Explore topic-wise MCQs in Engineering Mathematics.

This section includes 8 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.

Let f(x) = ex sinh(x) / x, let y(n) denote the nth derivative of f(x) at x = 0 then the expression for y(n) is given by

A. \(\sum_{i=0}^n \frac{c_{2i}^n}{2i+1}\)
B. \(\sum_{i=0}^n \frac{1}{2i+1}\)
C. 1
D. Has no general form
Answer» B. \(\sum_{i=0}^n \frac{1}{2i+1}\)
Discussion
2.

Let f(x)=\(\frac{e^x \times sin(x)}{x}\) and let the nth derivative at x = 0 be given by y(n) Then the value of the expression for y(n) is given by

A. \(\frac{\pi n}{4}\)
B. \(\sum_{i=0}^{i<=n}\frac{(-1)^i c_{2i}^n}{2i+1}\)
C. πn
D. \(\frac{\pi}{2n}\)
Answer» C. πn
Discussion
3.

For the given function f(x)=\(\sqrt{x^3+x^7}\) the values of first and second derivative at x = 1 are assumed as 0 and 1 respectively. Then the value of the third derivative could be

A. 54√2
B. 2√2
C. √2
D. Indeterminate
Answer» B. 2√2
Discussion
4.

If the first and second derivatives at x = 0 of the function f(x)=\(\frac{cos(x)}{x^2-x+1}\)were 2 and 3 then the value of the third derivative is

A. -3
B. 3
C. 2
D. 1
Answer» C. 2
Discussion
5.

Let f(x) = tan(x) and let y(n) denote the nth derivative of f(x) then the value of y(9998879879789776) is

A. 908090988
B. 0
C. 989
D. 1729
Answer» C. 989
Discussion
6.

Let f(x) = \(\sqrt{1-x^2}\) and let y(n) denote the nth derivative of f(x) at x = 0 then the value of 6y (1) y(2) + 2y(3) is

A. -998
B. 0
C. 998
D. -1
Answer» C. 998
Discussion
7.

Let f(x) = ln(x)/x+1 and let y(n) denote the nth derivative of f(x) at x = 1 then the value of 2y(100) + 100y(99)

A. (99)!
B. (-99)!
C. (100)!
D. (-98)!
Answer» C. (100)!
Discussion
8.

Let f(x) = sin(x)/1+x2. Let y(n) denote the nth derivative of f(x) at x = 0 then the value of y(100) + 9900y(98) is

A. 0
B. -1
C. 100
D. 1729
Answer» B. -1
Discussion