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1
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
STATEMENT - 1 : For every natural number $$n \ge 2,$$ $$${1 \over {\sqrt 1 }} + {1 \over {\sqrt 2 }} + ........ + {1 \over {\sqrt n }} > \sqrt n .$$$

STATEMENT - 2 : For every natural number $$n \ge 2,$$, $$$\sqrt {n\left( {n + 1} \right)} < n + 1.$$$

A
Statement - 1 is false, Statement - 2 is true
B
Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for statement - 1
C
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1
D
Statement - 1 is true, Statement - 2 is false
2
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
If the difference between the roots of the equation $${x^2} + ax + 1 = 0$$ is less than $$\sqrt 5 ,$$ then the set of possible values of $$a$$ is
A
$$\left( {3,\infty } \right)$$
B
$$\left( { - \infty , - 3} \right)$$
C
$$\left( { - 3,3} \right)$$
D
$$\left( { - 3,\infty } \right)$$
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
If the roots of the quadratic equation $${x^2} + px + q = 0$$ are $$\tan {30^ \circ }$$ and $$\tan {15^ \circ }$$, respectively, then the value of $$2 + q - p$$ is
A
2
B
3
C
0
D
1
4
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
All the values of $$m$$ for which both roots of the equation $${x^2} - 2mx + {m^2} - 1 = 0$$ are greater than $$ - 2$$ but less then 4, lie in the interval
A
$$ - 2 < m < 0$$
B
$$m > 3$$
C
$$ - 1 < m < 3$$
D
$$1 < m < 4$$
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