1
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+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
$${\sec ^2}\,\alpha $$
2
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+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
$$(n + 1)\,{(2c)^{1/n}}$$
3
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+2
-0.5
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
$$(\sqrt 2 ,\infty )$$
4
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
If b > a, then the equation (x - a) (x - b) - 1 = 0 has
A
both roots in (a, b)
B
both roots in (- $$\infty $$, a)
C
both roots in (b, + $$\infty $$)
D
one root in (- $$\infty $$, a) and the other in (b, + $$\infty $$)
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