61
If x1 (t) = 2sinπt + cos4πt and x2 (t) = 2sin5πt + 3sin13πt, then
A)
x1 and x2 both are periodic
B)
x1 and x2 both are not periodic
C)
x1 is periodic, but x2 is not periodic
D)
x1 is not periodic, but x2 is periodic
Answer & Solution
Answer: Option
A
62
A data sequence x[n] = {1, 2, 3, 4, 5} passes through a linear time-invariant system with impulse response h[n] = {5, 4, 3, 2, 1}. The output of the filter will be
A)
{6, 6, 6, 6, 6}
B)
{5, 8, 9, 8, 5}
C)
{5, 14, 26, 40, 55, 40, 26, 14, 5}
D)
{1, 4, 10, 20, 35, 44, 46, 40, 25}
Answer & Solution
Answer: Option
C
63
For a random variable 'x' having the probability density function (PDF) as shown in the above figure, what are the values of the mean and the variance, respectively?
A)
$$\frac{1}{2}$$ and $$\frac{2}{3}$$
B)
1 and $$\frac{4}{3}$$
C)
1 and $$\frac{2}{3}$$
D)
2 and $$\frac{4}{3}$$
Answer & Solution
Answer: Option
B
64
If the impulse response of a discrete-time system is h[n] = -5n u[-n - 1], then the system function H(z) is equal to
A)
$$\frac{{ - z}}{{z - 5}}$$ and the system is stable
B)
$$\frac{z}{{z - 5}}$$ and the system is stable
C)
$$\frac{{ - z}}{{z - 5}}$$ and the system is unstable
D)
$$\frac{z}{{z - 5}}$$ and the system is unstable
Answer & Solution
Answer: Option
B
65
For distortion less transmission through LTI system phase of H(ω) is
A)
Constant
B)
One
C)
Zero
D)
Linearly dependent on ω
Answer & Solution
Answer: Option
D
66
The autocorrelation of wide-sense random process is given by e-2|τ| . The peak value of the spectral density is
A)
2
B)
1
C)
$${{\text{e}}^{\frac{1}{2}}}$$
D)
e
Answer & Solution
Answer: Option
B
67
If the cumulative distribution function is Fx (x) then the probability density function fx (x) is given as
A)
$$\int {{F_x}\left( x \right)dx} $$
B)
$$\int {\frac{d}{{dx}}{F_x}\left( x \right)} $$
C)
$$\int {{F_x}\left( { - x} \right)dx} $$
D)
$$\frac{d}{{dx}}{F_x}\left( { - x} \right)$$
Answer & Solution
Answer: Option
B
68
The fundamental period T of a periodic-continuous time signal x(t), is
A)
the smallest positive constant satisfying the relation x(t) = x(t + mT) for every t and any integer m
B)
the positive constant satisfying the relation x(t) = x(t + mT) for every t and any integer m
C)
the largest positive constant satisfying the relation x(t) = x(t + mT) for any t and any integer m
D)
the smallest positive integer satisfying the relation x(t) = x(t + mT) for any t and any m
Answer & Solution
Answer: Option
A
69
The periodic signal x(t) = 5cos(ω0 t + 30°), signal is periodic with fundamental period . . . . . . . .
A)
$$\frac{{2\pi }}{{{\omega _0}}}$$
B)
$$\frac{\pi }{{{\omega _0}}}$$
C)
$$2\pi $$
D)
$$\frac{{{\omega _0}}}{{2\pi }}$$
Answer & Solution
Answer: Option
A
70
Match
List-I with
List-II and select the correct answer using the options given below:
List-I (Functions in the time domain)List-II (Fourier transform of the function)
a. Delta function
1. Delta function
b. Gate function
2. Gaussian function
c. Normalized Gaussian
3. Constant function
d. Sinusoidal function
4. Sampling Function
A)
a-1, b-2, c-4, d-3
B)
a-3, b-4, c-2, d-1
C)
a-1, b-4, c-2, d-3
D)
a-3, b-2, c-4, d-1
Answer & Solution
Answer: Option
B
