1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a{x^2} + bx + c = 0$$, then

$$\mathop {\lim }\limits_{x \to \alpha } {{1 - \cos \left( {a{x^2} + bx + c} \right)} \over {{{\left( {x - \alpha } \right)}^2}}}$$ is equal to
A
$${{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
B
0
C
$$ - {{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
D
$${{{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let f be differentiable for all x. If f(1) = -2 and f'(x) $$ \ge $$ 2 for
x $$ \in \left[ {1,6} \right]$$, then
A
f(6) $$ \ge $$ 8
B
f(6) < 8
C
f(6) < 5
D
f(6) = 5
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If $$f$$ is a real valued differentiable function satisfying

$$\left| {f\left( x \right) - f\left( y \right)} \right|$$ $$ \le {\left( {x - y} \right)^2}$$, $$x, y$$ $$ \in R$$
and $$f(0)$$ = 0, then $$f(1)$$ equals
A
-1
B
0
C
2
D
1
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately :
A
20.5
B
22.0
C
24.0
D
25.5
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