1
GATE CSE 1993
MCQ (Single Correct Answer)
+1
-0.3
Let $${\rm A}$$ be a finite set of size $$n$$. The number of elements in the power set of $${\rm A} \times {\rm A}$$ is
A
$${2^{{2^n}}}$$
B
$${2^{{n^2}}}$$
C
$${2^n}$$
D
$${n^2}$$
2
GATE CSE 1993
Numerical
+1
-0
If $$A = \left[ {\matrix{ 1 & 0 & 0 & 1 \cr 0 & { - 1} & 0 & { - 1} \cr 0 & 0 & i & i \cr 0 & 0 & 0 & { - i} \cr } } \right]$$ the matrix $${A^4},$$
calculated by the use of Cayley - Hamilton theoram (or) otherwise is
Your input ____
3
GATE CSE 1993
MCQ (More than One Correct Answer)
+1
-0.3
The eigen vector (s) of the matrix
$$\left[ {\matrix{ 0 & 0 & \alpha \cr 0 & 0 & 0 \cr 0 & 0 & 0 \cr } } \right],\alpha \ne 0$$ is (are)
A
$$\left( {0,0,\alpha } \right)$$
B
$$\left( {\alpha ,0,0} \right)$$
C
$$\left( {0,0,1} \right)$$
D
$$\left( {0,\alpha ,0} \right)$$
4
GATE CSE 1993
Fill in the Blanks
+1
-0
The value of the double integral $$\int\limits_0^1 {\int\limits_x^{{1 \over x}} {{x \over {1 + {y^2}}}\,\,dx\,\,dy = \_\_\_\_\_.} } $$
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