1
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
2
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
If $$\,\left| {z - {4 \over z}} \right| = 2,$$ then the maximum value of $$\,\left| z \right|$$ is equal to :
A
$$\sqrt 5 + 1$$
B
2
C
$$2 + \sqrt 2 $$
D
$$\sqrt 3 + 1$$
3
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
Let $$y$$ be an implicit function of $$x$$ defined by $${x^{2x}} - 2{x^x}\cot \,y - 1 = 0$$. Then $$y'(1)$$ equals
A
$$1$$
B
$$\log \,2$$
C
$$-\log \,2$$
D
$$-1$$
4
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
One ticket is selected at random from $$50$$ tickets numbered $$00, 01, 02, ...., 49.$$ Then the probability that the sum of the digits on the selected ticket is $$8$$, given that the product of these digits is zer, equals :
A
$${1 \over 7}$$
B
$${5 \over 14}$$
C
$${1 \over 50}$$
D
$${1 \over 14}$$
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