This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Curvature”.

1. The curvature of a function f(x) is zero. Which of the following functions could be f(x)

a) ax + b

b) ax^{2} + bx + c

c) sin(x)

d) cos(x)

View Answer

Explanation: The expression for curvature is

Given that k = 0 we have

f

^{”}(x) = 0

f(x) = a + b.

2. The curvature of the function f(x) = x^{2} + 2x + 1 at x = 0 is

a) ^{3}⁄_{2}

b) 2

c) ∣2 / 5^{3⁄2}∣

d) 0

View Answer

Explanation: The expression as we know is

3.The curvature of a circle depends inversely upon its radius r

a) True

b) False

View Answer

Explanation:Using parametric form of circle x = r.cos(t) : y = r.sin(t)

4.Find the curvature of the function f(x) = 3x^{3} + 4680x^{2} + 1789x + 181 at x = -520

a) 1

b) 0

c) ∞

d) -520

View Answer

Explanation: For a Cubic polynomial the curvature at x =

^{-b}⁄

_{3a}is zero because f

^{”}is zero at that point.

Looking at the form of the given point we can see that x =

^{-4680}⁄

_{3*3}

Thus, curvature is zero.

5.Let c(f(x)) denote the curvature function of given curve f(x). The value of c(c(f(x))) is observed

to be zero. Then which of the following functions could be f(x)

a) f(x) = x^{3} + x + 1

b) f(x)^{2} + y^{2} = 23400

c) f(x) = x^{19930} + x + 90903

d) No such function exist

View Answer

Explanation: We know that the curvature of a given circle is a constant function. Further, the curvature of any constant function is zero. Thus, we have to choose the equation of circle from the options.

6. The curvature of the function f(x) = x^{3} – x + 1 at x = 1 is given by

a) ∣^{6}⁄_{5} ∣

b) ∣^{3}⁄_{5} ∣

c) ∣^{6}⁄ 5^{3⁄2} ∣

d) ∣^{3}⁄ 5^{3⁄2}∣

View Answer

Explanation: Using expression for curvature we have

7.The curvature of a function depends directly on leading coefficient when x=0 which of the following could be f(x)

a) y = 323x^{3} + 4334x + 10102

b) y = x^{5} + 232x^{4} + 232x^{2} + 12344

c) y = ax^{5} + c

d) f(x) = x^{3} – x + 1

View Answer

Explanation: Using formula for curvature

y = 33x^{2} + 112345x + 8945

Observe numerator which is

Now this second derivative must be non zero for the above condition asked in the question

Looking at all the options we see that only quadratic polynomials can satisfy this.

8. Given x = k1e^{a1t} : y = k2e^{a2t} it is observed that the curvature function obtained is zero. What is the relation between a_{1} and a_{2}

a) a_{1} ≠ a_{2}

b) a_{1} = a_{2}

c) a_{1} = (a_{2})^{2}

d) a_{2} = (a_{1})^{2}

View Answer

Explanation: Using formula for Curvature in parametric form

9.The curvature function of some function is given to be k(x) = ^{1} ⁄ _{ [2 + 2x + x2]3 ⁄ 2} then which of the following functions

could be f(x)

a) ^{x2}⁄_{2} + x + 101

b) ^{x2}⁄_{4} + 2x + 100

c) x^{2} + 13x + 101

d) x^{3} + 4x^{2} + 1019

View Answer

Explanation:The equation for curvature Is

10. Consider the curvature of the function f(x) = e^{x} at x=0. The graph is scaled up by a factor of and the curvature is measured again at x=0.

What is the value of the curvature function at x=0 if the scaling factor tends to infinity

a) a

b) 2

c) 1

d) 0

View Answer

Explanation: If the scaling factor is then the function can be written as f(x) = e

^{ax}

Now using curvature formula we have

**Sanfoundry Global Education & Learning Series – Engineering Mathematics.**

To practice all areas of Engineering Mathematics, __here is complete set of 1000+ Multiple Choice Questions and Answers__.