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Question Bank No: 3

1. If $x \in R$ , the expression $\frac{x^{2} + 2 x - 11}{x - 3}$ does not take values in

a)		$(- \infty, 4)$
b)		$(12, \infty)$
c)		$R - (4, 12)$
d)		$(4, 12)$

2. The range of $f (x) = \frac{x^{2} - 3 x + 2}{x^{2} + x - 6}, x \in R,$ is

a)		R
b)		R $- {1}$
c)		R $- {- 3, 2}$
d)		R $- {- 3, - 2}$

3. If the root of the equation $a x^{2} + bx + c = 0$ is the reciprocal of a root of the equation $a^{'} x^{2} + b^{'} x + c^{'} = 0$ , then

a)		${(a a^{'} - c c^{'})}^{2} = (a b^{'} - b c^{'}) (a^{'} b - b^{'} c)$
b)		${(a a^{'} - b b^{'})}^{2} = (a b^{'} - b c^{'}) (a^{'} b - b^{'} c)$
c)		${(b c^{'} - b^{'} c)}^{2} = (a b^{'} - b c^{'}) (a^{'} b + b^{'} c)$
d)		${(b a^{'} - b^{'} c)}^{2} = (a b^{'} + b c^{'}) (a^{'} b - b^{'} c)$

4. If the roots of the equation $\frac{1}{x + p}$ + $\frac{1}{x + q}$ = $\frac{1}{r}$ are equal in magnitude but opposite in sign, then the product of the roots is

a)		$- 2 (p^{2} + q^{2}$ )
b)		$- (p^{2} + q^{2}$ )
c)		$- \frac{(p^{2} + q^{2})}{2}$
d)		$- pq$

5. If $x \in R$ and b< c, then $\frac{x^{2} - bc}{2 x - b - c}$ has no values

a)		in $(- \infty, b)$
b)		in $(c, \infty)$
c)		between b and c
d)		between $- c$ and $- b$

6. The range of $\frac{x^{2} - x + 1}{x^{2} + x + 1}$ , $x \in R$ is

a)		$(- \frac{1}{3}, 3)$
b)		$[\frac{1}{3}, 3]$
c)		R $- (\frac{1}{3}, 3)$
d)		R $- [\frac{1}{3}, 3]$

7. The range of $\frac{x^{2} - 2 x + 3}{x^{2} - 2 x - 8}$ , $x \in R$ is

a)		R
b)		R $- [- \frac{2}{9}, 1]$
c)		R $- (- \frac{2}{9}, 1]$
d)		$[- \frac{2}{9}, 1]$