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1
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
The quadratic equations $${x^2} - 6x + a = 0$$ and $${x^2} - cx + 6 = 0$$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
A
1
B
4
C
3
D
2
2
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
If $$\,\left| {z - {4 \over z}} \right| = 2,$$ then the maximum value of $$\,\left| z \right|$$ is equal to :
A
$$\sqrt 5 + 1$$
B
2
C
$$2 + \sqrt 2 $$
D
$$\sqrt 3 + 1$$
3
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
If the roots of the equation $$b{x^2} + cx + a = 0$$ imaginary, then for all real values of $$x$$, the expression $$3{b^2}{x^2} + 6bcx + 2{c^2}$$ is :
A
less than $$4ab$$
B
greater than $$-4ab$$
C
less than $$-4ab$$
D
greater than $$4ab$$
4
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
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