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1

IIT-JEE 2006

MCQ (Single Correct Answer)
Let $$a,\,b,\,c$$ be the sides of triangle where $$a \ne b \ne c$$ and $$\lambda \in R$$.
If the roots of the equation $${x^2} + 2\left( {a + b + c} \right)x + 3\lambda \left( {ab + bc + ca} \right) = 0$$ are real, then
A
$$\lambda < {4 \over 3}$$
B
$$\lambda > {5 \over 3}$$
C
$$\lambda \in \left( {{1 \over 3},\,{5 \over 3}} \right)$$
D
$$\lambda \in \left( {{4 \over 3},\,{5 \over 3}} \right)$$
2

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
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 2004 Screening

MCQ (Single Correct Answer)
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
$${p^3} + q\left( {3p + 1} \right) + {q^2} = 0$$
4

IIT-JEE 2003 Screening

MCQ (Single Correct Answer)
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
$${\sec ^2}\,\alpha $$

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