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277.

The linear operation L(x) is defined by the cross product L(x) = b × x , where b= [0 1 0]^T and x= [x1 x2 x3]^T are three dimensional vectors. The 3 x 3 matrix M of this operation satisfies

[2 marks]
Then the Eigen values of M are [2 marks]
(A) 0, + 1, -1
(B) 1, -1, 1
(C) i, -i, 1
(D) i, -i, 0

asked in Electrical Engineering, 2007

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278.

Let x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product. Then the determinant

[2 marks]
(A) is zero when x and y are linearly independent
(B) is positive when x and y are linearly independent
(C) is non-zero for all non-zero x and y
(D) is zero only when either x or y is zero

asked in Electrical Engineering, 2007

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279.

A loaded dice has following probability distribution of occurrences

Dice value
1
2
3
4
5
6

Probability
1/4 1/8
1/8
1/8
1/8
1/4

If three identical dice as the above are thrown, the probability of occurrence of value 1,5 and 6 on the three dice is [2 marks]
(A) same as that of occurrence of 3,4,5
(B) same as that of occurrence of 1,2.5
(C) 1/128
(D) 5/8

asked in Electrical Engineering, 2007

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280.

X(z) = 1-3z^-1, Y(z)= 1+2z^-2 are Z – transforms of two signals x[n], y[n] respectively. A linear time invariant system has the impulse response h[n] defined by these two signals as h[n] = x[n-1]* y[n] where * denotes discrete time convolution. Then the output of the system for the input δ[n-1]
[2 marks]
(A) has Z-transform z^-1 X(z) Y(z)
(B) equals δ [n-2] -3δ[n-3] + 2δ[n-4] - 6δ [n-5]
(C) has Z-transform 1-3z^-1 + 2z^-2 – 6z^-3
(D) does not satisfy any of the above three.

asked in Electrical Engineering, 2007

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281.

If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t) * r(t) their convolution, then the function u (t+1) * r(t-2) is given by
[2 marks]
(A) (1/2) (t-1) (t-2)
(B) (1/2) (t-1) (t-2)
(C) (1/2) (t-1)² u(t-1)
(D) none of these

asked in Electrical Engineering, 2007

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282.

The state equation for the current I₁ shown in the network shown below in terms of the voltage V_x and the independent source V, is given by

[2 marks]
(A) dI₁/dt = -1.4V_x -3.75 I₁ + 5V/4
(B) dI₁/dt = -1.4V_x -3.75 I₁ - 5V/4
(C) dI₁/dt = -1.4V_x +3.75 I₁ + 5V/4
(D) dI₁/dt = -1.4V_x +3.75 I₁ - 5V/4

asked in Electrical Engineering, 2007

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