1
GATE CSE 2015 Set 2
Numerical
+1
-0
The cardinally of the power set of $$\left\{ {0,1,2,\,\,....,\,\,10} \right.\left. \, \right\}$$ is _____________.
Your input ____
2
GATE CSE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Let $$𝑅$$ be the relation on the set of positive integers such that $$aRb$$ if and only if $$𝑎 $$ and $$𝑏$$ are distinct and have a common divisor other than $$1.$$ Which one of the following statements about $$𝑅$$ is true?
A
$$𝑅$$ is symmetric and reflexive but not transitive
B
$$𝑅$$ is reflexive but not symmetric and not transitive
C
$$𝑅$$ is transitive but not reflexive and not symmetric
D
$$𝑅$$ is symmetric but not reflexive and not transitive
3
GATE CSE 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
For a set A, the power set of A is denoted by 2A. If A = {5, {6}, {7}}, which of the following options are TRUE?

I. $$\phi \in {2^A}$$
II. $$\phi \subseteq {2^A}$$
III. $$\left\{ {5,\left\{ 6 \right\}} \right\} \in {2^A}$$
IV. $$\left\{ {5,\left\{ 6 \right\}} \right\} \subseteq {2^A}$$

A
I and III only
B
II and III only
C
I, II and III only
D
I, II and IV only
4
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 $$Y$$, $${f^{ - 1}}\left( {S \cap T} \right) = {f^{ - 1}}\left( S \right) \cap {f^{ - 1}}\left( T \right)$$
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Graduate Aptitude Test in Engineering
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CBSE
Class 12