Explore topic-wise MCQs in Engineering Mathematics.

This section includes 13 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.

f(x) = ln(10-x2), x=[-3,3], find the point in interval [-3,3] where slope of a tangent is zero,

A. 0
B. Rolle s Theorem is not applied, because function is not continuous in interval [-3,3]
C. Rolle s Theorem is not applied, because function is not differential in interval (-3,3)
D. 2
Answer» B. Rolle s Theorem is not applied, because function is not continuous in interval [-3,3]
Discussion
2.

Find value of c(a point in a curve where slope of tangent to curve is zero) where
f(x) = ( begin{cases}x^2-x & 0<x<1 3x^3-4x+1 & 1<x<2 end{cases} ), Given c (0,2)

A. 1.5
B. Rolle s Theorem is not applied, because function is not continuous in interval [0,2]
C. Rolle s Theorem is not applied, because function is not differential in interval (0,2)
D. Function is both continuous and differentiable but Rolle s theorem is not applicable as f(0) f(2)
Answer» D. Function is both continuous and differentiable but Rolle s theorem is not applicable as f(0) f(2)
Discussion
3.

Find value of c(a point in f(x) where slope of tangent to curve is zero) where
f(x) = ( begin{cases}Tan(x) & 0<x< /4 Cos(x) & /4<x< /2 end{cases} ), given c (0, /2)

A. <sup> </sup> <sub>4</sub>
B. Rolle s Theorem is not applied, because function is not continuous in interval [0, <sup> </sup> <sub>2</sub>]
C. Rolle s Theorem is not applied, because function is not differential in interval (0, <sup> </sup> <sub>2</sub>)
D. Function is both continuous and differentiable but Rolle s theorem is not applicable as f(0) f(<sup> </sup> <sub>2</sub>)
Answer» C. Rolle s Theorem is not applied, because function is not differential in interval (0, <sup> </sup> <sub>2</sub>)
Discussion
4.

Find the value of a & b if f(x) = ax2 + bx + sin(x) is continuous over [0, ] and differentiable over (0, ) and satisfy the Rolle s theorem at point c = 4.

A. 0.45,1.414
B. 0.45,-1.414
C. -0.45,1.414
D. -0.45,-1.414
Answer» C. -0.45,1.414
Discussion
5.

Find the value of a if f(x) = ax2+32x+4 is continuous over [-4, 0] and differentiable over (-4, 0) and satisfy the Rolle s theorem. Hence find the point in interval (-2,0) at which its slope of a tangent is zero

A. 2, -2
B. 2, -1
C. 8, -1
D. 8, -2
Answer» E.
Discussion
6.

f(x) = 3Sin(2x), is continuous over interval [0, ] and differentiable over interval (0, ) and c (0, )

A.
B. <sup> </sup> <sub>2</sub>
C. <sup> </sup> <sub>4</sub>
D. <sup> </sup> <sub>8</sub>
Answer» C. <sup> </sup> <sub>4</sub>
Discussion
7.

Find value of c where f(x) = sin(x) ex tan(x), c (0, )

A. Tan<sup>-1</sup>[-(2+c<sup>2</sup>)/(1+c<sup>2</sup>)
B. Tan<sup>-1</sup>[-(2-c<sup>2</sup>)/(1+c<sup>2</sup>)]
C. Tan<sup>-1</sup>[(2+c<sup>2</sup>)/(1+c<sup>2</sup>)]
D. Rolle s Theorem is not applied, Cannot find the value of c
Answer» E.
Discussion
8.

Find the value of c if f(x) = sin3(x)cos(x), is continuous over interval [0, 2] and differentiable over interval (0, 2) and c (0, 2)

A. 0
B. <sup> </sup> <sub>6</sub>
C. <sup> </sup> <sub>3</sub>
D. <sup> </sup> <sub>2</sub>
Answer» D. <sup> </sup> <sub>2</sub>
Discussion
9.

Find the value of c if f(x) = x(x-3)e3x, is continuous over interval [0,3] and differentiable over interval (0, 3) and c (0,3)

A. 0.369
B. 2.703
C. 0
D. 3
Answer» C. 0
Discussion
10.

Find the value of c(a point where slope of a atangent to curve is zero) if f(x) = Sin(x) is continuous over interval [0, ] and differentiable over interval (0, ) and c (0, )

A.
B. <sup> </sup> <sub>2</sub>
C. <sup> </sup> <sub>6</sub>
D. <sup> </sup> <sub>4</sub>
Answer» C. <sup> </sup> <sub>6</sub>
Discussion
11.

Rolle s theorem is applicable to the

A. Functions differentiable in closed interval [a, b] and continuous in open interval (a, b) only and having same value at point a and b
B. Functions continuous in closed interval [a, b] only and having same value at point a and b
C. Functions continuous in closed interval [a, b] and differentiable in open interval (a, b) only and having same value at point a and b
D. Monotonically Increasing funtions
Answer» D. Monotonically Increasing funtions
Discussion
12.

Rolle s Theorem is a special case of

A. Lebniz Theorem
B. Mean Value Theorem
C. Taylor Series of a function
D. Leibnit x Theorem
Answer» C. Taylor Series of a function
Discussion
13.

Rolle s Theorem tells about the

A. Existence of point c where derivative of a function becomes zero
B. Existence of point c where derivative of a function is positive
C. Existence of point c where derivative of a function is negative
D. Existence of point c where derivative of a function is either positive or negative
Answer» B. Existence of point c where derivative of a function is positive
Discussion