Explore topic-wise MCQs in Engineering Mathematics.

This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.

A function f(x) which is continuous and differentiable over the real domain exists such that f(n) (x) = [f(n + 1) (x)]2, f(0) = a and f(1)(0) = 1.

A. True
B. False
Answer» B. False
Discussion
2.

Let Mclaurin series of some f(x) be given recursively, where an denotes the coefficient of xn in the expansion. Also given an = an-1 / n and a0 = 1, which of the
following functions could be f(x)?

A. e<sup>x</sup>
B. e<sup>2x</sup>
C. c + e<sup>x</sup>
D. No closed form exists
Answer» B. e<sup>2x</sup>
Discussion
3.

Let (f(x)) denote the Taylor series for some function f(x). Then the value of ( ( (f(1729)))) 2 ( (f(1729))) + (f(1729)) is?

A. 1729
B. -1
C. 1
D. 0
Answer» E.
Discussion
4.

f(1) (n) = g(n) (0) holds good for some functions f(x) and g(x). Now let the coordinate axes containing graph g(x) be rotated by 30 degrees clockwise, then the corresponding Taylor series for the transformed g(x) is?

A. g(0)+ ( frac{e^x 1}{ sqrt{3}}+ frac{ sum_{n=1}^ infty f^{(1)}(n)x^n}{n!} )
B. (g(0) + frac{g^{(1)}.x}{1!} + frac{g^{(2)}(1).x^2}{2!}+ infty )
C. No unique answer exist
D. Such function is not continuous
Answer» B. (g(0) + frac{g^{(1)}.x}{1!} + frac{g^{(2)}(1).x^2}{2!}+ infty )
Discussion
5.

To find the value of sin(9) the Taylor Series expansion should be expanded with center as ___________

A. 9
B. 8
C. 7
D. Some delta (small) interval around 9
Answer» E.
Discussion
6.

Find the Taylor series expansion of the function cosh(x) centered at x = 0.

A. (1- frac{x^2}{2!}+ frac{x^4}{4!}+ . infty )
B. ( frac{x}{1!}+ frac{x^3}{3!}+ frac{x^5}{5!} . infty )
C. (1+ frac{x^2}{2!}+ frac{x^4}{4!}+ . infty )
D. (1+ frac{x}{1!}+ frac{x^2}{2!}+ . infty )
Answer» D. (1+ frac{x}{1!}+ frac{x^2}{2!}+ . infty )
Discussion
7.

Let (X) be the Taylor Series expansion of f(x) = x3 + x2 + 1019 centered at a = 1019, then what is the value of the expression 2( (1729))2 + (1729) * f(1729) 3(f(1729))2 + 1770?

A. 1770
B. 1729
C. 0
D. 1
Answer» B. 1729
Discussion
8.

What is the coefficient of x101729 in the series expansion of cos(sin(x))?

A. 0
B. <sup>1</sup> <sub>101729!</sub>
C. <sup>-1</sup> <sub>101729!</sub>
D. 1
Answer» B. <sup>1</sup> <sub>101729!</sub>
Discussion
9.

The Mclaurin Series expansion of sin(ex) is?

A. sin(1)+ ( frac{x.cos(1)}{1!}+ sum_{n=2}^{ infty} sum_{a=0}^{ infty} frac{x^n.(-1)^a}{n!} times frac{(2a+1)^n}{(2a+1)!} )
B. ( frac{e^x}{1!}+ frac{e^{3x}}{3!}+ frac{e^{5x}}{5!} infty )
C. (- frac{e^x}{1!}+ frac{e^{3x}}{3!}- frac{e^{5x}}{5!} infty )
D. ( sum_{n=2}^{ infty} sum_{a=0}^{ infty} frac{x^n.(-1)^a}{n!} times frac{(2a+1)^n}{(2a+1)!} )
Answer» B. ( frac{e^x}{1!}+ frac{e^{3x}}{3!}+ frac{e^{5x}}{5!} infty )
Discussion