EC GATE 2008 - Online Test
Q1. 
In the following transistor circuit, 
, and 𝛽 and all the capacitances are very large
, and 𝛽 and all the capacitances are very largeThe value of DC current IE is
Answer : Option A
Explaination / Solution:
For the given DC values the Thevenin equivalent circuit is as follows
Q2. The impulse response h(t) of linear time - invariant continuous time system is given by h(t) = exp(- 2t)u(t), where u(t) denotes the unit step function.
The output of this system, to the sinusoidal input x(t) = 2 cos 2t for all time t , is
Answer : Option D
Explaination / Solution:
Q3. All the four entries of the 2 × 2 matrix 
are nonzero, and one of its
eigenvalue is zero. Which of the following statements is true?
are nonzero, and one of its
eigenvalue is zero. Which of the following statements is true?
Answer : Option C
Explaination / Solution:
The product of Eigen value is equal to the determinant of the matrix. Since one
of the Eigen value is zero, the product of Eigen value is zero, thus determinant
of the matrix is zero.
Q4. The system of linear equations
4x + 2y = 7
2x + y = 6 has
Answer : Option B
Explaination / Solution:
Q5. The equation sin(z) = 10 has
Answer : Option A
Explaination / Solution:
No Explaination.
Q6. For real values of x , the minimum value of the function
f (x) = exp(x) + exp(- x) is
Answer : Option A
Explaination / Solution:
Q7. Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x = 0 ?
Answer : Option A
Explaination / Solution:
Q8. Which of the following is a solution to the differential equation 
Answer : Option B
Explaination / Solution:
Q9. The probability density function (pdf) of random variable is as shown below
The corresponding commutative distribution function CDF has the form
Answer : Option A
Explaination / Solution:
No Explaination.
Q10. The recursion relation to solve x = e-x using Newton - Raphson method is
Answer : Option C
Explaination / Solution:
