Mathematics II - Unit Wise Questions

Unit 1: Limits and Continuity
20 Questions

1. For all rational values of n, is equal to

1 marks | Asked in 2018-objective

11. If a function f(x) is defined as:

f(x) = 3x2 + 2            if x < 1

2x + 3                        if x > 1

4                                if x = 1

Discuss the continuity of function at x = 1.

5 marks | Asked in 2018

12.  Find the derivative of sin3x by using definition.

5 marks | Asked in 2018

2. If  then f(x) is said to be

a) Removable discontinuity

b) An ordinary discontinuity

c) Infinite discontinuity

d) Finite discontinuity

1 marks | Asked in 2018-objective

3. Derivative of tan-1x is equal to

1 marks | Asked in 2018-objective

13. Using L-Hospital's rule evaluate:

5 marks | Asked in 2018

14. If demand function and cost function are given by

P(Q) = 1-3Q and

C(Q) = Q2 – 2Q respectively, Where Q is the quality (number) of the product then

find output of the factor for the maximum profit.

5 marks | Asked in 2018

4. The value of is equal to,

a) ex    b) 1    c) 0    d) -1

1 marks | Asked in 2018-objective

15. Evaluate:

5 marks | Asked in 2018

5. The differential equation:is known as

a) Second degree second order

b) Second degree first order

c) First degree second order

d) First order second degree

1 marks | Asked in 2018-objective

6. One important condition to satisfy Rolle's Theorem by a function f(x) in [a, b] is

a) f(a) > f(b)    b) f(a) < f(b)    c) f(a) = f(b)    d) f(a) = f(b) ≠ 0

1 marks | Asked in 2018-objective

16. Solve:

5 marks | Asked in 2018

17. Examine the consistency of the system of equation and solve if possible.

x1 + x2 - x3 = 1

2x1 + 3x2 + 3x3 = 3

x1 - 3x2 + 3x3 = 2

5 marks | Asked in 2018

7. Formula for the composite trapezoidal rule is

1 marks | Asked in 2018-objective

8.While applying Simpson's 3/8 rule the number of sub-interval should be

a) Odd    b) 8    c) Even    d) Multiple of 3

1 marks | Asked in 2018-objective

9. In Gauss Elimination method the given system of simultaneous equation is transformed into

a) Lower tri-angular equation    b) Unit matrix    c) transpose matrix    d) upper triangular matrix

1 marks | Asked in 2018-objective

10. In Newton-Raphson method, if xn is an approximate solution of f(x) = 0 and f /(xn) ≠ 0 the next approximation is given by

1 marks | Asked in 2018-objective

18. Define Homogeneous equation and solve the following system of equations using Inverse Matrix Method.

-2x + 2y + z = -4

-8x + 7y – 4x = -47

9x – 8y + 5z = 55

10 marks | Asked in 2018

19. State Rolle's Theorem and interpret it geometrically. Verify Rolle's theorem for

f(x) = x2 – 4 in  - 3 ≤ x ≤ 3

5 marks | Asked in 2018

20. Using Composite Trapezoidal Rule, compute with four intervals. Find the absolute error of approximation from its actual value.

10 marks | Asked in 2018

Unit 2: Differentiation
0 Questions
Unit 3: Application of Differentiation
0 Questions
Unit 4: Integration and Its Applications
0 Questions
Unit 5: Differential Equations
0 Questions
Unit 6: Computational Method
0 Questions