1 | P a g e Centre for Collaboration of Industry and Institutions (CCII) – www.cmju.in
Question Booklet Code: C Duration: 2 Hours
Course: Diploma in Engineering in Architecture Assistantship Year: First Year
Paper Code: 702106 Paper Name: Engineering Mathematics
ATTEMPT ALL THE BELOW MENTIONED QUESTIONS:
1. What is the primary difference between
using anti-differentiation when finding a
definite versus an indefinite integral?
a) Indefinite integrals don't have defined
limits.
b) Definite integrals have defined limits.
c) The constant of integration, C.
d) There is no difference between definite and
indefinite integrals.
2. If θ approaches zero, then limit of
sin(θ)/θ is _____.
a) cos(θ)
b) 0
c) 1
d) This is indeterminate.
3. Let's say that f ''(k) = 0 @ (13, -2).
What does this mean?
a) There is definitely an inflection point at
that location.
b) There might be an inflection point at that
location.
c) There definitely is not an inflection point at
that location.
d) There's no way to tell without first knowing
what the specific function is.
4. What is the one thing done in antidifferentiation
that has no counterpart in
differentiation?
a) Adding a constant C.
b) Subtracting a constant C.
c) Dividing the new exponent by a constant C.
d) Nothing, they are equally matched step by
step.
5. What is a necessary condition for
L'Hopital's Rule to work?
a) The function must be determinate.
b) The function must be indeterminate.
c) The function must be inconsistent.
d) The function must possess at least three
non-zero derivatives.
6. What does du equal in ∫2x(x2 + 1)5 dx?
a) 2x
b) 2u du
c) 2x dx
d) 5u4
7. What is the second step of performing
anti-differentiation?
a) Divide the coefficient by the old
exponential value.
b) Subtract the new exponential value from
the coefficient.
c) Multiply the coefficient by the new
exponential value.
d) Divide the coefficient by the new
exponential value.
8. Which of the following is the best
integration technique to use for ∫2x(x2 +
1)5 dx?
a) The product rule.
b) The chain rule.
c) The power rule.
d) The substitution rule.
9. ∫1/x dx =
a) Undefined because you cannot divide by
zero.
b) loge(x)
c) ln(x)
d) ln(x) + C
10. What is the converted substitution
form of ∫12x2 (x3 + 1)5 dx?
a) 4∫u5 du
b) ∫u5 du
c) ¼ ∫u5 du
d) This cannot be solved by the substitution
method.
CMJ UNIVERSITY, SHILLONG
TERM END EXAMINATION - 2013
2 | P a g e Centre for Collaboration of Industry and Institutions (CCII) – www.cmju.in
11. A= [aij]m×n is a square matrix if
a) m < n
b) m > n
c) m = n
d) None of these
12. If A is a matrix of order 4 × 3 then
each row of matrix A contains
a) 12 elements
b) 4 elements
c) 3 elements
d) None of these
13. The number of all possible matrices of
order 2×3 with each entry 0 or1 is
a) 64
b) 12
c) 36
d) None of these
14. The given matrix A = __ _ _ _ _ _ _ _ __ is
a) Scalar
b) Diagonal Matrix
c) Unit Matrix
d) Square Matrix
15. If ___+ _ __− __ = _ −__ _+_ _ then the
values of x and y are
a) x=3,y=1
b) x=2,y=3
c) x=2,y=4
d) x=3,y=3
16. If A is of order m×n and B is of order
p×q then AB is defined only if
a) m = q
b) m = p
c) n = p
d) n = q
17. A matrix has 24 elements then the
possible orders it can have
a) 8
b) 6
c) 4
d) 2
18. If x ____ + y _−_ _ _ = ___ _ _ then the values
of x & y are
a) 3, 4
b) 3, -4
c) -3, -4
d) None of these
19. Two matrices A & B which have the
same order, are said to be
a) Equal
b) Comparable
c) Conformable for product AB
d) None of these
20. The matrix in which number of rows is
equal to number of columns is called
a) Square Matrix
b) Rectangular matrix
c) Diagonal Matrix
d) None of these
21. Let A be a 5×7 matrix then each
column of A contains
a) 7 elements
b) 5 elements
c) 35 elements
d) None of these
22. If λ С R, then λI2 is the Matrix
a)__ _ 0 0_
b)__ _ _ __
c)_0 _ _ 0_
d)__ 0 0 __
23. Matrices A & B inverse of each other
only if
a) AB = BA
b) AB – BA = 1
c) AB = O, BA = I
d) AB = BA = I
24. If A = _____ −____ ____ ____ _ then A + A’ = I
then value of _ is
a) _/6
b) _/3
c) _
d) 3_/2
25. If A =!_ _ _", B = ___ _ then AB
a) !2 8 3"
b) _283
_
c) !1 3"
d) None of these
3 | P a g e Centre for Collaboration of Industry and Institutions (CCII) – www.cmju.in
26. Given that . Select the correct
form for the differential from the list
below:
a)
b)
c)
d)
27. Differentiate the following equation
using the standard rules:
a)
b)
c)
d)
28. Differentiate the following equation:
a)
b)
c)
d)
29. Differentiate the following equation:
a)
b)
c)
d)
30. Differentiate the following equation:
a)
b)
c)
d)
31. Differentiate the following equation:
a)
b)
c)
d)
32. Differentiate the following equation:
a)
b)
c)
d)
4 | P a g e Centre for Collaboration of Industry and Institutions (CCII) – www.cmju.in
33. Differentiate the following equation:
a)
b)
c)
d)
34. Differentiate the following equation:
a)
b)
c)
d)
35. Differentiate the following equation:
a)
b)
c)
d)
36. If f(x) = 3x2, then F(x) =
a) 6x
b) x3
c) x3 + C
d) 6x + C
37. The two types of errors that are
related to differentials are:
a) Human, Absolute.
b) Absolute, Relative.
c) Relative, Controllable.
d) Controllable, Natural.
