Explore topic-wise MCQs in Fourier Analysis.

This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Fourier Analysis knowledge and support exam preparation. Choose a topic below to get started.

1.

Solve un+2 + 10 un+1 + 9 un = 2n.

A. (u_n = frac{2^{n+1}}{33}+ frac{(-9)^{n+1}}{88}+ frac{(-1)^{n+1}}{24} )
B. (u_n = frac{2^n}{33}+ frac{(-9)^n}{88}+ frac{(-1)^{n-1}}{24} )
C. (u_n = frac{2^{n+1}}{11}+ frac{(-9)^{n+1}}{88}+ frac{(-1)^n}{24} )
D. (u_n = frac{2^n}{11}+ frac{(-9)^n}{88}+ frac{(-1)^{n-1}}{24} )
Answer» C. (u_n = frac{2^{n+1}}{11}+ frac{(-9)^{n+1}}{88}+ frac{(-1)^n}{24} )
Discussion
2.

Find the difference equation of y = ax + b.

A. <sup>2</sup>y = 0
B. <sup>2</sup>y = 1
C. <sup>2</sup>y + 3 y = 2
D. <sup>2</sup>y + 4 y = 5
Answer» B. <sup>2</sup>y = 1
Discussion
3.

Find the difference equation of yn = A 3n + B 5n.

A. y<sub>n+2</sub> -16 y<sub>n+1</sub> + 15 y<sub>n-1</sub> = 0
B. y<sub>n+3</sub> -14 y<sub>n+1</sub> + 30 y<sub>n</sub> = 0
C. 2 y<sub>n+2</sub> -14 y<sub>n+1</sub> + 15 y<sub>n</sub> = 0
D. 2 y<sub>n+2</sub> -16 y<sub>n+1</sub> + 30 y<sub>n</sub> = 0
Answer» E.
Discussion
4.

Find the order of the difference equation yn+3 -3 yn+1 yn-2 = 4.

A. 3
B. 4
C. 5
D. 6
Answer» D. 6
Discussion
5.

Find the order of the difference equation 3yn 2yn yn = 3.

A. 3
B. 4
C. 2
D. 5
Answer» B. 4
Discussion
6.

Find u2 if (U(z) = frac{z^3+6z^2+9z+3}{(z-1)^4} ).

A. 8
B. 9
C. 10
D. 11
Answer» D. 11
Discussion
7.

The Z Transform of a function is given by (U(z) = frac{z^3+6z^2+9z+3}{(z-1)^4} ). Find the Z-Transform of un+2.

A. ( frac{10z^3+3z^2+7z^1-1}{(z-1)^4} )
B. ( frac{10z^4+3z^3+7z^2-z}{(z-1)^4} )
C. ( frac{10z^4+4z^3+7z^2-2z}{(z-1)^4} )
D. ( frac{10z^4+3z^3-4z}{(z-1)^4} )
Answer» C. ( frac{10z^4+4z^3+7z^2-2z}{(z-1)^4} )
Discussion
8.

Find the Z Transform of np.

A. (-z frac{d}{dz}(Z(n^{p-1})) )
B. (z frac{d}{dz}(Z(n^p)) )
C. (-z frac{d}{dz}(Z(n^{p+1})) )
D. (z frac{d}{dz}(Z(n^{p+1})) )
Answer» B. (z frac{d}{dz}(Z(n^p)) )
Discussion
9.

Find the value of u3 if (U(z) = frac{3z^2+2z+10}{(z-1)^4} ).

A. 12
B. 13
C. 14
D. 15
Answer» D. 15
Discussion
10.

Find the Z Transform of sinh n .

A. ( frac{sinh u2061 }{z^2-2z cosh u2061 +1} )
B. ( frac{1}{2} frac{sinh u2061 }{z^2-2z cosh u2061 +1} )
C. ( frac{z sinh u2061 )}{z^2-2z cosh u2061 +1} )
D. ( frac{z(z-sinh u2061 )}{z^2-2z cosh u2061 +1} )
Answer» B. ( frac{1}{2} frac{sinh u2061 }{z^2-2z cosh u2061 +1} )
Discussion
11.

Find the inverse Z Transform of (log frac{z}{z+1} ).

A. ( frac{(-1)^n}{n} )
B. ( frac{(-1)^{n+1}}{n} )
C. ( frac{1}{n} )
D. ( frac{(-1)^n}{n+1} )
Answer» B. ( frac{(-1)^{n+1}}{n} )
Discussion
12.

Find the inverse Z- Transform of (( frac{z}{z-a})^3 ).

A. ( frac{1}{2} . (n+1) (n-2) a^{n-2} U(n) )
B. ( frac{1}{2} . (n-1) (n-2) a^{n-3} U(n) )
C. ( frac{1}{2} . (n-1) (n+2) a^{n-1} U(n) )
D. ( frac{1}{2} . (n+1) (n+2) a^n U(n) )
Answer» E.
Discussion
13.

Find the function whose Z transform is (e^{ frac{1}{z}} ).

A. log(n)
B. ( frac{1}{n} )
C. ( frac{1}{n!} )
D. ( frac{1}{(n+1)!} )
Answer» D. ( frac{1}{(n+1)!} )
Discussion
14.

Find the function whose Z Transform is ( frac{1}{z} ).

A. (n)
B. (n+1)
C. U(n)
D. U(n+1)
Answer» C. U(n)
Discussion
15.

Find the Z-Transform of (^nC_p ).

A. (1-z<sup>-1</sup>)<sup>n</sup>
B. (1+z<sup>-1</sup>)<sup>n</sup>
C. (1-z<sup>-1</sup>)<sup>-n</sup>
D. (1+z<sup>-1</sup>)<sup>-n</sup>
Answer» C. (1-z<sup>-1</sup>)<sup>-n</sup>
Discussion