1
GATE CSE 2011
+2
-0.6
$$\left[ A \right]$$ is a square matrix which is neither symmetric nor skew-symmetric and $${\left[ A \right]^T}$$ is its transpose. The sum and differences of these matrices and defined as $$\left[ S \right] = \left[ A \right] + {\left[ A \right]^T}$$ and $$\left[ D \right] = \left[ A \right] - {\left[ A \right]^T}$$ respectively. Which of the following statements is true?
A
Both $$\left[ S \right]$$ and $$\left[ D \right]$$ are symmetric
B
Both $$\left[ S \right]$$ and $$\left[ D \right]$$ are skew-symmetric
C
$$\left[ S \right]$$ is skew-symmetric and $$\left[ D \right]$$ is symmetric
D
$$\left[ S \right]$$ is symmetric and $$\left[ D \right]$$ is skew symmetric
2
GATE CSE 2011
+2
-0.6
Consider a finite sequence of random values $$X = \left\{ {{x_1},{x_2},{x_3}, - - - - - {x_n}} \right\}..$$ Let $${\mu _x}$$ be the mean and $${\sigma _x}$$ be the standard deviation of $$X.$$ Let another finite sequence $$Y$$ of equal length be derived from this $${y_i} = a.{x_i} + b,$$ where $$a$$ and $$b$$ are positive constants. Let $${\mu _y}$$ be the mean and $${\sigma _y}$$ be the standard deviation of this sequence. Which one of the following statements is incorrect?
A
Index position of mode of $$X$$ in $$X$$ is the same as the index position of mode of $$Y$$ in $$Y$$.
B
Index position of median of $$X$$ in $$X$$ is the same as the index position of median of $$Y$$ in $$Y.$$
C
$${\mu _y} = a{\mu _x} + b$$
D
$${\sigma _y} = a{\sigma _x} + b$$
3
GATE CSE 2011
+1
-0.3
A Computer handles several interrupt sources of which the following are relevant for this question:

$$* \,\,\,$$ Interrupt from $$CPU$$ temperature sensor (raises interrupt if $$CPU$$ temperature is too high)

$$* \,\,\,$$ Interrupt from Mouse (raises interrupt if the mouse is moved or a button is pressed)

$$* \,\,\,$$ Interrupt from keyboard (raises interrupt when a key is pressed or release)

$$* \,\,\,$$ Interrupt from Hard Disk (raises interrupt when a disk read is completed)>/p>

Which one these will be handled at the HIGHEST priority?

A
Interrupt from Hard Disk
B
Interrupt from Mouse
C
Interrupt from Keyboard
D
Interrupt from $$CPU$$ temperature sensor.
4
GATE CSE 2011
+1
-0.3
Let the time taken to switch between user and kernel modes of execution be $${t_1}$$ while the time taken to switch between two processes be $${t_2}$$.

Which of the following is TRUE?

A
$${t_1} > {t_2}$$
B
$${t_1} = {t_2}$$
C
$${t_1} < {t_2}$$
D
Nothing can be said about the relation between $${t_1}$$ and $${t_2}.$$
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