1. FE Exam Tutorial

2. Math syllabus Analytic Geometry x Roots of Equations Calculus
Chemical
Civil
Electrical & Computer
Mechanical
Environmental
Industrial
General
Analytic Geometry x
Roots of Equations
Calculus
Differential Equations
Vector Analysis
Algebra and Trigonometry
Complex Numbers
Discrete Math
Linear Algebra
Numerical Methods
Matrix Operations

3. 1. Vectors

4. What can you say about two vectors whose dot product is negative?
The vectors are orthogonal
Angle between vectors is <90o
Angle between vectors is >90o

5. If two vectors u and v are orthogonal to each other, then u.v=-1 1

6. END

7. 2. Analytic Geometry

8. Two straight lines are perpendicular to each other
Two straight lines are perpendicular to each other. The product of the slope of the two lines is -1 1
Cannot be determined

9. END

10. 3. Roots of Equations

11. The value of x that satisfies f (x)=0 is called the
root of equation f (x)=0
root of function f (x)
zero of equation f (x)=0
none of the above

12. A quadratic equation has ______ root(s)
one
two
three
cannot be determined

13. For a certain cubic equation, at least one of the roots is known to be a complex root. The total number of complex roots the cubic equation has is
one
two
three
cannot be determined

14. Equation such as tan (x)=x has __ root(s)
zero
one
two
infinite

15. A polynomial of order n has zeros

16. The velocity of a body is given by v (t)=5e-t+4, where t is in seconds and v is in m/s. The velocity of the body is 6 m/s at t = s s s
1.609 s

17. END

18. 4. Numerical Methods

19. The number of significant digits in 2.30500 is4 5 6

20. END

21. 5. Ordinary Differential Equations

22. In the differential equation
the variable x is the variable
Independent
Dependent

23. In the differential equation
the variable y is the variable
Independent
Dependent

24. Ordinary differential equations can have these many dependent variables.
one
two
any positive integer

25. Ordinary differential equations can have these many independent variables.
one
two
any positive integer

26. A differential equation is considered to be ordinary if it has
one dependent variable
more than one dependent variable
one independent variable
more than one independent variable

27. Classify the differential equation
linear
nonlinear
undeterminable to be linear or nonlinear

28. Classify the differential equation
linear
nonlinear
linear with fixed constants
undeterminable to be linear or nonlinear

29. Classify the differential equation
linear
nonlinear
linear with fixed constants
undeterminable to be linear or nonlinear

30. The velocity of a body is given by
Then the distance covered by the body from t=0 to t=10 can be calculated by solving the differential equation for x(10) for

31. The form of the exact solution tois

32. END

33. 6. Matrices

34. The size of matrix is

35. The c32 entity of the matrix
6.3
does not exist

36. Given
then if [C]=[A]+[B], c12= 6 12

37. Given
then if [C]=[A]-[B], c23= -3 3 9

38. A square matrix [A] is lower triangular if

39. A square matrix [A] is upper triangular if

40. An identity matrix [I] needs to satisfy the following
matrix is square
all of the above

41. Given
then if [C]=[A][B], then c31=
-57
-45 57
Does not exist

42. The following system of equations x + y=2 6x + 6y=12 has solution(s).no
one
more than one but finite number of
infinite

43. END

44. 7. Differential Calculus

45. To find velocity from the location vs time data of the body, the mathematical procedure used is
Differentiation
Integration

46. The definition of the derivative of a function f (x) is

47. The exact derivative of f (x)=x 3 at x=5 is most nearly
25.00
75.00
106.25
125.00

48. Given y=sin (2x), dy/dx at x=3
0.9600
0.9945
1.920
1.989

49. END

50. 8. Integral Calculus

51. To find the velocity from acceleration vs time data, the mathematical procedure used is
Differentiation
Integration

52. Physically, integrating
means finding the
Area under the curve from a to b
Area to the left of point a
Area to the right of point b
Area above the curve from a to b

53. The value of the integralx3
x3 +C
x3/3
x3/3 +C 2x

54. Given the f(x) vs x curve, and the magnitude of the areas as shown, the value ofy x a 5 7 2 b c 5 12 14
Cannot be determined

55. Given the f(x) vs x curve, and the magnitude of the areas as shown, the value ofy x a 5 7 2 b c -7 -2 7 12

56. Given the f(x) vs x curve, and the magnitude of the areas as shown, the value ofy x a 5 7 2 b c -7 -2 12
Cannot be determined

57. 9. Partial Differential Equations

58. The number of independent variable(s) for partial differential equations is more than or equal to _____.
one
two
three
four

59. END