Let f (x) = (x a) (x b) (x c), a < b < c. Then f'(x) = 0 has two roots. At which interval does these roots belongs?

At least one root in (a, b) and at least one root in (b, c)

Neither in (a, b) nor in (b, c)

Explore topic-wise MCQs in Mathematics.

This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.

1.	Let f (x) = (x a) (x b) (x c), a < b < c. Then f'(x) = 0 has two roots. At which interval does these roots belongs?
A.	Both the roots in (a, b)
B.	At least one root in (a, b) and at least one root in (b, c)
C.	Both the roots in (b, c)
D.	Neither in (a, b) nor in (b, c)
Answer» C. Both the roots in (b, c)

Discussion

2.	Is Rolle s theorem valid for f(x) = x² 3x + 4 in the interval [1, 2]?
A.	Yes
B.	No
C.	Depends on x
D.	Data not sufficient
Answer» B. No

Discussion

3.	What will be the value of ( lim limits_{x rightarrow 1} x^{ frac{1}{1-x}} )?
A.	1/e
B.	e
C.	0
D.	1
Answer» B. e

Discussion

4.	At which point does f(x) will attain local minima if f(x) = ₀ ^x (t+1)(e^t 1)(t 2)(t + 4) dt?
A.	0
B.	-1
C.	1
D.	-4
Answer» C. 1

Discussion

5.	If f(x) = \|4x x² 3\| when x [0, 4], then, which of the following is correct?
A.	x = 1 is the global maximum
B.	x = 2 is the global maximum
C.	x = 3 is the global maximum
D.	x = 0 is the global maximum
Answer» D. x = 0 is the global maximum

Discussion

6.	What is the value of ( )⁰ and 1?
A.	(0, 1)
B.	(1, 0)
C.	They are indeterminate form
D.	(1, 1)
Answer» D. (1, 1)

Discussion

7.	What will be the maximum area of an isosceles triangle inscribed in the ellipse x²/a² + y²/b² = 1 if its vertex at one end of the major axis?
A.	3 3/4 ab sq units
B.	3 3/2 ab sq units
C.	3/2 ab sq units
D.	3/4 ab sq units
Answer» B. 3 3/2 ab sq units

Discussion

8.	f(x) is a polynomial of degree 4, vanishes at x = -1 and has local minimum/maximum at x = 1, x = 2, and x = 3. If, _-2 ² f(x) dx = -1348/15. Then what is the value of f(x)?
A.	x<sup>4</sup> 8x<sup>3</sup> + 22x<sup>2</sup> 24x 55
B.	x<sup>4</sup> 8x<sup>3</sup> + 22x<sup>2</sup> 24x + 55
C.	x<sup>4</sup> 8x<sup>3</sup> 22x<sup>2</sup> 24x 55
D.	Data not sufficient
Answer» B. x<sup>4</sup> 8x<sup>3</sup> + 22x<sup>2</sup> 24x + 55

Discussion

Explore topic-wise MCQs in Mathematics.

Let f (x) = (x a) (x b) (x c), a < b < c. Then f'(x) = 0 has two roots. At which interval does these roots belongs?

Is Rolle s theorem valid for f(x) = x2 3x + 4 in the interval [1, 2]?

What will be the value of ( lim limits_{x rightarrow 1} x^{ frac{1}{1-x}} )?

At which point does f(x) will attain local minima if f(x) = 0 x (t+1)(et 1)(t 2)(t + 4) dt?

If f(x) = |4x x2 3| when x [0, 4], then, which of the following is correct?

What is the value of ( )0 and 1 ?

What will be the maximum area of an isosceles triangle inscribed in the ellipse x2/a2 + y2/b2 = 1 if its vertex at one end of the major axis?

f(x) is a polynomial of degree 4, vanishes at x = -1 and has local minimum/maximum at x = 1, x = 2, and x = 3. If, -2 2 f(x) dx = -1348/15. Then what is the value of f(x)?

Is Rolle s theorem valid for f(x) = x² 3x + 4 in the interval [1, 2]?

At which point does f(x) will attain local minima if f(x) = ₀ ^x (t+1)(e^t 1)(t 2)(t + 4) dt?

If f(x) = |4x x² 3| when x [0, 4], then, which of the following is correct?

What is the value of ( )⁰ and 1?

What will be the maximum area of an isosceles triangle inscribed in the ellipse x²/a² + y²/b² = 1 if its vertex at one end of the major axis?

f(x) is a polynomial of degree 4, vanishes at x = -1 and has local minimum/maximum at x = 1, x = 2, and x = 3. If, _-2 ² f(x) dx = -1348/15. Then what is the value of f(x)?