1
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
Statement - 1 : The variance of first n even natural numbers is $${{{n^2} - 1} \over 4}$$

Statement - 2 : The sum of first n natural numbers is $${{n\left( {n + 1} \right)} \over 2}$$ and the sum of squares of first n natural numbers is $${{n\left( {n + 1} \right)\left( {2n + 1} \right)} \over 6}$$
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
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to
A
20.0
B
10.1
C
20.2
D
10.0
3
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
For real x, let f(x) = x3 + 5x + 1, then
A
f is one-one but not onto R
B
f is onto R but not one-one
C
f is one-one and onto R
D
f is neither one-one nor onto R
4
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
Let $$f\left( x \right) = {\left( {x + 1} \right)^2} - 1,x \ge - 1$$

Statement - 1 : The set $$\left\{ {x:f\left( x \right) = {f^{ - 1}}\left( x \right)} \right\} = \left\{ {0, - 1} \right\}$$.

Statement - 2 : $$f$$ is a bijection.
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
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