1
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
$${p^3} + q\left( {3p + 1} \right) + {q^2} = 0$$
2
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
$$2 < a < 5$$
3
IIT-JEE 2003 Screening
+2
-0.5
If $$\,\alpha \in \left( {0,{\pi \over 2}} \right)\,\,then\,\,\sqrt {{x^2} + x} + {{{{\tan }^2}\alpha } \over {\sqrt {{x^2} + x} }}$$ is always greater than or equal to
A
$$2\,\tan \alpha \,$$
B
1
C
2
D
$${\sec ^2}\,\alpha$$
4
IIT-JEE 2002 Screening
+2
-0.5
If $${a_1},{a_2}.......,{a_n}$$ are positive real numbers whose product is a fixed number c, then the minimum value of $${a_1} + {a_2} + ..... + {a_{n - 1}} + 2{a_n}$$ is
A
$$n{(2c)^{1/n}}$$
B
$$(n + 1){c^{1/n}}$$
C
$$2n{c^{1/n}}$$
D
$$(n + 1)\,{(2c)^{1/n}}$$
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