Explore topic-wise MCQs in Discrete Mathematics.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

Determine the radius of convergence and interval of convergence for the power series: n=0 (x 7)n+1/nn.

A. 0, 1<x<1
B. , <x<
C. 1, 2<x<2
D. 2, 1<x<1
Answer» C. 1, 2<x<2
Discussion
2.

What is the radius of convergence and interval of convergence for the power series n=0m!(2x-1)m?

A. 3, 12
B. 1, 0.87
C. 2, 5.4
D. 0, 1/2
Answer» E.
Discussion
3.

Find the power series representation for the function f(x)=x/4 x.

A. <sub>n=0</sub>x<sup>n+1</sup>/4<sup>n+1</sup>
B. <sub>n=0</sub>x<sup>n+1</sup>4<sup>n</sup>
C. <sub>n=0</sub>x<sup>n</sup>4<sup>n</sup>
D. <sub>n=0</sub>x<sup>n+1</sup>
Answer» B. <sub>n=0</sub>x<sup>n+1</sup>4<sup>n</sup>
Discussion
4.

Determine a power series representation for the function g(x)=ln(7 x).

A. <sub>n</sub>=0 x<sup>n+1</sup>/7<sup>n+1</sup>
B. ln(14) <sub>n</sub>=0 x<sup>n+1</sup>/7n
C. ln(7) <sub>n</sub>=0 x<sup>n+1</sup>/7<sup>n+1</sup>
D. ln <sub>n</sub>=0 x/7<sup>n+1</sup>
Answer» D. ln <sub>n</sub>=0 x/7<sup>n+1</sup>
Discussion
5.

Determine the interval and radius of convergence for the power series: n=17n/n(3x 1)n-1.

A. (2x+1)/6
B. 7|3x 1|
C. 5|x+1|
D. 3!*|4x 9|
Answer» C. 5|x+1|
Discussion
6.

Which of the following series is called the formal power series ?

A. b<sub>0</sub>+b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup>
B. b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup>
C. 1/2b<sub>0</sub>+1/3b<sub>1</sub>x+1/4b<sub>2</sub>x<sup>2</sup>+ +1/nb<sub>n</sub>x<sup>n</sup>
D. n<sup>2</sup>(b<sub>0</sub>+b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup>)
Answer» B. b<sub>1</sub>x+b<sub>2</sub>x<sup>2</sup>+ +b<sub>n</sub>x<sup>n</sup>
Discussion
7.

The third term of a geometric progression with common ratio equal to half the initial term is 81. Determine the 12th term.

A. 3<sup>12</sup>
B. 4<sup>15</sup>
C. 6<sup>8</sup>
D. 5<sup>9</sup>
Answer» B. 4<sup>15</sup>
Discussion
8.

The explicit formula for the geometric sequence 3, 15, 75, 375, is _______

A. 2*6! * 3<sup>n-1</sup>
B. 3 * 5<sup>n-1</sup>
C. 3! * 8<sup>n-1</sup>
D. 7 * 4<sup>n-1</sup>
Answer» C. 3! * 8<sup>n-1</sup>
Discussion