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1

### IIT-JEE 2003 Screening

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
$${\sec ^2}\,\alpha$$
2

### IIT-JEE 2002 Screening

The set of all real numbers x for which $${x^2} - \left| {x + 2} \right| + x > 0$$, is
A
$$( - \infty ,\, - 2) \cup (2,\infty )$$
B
$$( - \infty ,\, - \sqrt 2 ) \cup (\sqrt 2 ,\infty )$$
C
$$( - \infty ,\, - 1) \cup (1,\infty )$$
D
$$(\sqrt 2 ,\infty )$$
3

### IIT-JEE 2002 Screening

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
$$(n + 1)\,{(2c)^{1/n}}$$
4

### IIT-JEE 2000 Screening

For the equation $$3{x^2} + px + 3 = 0$$. p > 0, if one of the root is square of the other, then p is equal to
A
1/3
B
1
C
3
D
2/3

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