1
IIT-JEE 1984
True or False
+1
-0
There exists a value of $$\theta $$ between 0 and $$2\pi $$ that satisfies the equation $$\,\,{\sin ^4}\theta - 2{\sin ^2}\theta - 1 = 0.$$
A
TRUE
B
FALSE
2
IIT-JEE 1984
True or False
+1
-0
If the complex numbers, $${Z_1},{Z_2}$$ and $${Z_3}$$ represent the vertics of an equilateral triangle such that
$$\left| {{Z_1}} \right| = \left| {{Z_2}} \right| = \left| {{Z_3}} \right|$$ then $${Z_1} + {Z_2} + {Z_3} = 0.$$
A
TRUE
B
FALSE
3
IIT-JEE 1984
MCQ (Single Correct Answer)
+3
-0.75
$$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)$$ is equal to
A
$${1 \over 2}$$
B
$$\cos {\pi \over 8}$$
C
$${1 \over 8}$$
D
$${{1 + \sqrt 2 } \over {2\sqrt 2 }}$$
4
IIT-JEE 1984
Subjective
+2
-0
If 1, $${{a_1}}$$, $${{a_2}}$$......,$${a_{n - 1}}$$ are the n roots of unity, then show that (1- $${{a_1}}$$) (1- $${{a_2}}$$) (1- $${{a_3}}$$) ....$$(1 - \,a{ - _{n - 1}}) = n$$
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