Bissoy
Login
Get Advice on Live Video Call
Earn $ Cash $ with
consultations on Bissoy App
Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete-time system has the input-output relationship,<br>$$y\left( n \right) = \left\{ \matrix{ \matrix{ {x\left( n \right),} & {n \ge 1} \cr } \hfill \cr \matrix{ {0,} & {n = 0} \cr } \hfill \cr \matrix{ {x\left( {n + 1} \right),} & {n \le - 1} \cr } \hfill \cr} \right.$$<br>where x(n) is the input and y(n) is the output.<br>The above system has the properties
A
P, S but not Q, R
B
P, Q, S but not R
C
P, Q, R, S
D
O, R, S but not P
Correct Answer:
P, S but not Q, R
Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 \end{array}} \right
A
\
B
<br>It is given that A has only one real eigen value.<br>Then the real eigen value of A is
C
<p><span>A.</span> -2.5
D
</span> 0
Let the function
\[{\text{f}}\left( \theta \right) = \left| {\begin{array}{*{20}{c}} {\sin \theta }&{\cos \theta }&{\tan \theta } \\ {\sin \left( {\frac{\pi }{6}} \right)}&{\cos \left( {\frac{\pi }{6}} \right)}&{\tan \left( {\frac{\pi }{6}} \right)} \\ {\sin \left( {\frac{\pi }{3}} \right)}&{\cos \left( {\frac{\pi }{3}} \right)}&{\tan \left( {\frac{\pi }{3}} \right)} \end{array}} \right|\
A
<br>where \\
B
and \ denote the derivative of f with respect to \. Which of the following statements is/are TRUE?<br>I. There exists \ such that \<br>II. There exists \ such that\
C
<p><span>A.</span> l only
D
</span> ll only
Let A be an m × n matrix and Ban n × m matrix. It is given that determinant ($$I$$
m
+ AB) = determinant ($$I$$
n
+ BA), where $$I$$
k
is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right
A
\
B
<p><span>A.</span> 2
C
</span> 5
If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?
A
0
B
5
C
1
D
4
If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$ + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$ + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$ + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$ is?
A
0
B
1
C
4
D
1 + abcd
The Hamiltonian of a particle is given by $$H = \frac{{{p^2}}}{{2m}} + V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right) + \phi \left( { + \left| {\overrightarrow {\bf{r}} } \right|} \right)\overrightarrow {\bf{L}} .\overrightarrow {\bf{S}} ,$$ where $$\overrightarrow {\bf{S}} $$ is the spin, $$V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$ and $$\phi \left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$ are potential functions and $$\overrightarrow {\bf{L}} \left( { = \overrightarrow {\bf{r}} \times \overrightarrow {\bf{p}} } \right)$$ is the angular momentum. The Hamiltonian does not commute with
A
$$\overrightarrow {\bf{L}} + \overrightarrow {\bf{S}} $$
B
$$\overrightarrow {{{\bf{S}}^2}} $$
C
$${L_z}$$
D
$$\overrightarrow {{{\bf{L}}^2}} $$
The value of the expression $$\frac{{{{\left( {a - b} \right)}^2}}}{{\left( {b - c} \right)\left( {c - a} \right)}} + $$ $$\frac{{{{\left( {b - c} \right)}^2}}}{{\left( {a - b} \right)\left( {c - a} \right)}} + $$ $$\frac{{{{\left( {c - a} \right)}^2}}}{{\left( {a - b} \right)\left( {b - c} \right)}}$$ = ?
A
0
B
3
C
$$\frac{1}{3}$$
D
2
$$\frac{{{{\left( {4.53 - 3.07} \right)}^2}}}{{\left( {3.07 - 2.15} \right)\left( {2.15 - 4.53} \right)}} + \, $$ $$\frac{{{{\left( {3.07 - 2.15} \right)}^2}}}{{\left( {2.15 - 4.53} \right)\left( {4.53 - 3.07} \right)}} + \,\, $$ $$\frac{{{{\left( {2.15 - 4.53} \right)}^2}}}{{\left( {4.53 - 3.07} \right)\left( {3.07 - 2.15} \right)}}$$ is simplified to :
A
0
B
1
C
2
D
3
Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 0&1&0&0 \\ 1&0&0&0 \\ 0&0&0&{ - 2i} \\ 0&0&{2i}&0 \end{array}} \right
A
\
B
are
C
<p><span>A.</span> -2, -1, 1, 2
D
</span> -1, 1, 0, 2
Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.
A
Causal, LP
B
BIBO, LTI
C
BIBO, Causal, LTI
D
LP, LTI
