GATE CSE 2014 Set 3 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

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Let $$X$$ and $$Y$$ be finite sets and $$f:X \to Y$$ be a function. Which one of the following statements is TRUE?

For any subsets $$A$$ and $$B$$ of $$X$$, $$\left| {f\left( {A \cup B} \right)} \right| = \left| {f\left( A \right)} \right| + \left| {f\left( B \right)} \right|$$

For any subsets $$A$$ and $$B$$ of $$X$$, $${f\left( {A \cap B} \right)}$$ $$=$$ $$f\left( A \right) \cap f\left( B \right)$$

For any subsets $$\left| {f\left( {A \cap B} \right)} \right| = \min \left\{ {\left| {f\left( A \right)} \right|,\left| {f\left( B \right)} \right|} \right\}$$

for any subsets $$S$$ and $$T$$ of $$Y$$, $${f^{ - 1}}\left( {S \cap T} \right) = {f^{ - 1}}\left( S \right) \cap {f^{ - 1}}\left( T \right)$$

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

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Which one of the following statements is TRUE about every $$n\,\, \times \,n$$ matrix with only real eigen values?

If the trace of the matrix is positive and the determinant of the negative, at least one of its eigen values is negative.

If the trace of the matrix is positive, all its eigen values are positive.

If the determinanant of the matrix is positive, all its eigen values are positive.

If the product of the trace and determination of the matrix is positive, all its eigen values are positive.

GATE CSE 2014 Set 3

Numerical

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If $${V_1}$$ and $${V_2}$$ are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of $${V_1}\, \cap \,\,{V_2}$$ is _________________.

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GATE CSE 2014 Set 3

Numerical

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If $$\int_0^{2\pi } {\left| {x\sin x} \right|dx = k\pi ,} $$ then the values of $$k$$ is equal to _________ .

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