1
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
A
$${5 \over 2}$$
B
$${11 \over 2}$$
C
6
D
$${13 \over 2}$$
2
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let $$f:R \to R$$ be a positive increasing function with

$$\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1$$. Then $$\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} = $$
A
$${2 \over 3}$$
B
$${3 \over 2}$$
C
3
D
1
3
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
The number of complex numbers z such that $$\left| {z - 1} \right| = \left| {z + 1} \right| = \left| {z - i} \right|$$ equals :
A
1
B
2
C
$$\infty $$
D
0
4
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let $$f:R \to R$$ be defined by $$$f\left( x \right) = \left\{ {\matrix{ {k - 2x,\,\,if} & {x \le - 1} \cr {2x + 3,\,\,if} & {x > - 1} \cr } } \right.$$$

If $$f$$has a local minimum at $$x=-1$$, then a possible value of $$k$$ is

A
$$0$$
B
$$ - {1 \over 2}$$
C
$$-1$$
D
$$1$$
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