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1

### IIT-JEE 2007

Let $$\alpha ,\,\beta$$ be the roots of the equation $${x^2} - px + r = 0$$ and $${\alpha \over 2},\,2\beta$$ be the roots of the equation $${x^2} - qx + r = 0$$. Then the value of $$r$$
A
$${2 \over 9}\left( {p - q} \right)\left( {2q - p} \right)$$
B
$${2 \over 9}\left( {q - p} \right)\left( {2p - q} \right)$$
C
$${2 \over 9}\left( {q - 2p} \right)\left( {2q - p} \right)$$
D
$${2 \over 9}\left( {2p - q} \right)\left( {2q - p} \right)$$
2

### IIT-JEE 2006

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
$$\lambda \in \left( {{4 \over 3},\,{5 \over 3}} \right)$$
3

### IIT-JEE 2004 Screening

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
$$2 < a < 5$$
4

### IIT-JEE 2004 Screening

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
$${p^3} + q\left( {3p + 1} \right) + {q^2} = 0$$

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