {z - i} \right),$$ then $$\,\left| \omega \right| = 1$$ implies that, in the complex plane,
A
$$z$$ lies on the imaginary axis
B
$$z$$ lies on the real axis
C
$$z$$ lies on the unit circle
D
none of these
2
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)} \right]$$ is
A
$${{6 \over 17}}$$
B
$${{7 \over 16}}$$
C
$${{16 \over 7}}$$
D
none
3
IIT-JEE 1983
Subjective
+2
-0
Show that $$1+x$$ $$In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^2}} $$ for all $$x \ge 0$$
4
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
If $$y = a\,\,In\,x + b{x^2} + x$$ has its extreamum values at $$x=-1$$ and $$x=2$$, then
A
$$a = 2,b = - 1$$
B
$$a = 2,b = - {1 \over 2}$$
C
$$a = - 2,b = {1 \over 2}$$
D
none of these
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