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1

### IIT-JEE 2008

Let $$a,\,b,c$$, $$p,q$$ be real numbers. Suppose $$\alpha ,\,\beta$$ are the roots of the equation $${x^2} + 2px + q = 0$$ and $$\alpha ,{1 \over \beta }$$ are the roots of the equation $$a{x^2} + 2bx + c = 0,$$ where $${\beta ^2} \in \left\{ { - 1,\,0,\,1} \right\}$$

STATEMENT - 1 : $$\left( {{p^2} - q} \right)\left( {{b^2} - ac} \right) \ge 0$$
and STATEMENT - 2 : $$b \ne pa$$ or $$c \ne qa$$

A
STATEMENT - 1 is True, STATEMENT - 2 is True;
STATEMENT - 2 is a correct explanation for
STATEMENT - 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True;
STATEMENT - 2 is NOT a correct explanation for
STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False
D
STATEMENT - 1 is False, STATEMENT - 2 is True
2

### 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
$${2 \over 9}\left( {2p - q} \right)\left( {2q - p} \right)$$
3

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

### 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
$$2 < a < 5$$

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

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NEET

Class 12