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Engineering Maths - Calculus Online Exam Quiz

Important questions about Engineering Maths - Calculus. Engineering Maths - Calculus MCQ questions with answers. Engineering Maths - Calculus exam questions and answers for students and interviews.

3. The value of a =

Options

A : >0

B : 2

C : 0 - 1 + 100 - 10 + 1

D : undefined

4. The interval in which the Lagrange's theorem is applicable for the function f(x) = 1/x is

Options

A : [-3, 3]

B : [-2, 2]

C : [2, 3]

D : [-1, 1]

5. If f(x) = | x | , then for interval [-1, 1] ,f(x)

Options

A : satisfied all the conditions of Rolle's Theorem

B : satisfied all the conditions of Mean Value Theorem

C : does not satisfied the -conditions of Mean Value Theorem

D : None of these

6. The minimum value of | x 2 - 5x + 21 | is

Options

A : -5

B : 0

C : -1

D : -2

8. Value of the definite integral

Options

A : -2ln2

B : 2

C : 0

D : (ln2) 2

9. The function f(x) = 3x(x - 2) has a

Options

A : minimum at x = 1

B : maximum at x = 1

C : minimum at x = 2

D : maximum at x = 2

10. What is the derivative of f(x) = | x | at x = 0

Options

A : 1

B : -1

C : 0

D : Does not exist

11. Minimum point of the function

Options

A : x=1

B : x= -1

C : x=0

D : x= 1/√3

12.

Options

A : 0

B : ∞

C : 1

D : -1

13. If f (0) = 2 and f (x) = 1 /  (5-x 2 ), then lower and upper bound of f(1) estimated by the mean value theorem are

Options

A : 1.9,2.2

B : 2.2,2.25

C : 2.25,2.5

D : None of these

15. Maxima and Minima occur

Options

A : simultaneously

B : once

C : alternately

D : rarely

16. If x + y = k, x > 0, y > 0, then xy is maximum when

Options

A : x = ky

B : kx = y

C : x = y

D : None of these

17. Which of the following is correct ?

Options

A : f(a) is an extreme value of f(x) if f '(a)=0

B : If f(a) is an extreme value of f(x), then f '(a) = 0

C : If f '(a) = 0, then f (a) is an extreme value of f(x)

D : all of these

18. Let f(x) = |x|, then

Options

A : f'(0) = 0

B : f(x) is maximum at x = 0

C : f(x) is minimum at x = 0

D : None of these

19. The maxima and minima of the function f(x) = 2x 3 - 15x 2 + 36x + 10 occur respectively at

Options

A : x= 3 and x = 2

B : x = 1 and x = 3

C : x = 2 and x = 3

D : x = 3 and x = 4

20. Limit of the following series as x approaches π/2 is

Options

A : 2π/3

B : π/2

C : π/3

D : 1

21. Value of 'c' of the mean value theorem for the function f(x) = x(x - 2), when a = 0, b = 3/2, is

Options

A : 3/4

B : 1/2

C : 3/2

D : 1/4

22. If f(x , y) = x 2 + y 2 , then ∇ 2 f is

Options

A : 4

B : 2

C : 0

D : 4(x + y) 2

23. The value of integral

Options

A : 0

B : 0.25

C : 1

D : ∞

24. Angle between two unit-magnitude coplanar vectors P(0.866, 0.500, 0) and Q(0.259, 0.966, 0) will be

Options

A : 0 0

B : 30 0

C : 45 0

D : 60 0

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