1
IIT-JEE 1983
Subjective
+2
-0
Show that $$$16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \over {15}}} \right)\cos \left( {{{8\pi } \over {15}}} \right)\cos \left( {{{16\pi } \over {15}}} \right) = 1$$$
2
IIT-JEE 1983
Subjective
+2
-0
If one root of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the $$n$$-th power of the other, then show that $$${\left( {a{c^n}} \right)^{{1 \over {n + 1}}}} + {\left( {{a^n}c} \right)^{{1 \over {n + 1}}}} + b = 0$$$
3
IIT-JEE 1983
Subjective
+2
-0
Find all real values of $$x$$ which satisfy $${x^2} - 3x + 2 > 0$$ and $${x^2} - 2x - 4 \le 0$$
4
IIT-JEE 1983
True or False
+1
-0
The equation $$2{x^2} + 3x + 1 = 0$$ has an irrational root.
A
TRUE
B
FALSE
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