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HEMALATHA S

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Mathematics

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Allied Mathematics ICS: Internal MCQ

HEMALATHA S

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20 questions

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1. Multiple Choice
1 minute
1 pt
Find $L^{-1}\left(\frac{s}{s^2+25}\right)$
cos 25t
sin 5t
cos 5t
2. Multiple Choice
1 minute
1 pt
$L^{-1}\left(\frac{6}{\left(s\right)}-\frac{4s}{s^2+25}\right)$ What is the property use to find the Inverse Laplace Transform of this equation?
Second Shifting Property
First Shifting Property
Linearity Property
Convolution theorem
3. Multiple Choice
1 minute
1 pt
$L^{-1}\left(\frac{24}{s^5}\right)$ is $t^4$ . What is $L^{-1}\left(\frac{1}{s^{\left(5\right)}}\right)$ ?
$\frac{24}{s^5}$
$\frac{1}{24}t^4$
$\frac{1}{24}t^5$
4. Multiple Choice
1 minute
1 pt
$L^{-1}\left(\frac{1}{\left(s-3\right)^2}\right)$
$e^{2t}t$
$e^tt^2$
$e^{3t}t$
5. Multiple Choice
1 minute
1 pt
Find the partial fraction for $\frac{\left(2s-8\right)}{\left(s-2\right)\left(s-3\right)}$
$\frac{2}{s-2}-\frac{4}{s-3}$
$\frac{3}{s-2}-\frac{2}{s-3}$
$\frac{4}{s-2}-\frac{2}{s-3}$
6. Multiple Choice
1 minute
1 pt
Define this property: $L\left(f\left(t\right)e^{at}\right)=F\left(s-a\right)$
Linearity Property
First Shifting Property
Convolution Theorem
Second Shifting Property
7. Multiple Choice
1 minute
1 pt
Find $L\left(e^{3t}\left(t^3-3t^2+5t\right)\right)$
$\frac{2}{\left(s-3\right)^4}-\left(\frac{3}{\left(\left(s-3\right)^3\right)}\right)+\frac{5}{\left(s-3\right)^2}$
$\frac{6}{\left(s-3\right)^4}-\left(\frac{6}{\left(s-3\right)^3}\right)+\frac{5}{\left(s-3\right)^2}$
$\frac{2}{\left(s-3\right)^3}-\left(\frac{3}{\left(s-3\right)^{\left(2\right)}}\right)+\frac{5}{s-3}$
8. Multiple Choice
1 minute
1 pt
$L\left(t\ \cos\ 6t\right)$ Which Laplace property is use to solve this?
Linearity Property
Derivative of Laplace Transform
First Shifting Property
Second Shifting Property
9. Multiple Choice
1 minute
1 pt
Given $g\left(t\right)=e^{5t}f\left(t\right)$ , what is G(s)?
$G\left(s\right)=F\left(s-5\right)$
$G\left(s\right)=\left(-1\right)^5\frac{\text{d}^5F\left(s\right)}{\text{d}s^5}$
$G\left(s\right)=F\left(s+5\right)$
$G\left(s\right)=\left(-1\right)^4\frac{\text{d}^4F\left(s\right)}{\text{d}s^4}$
10. Multiple Choice
1 minute
1 pt
Which one is the correct definition of Laplace Transform?
$F\left(s\right)=\int_0^{\infty}e^{-st}f\left(t\right)dt$
$F\left(s\right)=\int_0^tf\left(t\right)g\left(t-u\right)$
11. Multiple Choice
30 seconds
1 pt
Sum of the Eigen values of a matrix is equal to ----- of the matrix
determinant
product
trace
sum
12. Multiple Choice
30 seconds
1 pt
Eigen vectors corresponding to distinct Eigen values are
linearly independent
linearly dependent
normalized
none of the above
13. Multiple Choice
30 seconds
1 pt
Eigen values of an Identity matrix of order 4 are
0, 1. 0, 1
0, 0, 0, 0
1, 1, 1, 1
none of these
14. Multiple Choice
30 seconds
1 pt
If Eigen values of a matrix are 0, 1, 2 , then matrix will be
Non-singular
Singular
Both
None of these
15. Multiple Choice
30 seconds
1 pt
Eigen values of a skew symmetric matrix are
Negative
Real
purely imaginary or zero
none of these
16. Multiple Choice
30 seconds
1 pt
The set of vectors consisting of zero vector is
always L.I.
never L.I.
May be L.I.
None of these
17. Multiple Choice
30 seconds
1 pt
If A is a symmetric matrix and n∊N then Aⁿ is
Symmetric
Skew symmetric
A diagonal matrix
none of these
18. Multiple Choice
30 seconds
12 pts
What is the formula for the determinant of a 2x2 matrix?
ad-bc
ab-cd
ad+bc
(a+d)(b+c)
19. Multiple Choice
30 seconds
1 pt
Which option below correctly shows the steps to find the inverse of this matrix?
No Inverse Exists
20. Fill in the Blank
30 seconds
1 pt
What is the denominator of your answer when you simplify the given expression:
Answer choices
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Allied Mathematics ICS: Internal MCQ

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Allied Mathematics ICS: Internal MCQ

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