1
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Consider the function, $$f\left( x \right) = \left| {x - 2} \right| + \left| {x - 5} \right|,x \in R$$

Statement - 1 : $$f'\left( 4 \right) = 0$$

Statement - 2 : $$f$$ is continuous in [2, 5], differentiable in (2, 5) and $$f$$(2) = $$f$$(5)
A
Statement - 1 is false, statement - 2 is true
B
Statement - 1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1
C
Statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1
D
Statement - 1 is true, statement - 2 is false
2
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Let $$a,b \in R$$ be such that the function $$f$$ given by $$f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \ne 0$$ has extreme values at $$x=-1$$ and $$x=2$$

Statement-1 : $$f$$ has local maximum at $$x=-1$$ and at $$x=2$$.

Statement-2 : $$a = {1 \over 2}$$ and $$b = {-1 \over 4}$$

A
Statement - 1 is false, Statement - 2 is true.
B
Statement - 1 is true , Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.
C
Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.
D
Statement - 1 is true, Statement - 2 is false.
3
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow a $$ and $$\overrightarrow b $$ be two unit vectors. If the vectors $$\,\overrightarrow c = \widehat a + 2\widehat b$$ and $$\overrightarrow d = 5\widehat a - 4\widehat b$$ are perpendicular to each other, then the angle between $$\overrightarrow a $$ and $$\overrightarrow b $$ is :
A
$${\pi \over 6}$$
B
$${\pi \over 2}$$
C
$${\pi \over 3}$$
D
$${\pi \over 4}$$
4
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Three numbers are chosen at random without replacement from $$\left\{ {1,2,3,..8} \right\}.$$ The probability that their minimum is $$3,$$ given that their maximum is $$6,$$ is :
A
$${3 \over 8}$$
B
$${1 \over 5}$$
C
$${1 \over 4}$$
D
$${2 \over 5}$$
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