Consider the system

**A. **
**B. ** Only p = 0 and q = 0 result in controllability

**C. ** The system is uncontrollable for all values of p and q

**D. ** We cannot conclude about controllability from the given data

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

**Explaination / Solution: **

where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true ?

The system is completely state controllable for any nonzero values of p and q

Since S is singular, system is completely uncontrollable for all values of p and q .

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Consider two independent random variables X and Y with identical distributions. The variables X and Y take values 0, 1 and 2 with probabilities 1/2,1/4 and 1/4 respectively. What is the conditional probability P(X + Y = 2 X - Y = 0) ?

**A. ** 0

**B. ** 1/16

**C. ** 1/6

**D. ** 1

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

**Explaination / Solution: **

We have

We have

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The Taylor series expansion of is given by

**A. **

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

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Given that F(s) is the one-side Laplace transform of f (t), the Laplace transform

**A. **

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

By property of unilateral laplace transform

By property of unilateral laplace transform

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Match each differential equation in Group I to its family of solution curves from Group II

**A. ** A - 2, B - 3,C - 3,D - 1

**B. ** A - 1, B - 3,C - 2,D - 1

**C. ** A - 2, B - 1,C - 3,D - 3

**D. ** A - 3, B - 2,C - 1,D - 2

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

**Explaination / Solution: **

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The Eigen values of following matrix are

**A. ** 3, 3 + 5j, 6 - j

**B. ** -6 + 5j, 3 + j, 3 - j

**C. ** 3 + j, 3 - j, 5 + j

**D. ** 3, - 1 + 3j, - 1 - 3j

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

**Explaination / Solution: **

Sum of the principal diagonal element of matrix is equal to the sum of Eigen values. Sum of the diagonal element is -1 - 1 + 3 = 1.In only option (D), the sum of Eigen values is 1.

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The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence {1,0,2,3} is

**A. ** [0, -2 + 2j , 2, -2 - 2j ]

**B. ** [2, 2 + 2j , 6, 2 - 2j ]

**C. ** [6, 1 - 3j , 2, 1 + 3j ]

**D. ** [6, -1 + 3j , 0, -1 - 3j ]

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

**Explaination / Solution: **

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A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean X as 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true ?

**A. ** Both the student and the teacher are right

**B. ** Both the student and the teacher are wrong

**C. ** The student is wrong but the teacher is right

**D. ** The student is right but the teacher is wrong

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

**Explaination / Solution: **

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