The ROC of z -transform of the discrete time sequence

**A. ** 1/3< |Z| < 1/2

**B. ** |Z| > 1/2
**C. ** |Z| < 1/2
**D. ** 2<|Z| < 3

**Answer : ****Option A**

**Explaination / Solution: **

Taking z transform we have

Taking z transform we have

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Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y - z plane and parallel to the y axis. The other wire is in the x - y plane and parallel to the x - axis. Which components of the resultingmagnetic field are non-zero at the origin ?

**A. ** x,y,z components

**B. ** x,y components

**C. ** y, z components

**D. ** x,z components

**Answer : ****Option D**

**Explaination / Solution: **

Due to 1 A current wire in x - y plane, magnetic field be at origin will be in x direction.

Due to 1 A current wire in y - z plane, magnetic field be at origin will be in z direction.

Thus x and z component is non-zero at origin.

Due to 1 A current wire in x - y plane, magnetic field be at origin will be in x direction.

Due to 1 A current wire in y - z plane, magnetic field be at origin will be in z direction.

Thus x and z component is non-zero at origin.

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If a vector field is related to another vector field through which of the following is true? (Note : C and SC refer to any closed contour and any surface whose boundary is C . )

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option B**

**Explaination / Solution: **

Hence (B) is correct option.

Hence (B) is correct option.

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A magnetic field in air is measured to be What current distribution leads to this field ?

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option C**

**Explaination / Solution: **

[Hint : The algebra is trivial in cylindrical coordinates.]

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In the interconnection of ideal sources shown in the figure, it is known that the 60 V source is absorbing power.

Which of the following can be the value of the current source I ?

Circuit is as shown below

Since 60 V source is absorbing power. So, in 60 V source current flows from + to - ve direction So,

I + I1 = 12

I = 12 - I1

I is always less then 12 A So, only option (A) satisfies this conditions.

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If the transfer function of the following network is

**A. ** R/4

**B. ** R/2

**C. ** R

**D. ** 2R

**Answer : ****Option C**

**Explaination / Solution: **

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The built-in potential of the junction

**A. ** is 0.70 V

**B. ** is 0.76 V

**C. ** is 0.82 V

**D. ** Cannot be estimated from the data given

**Answer : ****Option B**

**Explaination / Solution: **

We know that

We know that

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The order of the differential equation

**A. ** 1

**B. ** 2

**C. ** 3

**D. ** 4

**Answer : ****Option B**

**Explaination / Solution: **

The highest derivative terms present in DE is of 2nd order.

The highest derivative terms present in DE is of 2nd order.

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A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield heads?

**A. **
**B. **
**C. **
**D. **
**Answer : ****Option C**

**Explaination / Solution: **

Number of elements in sample space is 2^{10} Only one element "H,H,T,T,T,T,T,T,T,T, is event. Thus probability is 1/2^{10}

(1/2)^{2}

^{10 }C_{2}(1/2)

(1/2)^{10}

^{10 }C_{2}(1/2)^{10}

Number of elements in sample space is 2

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We have

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