For the infinitely defined discontinuous function ( begin{cases}x+sin(2x)& :x in [0, pi] x+sin(4x)& :x in ( pi,2 pi] x+sin(6x)& :x in (2 pi,3 pi] . . x+sin(2nx)& :x in [(n-1) pi,n pi) . . end{cases} )

nHow many points c [0,16x] exist, such that f'(c) = 1

For the function f(x) = x3 + x + 1. We do not have any Rolles point. The coordinate axes are transformed by rotating them by 60 degrees in anti-clockwise sense. The new Rolles point is?

The function can never have a Rolles point

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)= ( frac{x^{100}}{100}+ frac{x^{101}}{101}+ infty ). Find a point c (- , ) such that f'(c) = 0
A.	1
B.	2
C.	0
D.	-1
Answer» D. -1

Discussion

2.	A function f(x) with n roots should have n 1 unique Lagrange points.
A.	True
B.	False
Answer» C.

Discussion

3.	Let f(x)= (x- frac{x^3}{3^2.2!}+ frac{x^5}{5^2.4!}- frac{x^7}{7^2.6!}+ infty ). Find a point nearest to c such that f'(c) = 1
A.	1
B.	0
C.	2.3445 * 10<sup>-9</sup>
D.	458328.33 * 10<sup>-3</sup>
Answer» E.

Discussion

4.	For the infinitely defined discontinuous function ( begin{cases}x+sin(2x)& :x in [0, pi] x+sin(4x)& :x in ( pi,2 pi] x+sin(6x)& :x in (2 pi,3 pi] . . x+sin(2nx)& :x in [(n-1) pi,n pi) . . end{cases} )
A.	nHow many points c [0,16x] exist, such that f'(c) = 1
B.	256
C.	512
D.	16
E.	0
Answer» B. 256

Discussion

5.	For a third degree monic polynomial, it is seen that the sum of roots are zero. What is the relation between the minimum angle to be rotated to have a Rolles point ( in Radians) and the cyclic sum of the roots taken two at a time c
A.	= <sup> </sup> <sub>180</sub> * tan<sup>-1</sup>(c)
B.	Can never have a Rolles point
C.	= <sup>180</sup> <sub> </sub> tan<sup>-1</sup>(c)
D.	= tan<sup>-1</sup>(c)
Answer» E.

Discussion

6.	What is the minimum angle by which the coordinate axes have to be rotated in anticlockwise sense (in Degrees), such that the function f(x) = 3x³ + 5x + 1016 has at least one Rolles point
A.	<sup> </sup> <sub>180</sub> tan<sup>-1</sup>(5)
B.	tan<sup>-1</sup>(5)
C.	<sup>180</sup> <sub> </sub> tan<sup>-1</sup>(5)
D.	-tan<sup>-1</sup>(5)
Answer» D. -tan<sup>-1</sup>(5)

Discussion

7.	For the function f(x) = x³ + x + 1. We do not have any Rolles point. The coordinate axes are transformed by rotating them by 60 degrees in anti-clockwise sense. The new Rolles point is?
A.	( frac{ sqrt{3}}{2} )
B.	The function can never have a Rolles point
C.	(3^{ frac{1}{2}} )
D.	( sqrt{ frac{ sqrt{3}-1}{3}} )
Answer» E.

Discussion

8.	For the function f(x) = x² 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes?
A.	<sup>3</sup> <sub>2</sub>
B.	<sup>1</sup> <sub>2</sub>
C.	<sup>5</sup> <sub>2</sub>
D.	1
Answer» B. <sup>1</sup> <sub>2</sub>

Discussion

Explore topic-wise MCQs in Engineering Mathematics.

Let f(x)= ( frac{x^{100}}{100}+ frac{x^{101}}{101}+ infty ). Find a point c (- , ) such that f'(c) = 0

A function f(x) with n roots should have n 1 unique Lagrange points.

Let f(x)= (x- frac{x^3}{3^2.2!}+ frac{x^5}{5^2.4!}- frac{x^7}{7^2.6!}+ infty ). Find a point nearest to c such that f'(c) = 1

For the infinitely defined discontinuous function ( begin{cases}x+sin(2x)& :x in [0, pi] x+sin(4x)& :x in ( pi,2 pi] x+sin(6x)& :x in (2 pi,3 pi] . . x+sin(2nx)& :x in [(n-1) pi,n pi) . . end{cases} )

For a third degree monic polynomial, it is seen that the sum of roots are zero. What is the relation between the minimum angle to be rotated to have a Rolles point ( in Radians) and the cyclic sum of the roots taken two at a time c

What is the minimum angle by which the coordinate axes have to be rotated in anticlockwise sense (in Degrees), such that the function f(x) = 3x3 + 5x + 1016 has at least one Rolles point

For the function f(x) = x3 + x + 1. We do not have any Rolles point. The coordinate axes are transformed by rotating them by 60 degrees in anti-clockwise sense. The new Rolles point is?

For the function f(x) = x2 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes?

For the infinitely defined discontinuous function
( begin{cases}x+sin(2x)& :x in [0, pi] x+sin(4x)& :x in ( pi,2 pi] x+sin(6x)& :x in (2 pi,3 pi] . . x+sin(2nx)& :x in [(n-1) pi,n pi) . . end{cases} )

What is the minimum angle by which the coordinate axes have to be rotated in anticlockwise sense (in Degrees), such that the function f(x) = 3x³ + 5x + 1016 has at least one Rolles point

For the function f(x) = x³ + x + 1. We do not have any Rolles point. The coordinate axes are transformed by rotating them by 60 degrees in anti-clockwise sense. The new Rolles point is?

For the function f(x) = x² 2x + 1. We have Rolles point at x = 1. The coordinate axes are then rotated by 45 degrees in anticlockwise sense. What is the position of new Rolles point with respect to the transformed coordinate axes?