1
IIT-JEE 2004 Screening
+2
-0.5
If $$\omega$$ $$\left( { \ne 1} \right)$$ be a cube root of unity and $${\left( {1 + {\omega ^2}} \right)^n} = {\left( {1 + {\omega ^4}} \right)^n},$$ then the least positive value of n is
A
2
B
3
C
5
D
6
2
IIT-JEE 2004 Screening
+2
-0.5
Given both $$\theta$$ and $$\phi$$ are acute angles and $$\sin \,\theta = {1 \over 2},\,$$ $$\cos \,\phi = {1 \over 3},$$ then the value of $$\theta + \phi$$ belongs to
A
$$\left( {{\pi \over 3},\left. {{\pi \over 2}} \right]} \right.$$
B
$$\left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$
C
$$\left( {{{2\pi } \over 3},\left. {{{5\pi } \over 6}} \right]} \right.$$
D
$$\left( {{{5\pi } \over 6},\pi } \right]$$
3
IIT-JEE 2004 Screening
+2
-0.5
If one root is square of the other root of the equation $${x^2} + px + q = 0$$, then the realation between $$p$$ and $$q$$ is
A
$${p^3} - q\left( {3p - 1} \right) + {q^2} = 0$$
B
$${p^3} - q\left( {3p + 1} \right) + {q^2} = 0$$
C
$${p^3} + q\left( {3p - 1} \right) + {q^2} = 0$$
D
$${p^3} + q\left( {3p + 1} \right) + {q^2} = 0$$
4
IIT-JEE 2004 Screening
+2
-0.5
For all $$'x',{x^2} + 2ax + 10 - 3a > 0,$$ then the interval in which '$$a$$' lies is
A
$$a < - 5$$
B
$$- 5 < a < 2$$
C
$$a > 5$$
D
$$2 < a < 5$$
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