GATE IN 2013 | GATE IN Year Wise Previous Years Questions

GATE IN 2013

MCQ (Single Correct Answer)

-0.3

The dimension of the null space of the matrix $$\left[ {\matrix{ 0 & 1 & 1 \cr 1 & { - 1} & 0 \cr { - 1} & 0 & { - 1} \cr } } \right]$$ is

$$0$$

$$1$$

$$2$$

$$3$$

GATE IN 2013

MCQ (Single Correct Answer)

-0.6

One pair of eigenvectors corresponding to the two eigen values of the matrix $$\left[ {\matrix{ 0 & { - 1} \cr 1 & {0 - } \cr } } \right]$$

$$\left[ {\matrix{ 1 \cr { - j} \cr } } \right],\left[ {\matrix{ j \cr { - 1} \cr } } \right]$$

$$\left[ {\matrix{ 0 \cr 1 \cr } } \right],\left[ {\matrix{ { - 1} \cr 0 \cr } } \right]$$

$$\left[ {\matrix{ 1 \cr j \cr } } \right],\left[ {\matrix{ 0 \cr 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 \cr j \cr } } \right],\left[ {\matrix{ j \cr 1 \cr } } \right]$$

GATE IN 2013

MCQ (Single Correct Answer)

-0.3

For a vector $$E,$$ which one of the following statements is NOT TRUE?

If $$\nabla .E = 0,E$$ is called

If $$\nabla \times E = 0,$$ $$E$$ is called conservative

If $$\nabla \times E = 0,$$ $$E$$ is called irrotational

If $$\nabla .E = 0,E$$ is called irrotational

GATE IN 2013

MCQ (Single Correct Answer)

-0.3

A continuous random variable $$X$$ has a probability density function $$f\left( x \right) = {e^{ - x}},0 < x < \infty .$$ Then $$P\left\{ {X > 1} \right\}$$ is

$$0.368$$

$$0.5$$

$$0.632$$

$$1.0$$

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