EC GATE 2009 - Online Test
Q1. Consider the system
where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true ?
Answer : Option C
Explaination / Solution:
Since S is singular, system is completely uncontrollable for all values of p and q .
Q2. 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) ?
Answer : Option C
Explaination / Solution:
We have
Q3. The Taylor series expansion of 
is given by
is given by
Answer : Option D
Explaination / Solution:
Q4. Given that F(s) is the one-side Laplace transform of f (t), the Laplace transform 
Answer : Option B
Explaination / Solution:
By property of unilateral laplace transform
Q5. Match each differential equation in Group I to its family of solution curves from Group II
Answer : Option B
Explaination / Solution:
Q6. The Eigen values of following matrix are
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.
Q7. The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence {1,0,2,3} is
Answer : Option D
Explaination / Solution:
Q8. 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 ?
Answer : Option B
Explaination / Solution:
