1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Consider the following statements
P : Suman is brilliant
Q : Suman is rich
R : Suman is honest
The negation of the statement,

“Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as :
A
$$ \sim \left[ {Q \leftrightarrow \left( {P \wedge \sim R} \right)} \right]$$
B
$$ \sim Q \leftrightarrow P \wedge R$$
C
$$ \sim \left( {P \wedge \sim R} \right) \leftrightarrow Q$$
D
$$ \sim P \wedge \left( {Q \leftrightarrow \sim R} \right)$$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals
A
4
B
5
C
2
D
3
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $R$ be the set of real numbers.

Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$.

Statement II : $ B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $R$.
A
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
B
Statement I is true, Statement II is false.
C
Statement I is false, Statement II is true.
D
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three non-zero vectors which are pairwise non-collinear. If $\overrightarrow a+3 \overrightarrow b$ is collinear with $\overrightarrow c$ and $\overrightarrow b+2 \overrightarrow c$ is collinear with $\overrightarrow a$, then $\overrightarrow a+\overrightarrow b+6 \overrightarrow c$ is :
A
$\overrightarrow a+\overrightarrow c$
B
$\overrightarrow c$
C
$\overrightarrow a$
D
$\overrightarrow 0$
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