1
GATE CSE 2014 Set 3
Numerical
+2
-0
Let S be a sample space and two mutually exclusive events A and B be such that $$A\, \cup \,B = \,S$$. If P(.) denotes the probability of the event, the maximum value of P(A) P(B) is ________________.
2
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The CORRECT formula for the sentence, "not all rainy days are cold" is
A
$$\forall d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$
B
$$\forall d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$
C
$$\exists d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$
D
$$\exists d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$
3
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Let $$X$$ and $$Y$$ be finite sets and $$f:X \to Y$$ be a function. Which one of the following statements is TRUE?
A
For any subsets $$A$$ and $$B$$ of $$X$$, $$\left| {f\left( {A \cup B} \right)} \right| = \left| {f\left( A \right)} \right| + \left| {f\left( B \right)} \right|$$
B
For any subsets $$A$$ and $$B$$ of $$X$$, $${f\left( {A \cap B} \right)}$$ $$=$$ $$f\left( A \right) \cap f\left( B \right)$$
C
For any subsets $$\left| {f\left( {A \cap B} \right)} \right| = \min \left\{ {\left| {f\left( A \right)} \right|,\left| {f\left( B \right)} \right|} \right\}$$
D
for any subsets $$S$$ and $$T$$ of $$Y$$, $${f^{ - 1}}\left( {S \cap T} \right) = {f^{ - 1}}\left( S \right) \cap {f^{ - 1}}\left( T \right)$$
4
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Which one of the following statements is TRUE about every $$n\,\, \times \,n$$ matrix with only real eigen values?
A
If the trace of the matrix is positive and the determinant of the negative, at least one of its eigen values is negative.
B
If the trace of the matrix is positive, all its eigen values are positive.
C
If the determinanant of the matrix is positive, all its eigen values are positive.
D
If the product of the trace and determination of the matrix is positive, all its eigen values are positive.
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