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1

GATE CSE 2015 Set 2

Numerical
Perform the following operations on the matrix $$\left[ {\matrix{ 3 & 4 & {45} \cr 7 & 9 & {105} \cr {13} & 2 & {195} \cr } } \right]$$
(i) Add the third row to the second row
(ii) Subtract the third column from the first column.

The determinant of the resultant matrix is _________.

Your Input ________

Answer

Correct Answer is 0
2

GATE CSE 2015 Set 2

Numerical
The larger of the two eigenvalues of the matrix $$\left[ {\matrix{ 4 & 5 \cr 2 & 1 \cr } } \right]$$ is ______.
Your Input ________

Answer

Correct Answer is 6
3

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)
Let $$\,\,f\left( x \right) = {x^{ - \left( {1/3} \right)}}\,\,$$ and $${\rm A}$$ denote the area of the region bounded by $$f(x)$$ and the $$X-$$axis, when $$x$$ varies from $$-1$$ to $$1.$$ Which of the following statements is/are TRUE?
$${\rm I}.$$ $$f$$ is continuous in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}.$$ $$f$$ is not bounded in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}{\rm I}.$$ $${\rm A}$$ is nonzero and finite
A
$${\rm I}$$$${\rm I}$$ only
B
$${\rm I}$$$${\rm I}$$$${\rm I}$$ only
C
$${\rm I}$$$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ only
D
$${\rm I}$$, $${\rm I}$$$${\rm I}$$, and $${\rm I}$$$${\rm I}$$$${\rm I}$$
4

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)
Consider the following two statements.

$$S1:$$ If a candidate is known to be corrupt, then he will not be elected
$$S2:$$ If a candidate is kind, he will be elected

Which one of the following statements follows from $$S1$$ and $$S2$$ as per sound inference rules of logic?

A
If a person is known to be corrupt, he is kind
B
If a person is not known to be corrupt, he is not kind
C
If a person is kind, he is not known to be corrupt
D
If a person is not kind, he is not known to be corrupt

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