38. Mathematically, what is a differential?
a) A method of directly relating how changes
in a dependent variable affect changes in an
independent variable.
b) A word used to relate differences in a
mathematical value with variable values.
c) A method of directly relating how changes
in an independent variable affect changes in a
dependent variable.
d) None of the Above
39. The 2nd derivative of a function at
point P is 0, and concavity is positive for
values to the right of P. What must the
concavity be to the left of P for P to be an
inflection point?
a) The concavity must also be positive.
b) The concavity must be negative.
c) The concavity must be neutral (0).
d) The concavity must be imaginary.
40. At what value of q is the concavity of
w(q) = -2, if w(q) = q4 - 16?
a) At q = fourth root of 14.
b) At q = 0.
c) Never; w(q) is always concave down.
d) Never; w(q) is always concave up.
41. What is needed to fully determine an
anti-differentiated function?
a) A lot of luck.
b) A boundary condition.
c) What its value is at (0, 0).
d) Its real world application.
42. It has been determined that g(p) has
a maximum at p = -47.6. What can be
said of the function's concavity at that
point?
a) g ''(p) = 0
b) g ''(p) > 0
c) g ''(p) < 0
d) There's no way to tell without first knowing
what the specific function is.
43. What are the values of C0 and C1 in
d(t) = C1 + C0t - 16t2, if d(1) = 4 and v(2)
= -65?
a) C0 = -1, C1 = 21
b) C0 = 1, C1 = -21
c) C0 = -1, C1 = 19
d) C0 = 0, C1 = 1
5 | P a g e Centre for Collaboration of Industry and Institutions (CCII) – www.cmju.in
44. G(d) was determined to be 3d + C;
here, C is called:
a) the constant of differentiation.
b) the constant of anti-differentiation.
c) the constant of integration.
d) the constant of death and taxes.
45. Does f(c) = (c + 2)3 - 2 have an
inflection point? If so, where is it located?
a) Yes, at (-2, -2)
b) Yes, at (2, -2)
c) Yes, at (8, -2)
d) No
46. If which of
the following is false?
a)
b)
c)
d)
47. If A and B are n × n matrices, which of
the following does not equal (A + B)2 ?
a) A2 + 2AB + B2
b) (A + B)A + (A + B)B
c) A2 + AB + BA + B2
d) (B + A)2
48. If A, B, and C are n × n matrices,
which of the following equalities is
invalid? Note: D′ is the transpose of D.
a) (ABC)′ = C′B′A′
b) (A + A + 2B)′ = 2B′ + 2A′
c) (A + A)′ = 2A′
d) ((AB)2)′ = (B′)2(A′)2
49. The n × n matrix P is idempotent
if P2 = P and orthogonal if P′P = I. Which
of the following is false?
a)If P and Q are orthogonal n × n matrices,
then PQ is orthogonal
b)If P and Q are idempotent n × n matrices
and PQ = QP = O, then P + Q is idempotent
c) is orthogonal
d)If P is idempotent, then −P is idempotent
50. Which of the following statements is
correct?
a) Suppose A is n × n, x is n × 1, and Ax = 0
has only the trivial solution. Then Ax = b has
solutions for any n × 1 vector b
b) It is possible to construct a linear system
with exactly 5 different solutions
c) A linear system with more equations than
unknowns cannot have solutions
d) A linear system can only have an infinite
number of solutions if there are more variables
than equations
51. For which values of t does the
following linear equation system have
infinitely many solutions?
a) t = 2
b) t = 2 and t = −3
c) The system does not have infinitely many
solutions for any value of t
d) t = −3
52. Using Gaussian elimination, the
solutions of can be
deduced from the augmented matrix
. For which values
of a, b, and c are there infinitely many
solutions?
a) If c = 1
b) Never
c) If a = b and c = 1
d) If a ≠ b
53. If a = (3, 4, 0) and b = (0, 2, −3),
then is equal to:
a) 3
b) 0
c) −3
d) 2
54. The straight line in through the
point (−1, 3, 3) pointing in the direction
of the vector (1, 2, 3) hits the x1x2-plane
at the point
a) Never
b) (−2, 1, 0)
c) (1, 3, 0)
d) (2, −1, 0)
55. The plane in through the point (−1,
3, 3), which is orthogonal to the vector
(1, 2, 3), has the equation
a) x − 2y − 3z = −16
b) x + 2y + 3z = 11
c) −x + 3y + 3z = 14
d) x + 2y + 3z = 14
6 | P a g e Centre for Collaboration of Industry and Institutions (CCII) – www.cmju.in
56. Differentiate the right-hand side of
the following statements to decide which
statement is false.
a)
b)
c)
d)
57. is equal to
a) 21
b) −5/8
c) 15
d) 65/3
58. is equal to
a) 3/8
b) ln 8
c)
d) −3/8
59. Which formula is incorrect?
a)
b)
c)
d)
60. is equal to
a)
b)
c)
d)
61. What is the area bounded by the
graph of y = 8 − x2 and y = x2?
a) 32/3
b) 0
c) −64/3
d) 64/3
62. with p ≠ 1, is equal to
a)
b)
c)
d)
63. is equal to
a) 2
b) 18
c) Does not exist
d) −36/27
64. If for all t and x(2) = 1,
then
a) x(t) = 2 − e−t+2
b)
c) x(t) = e−t
d) x(t) = e2−t
65. for all t > 0 with x(1) =
2 has the solution
a) x(t) = t2 + t
b) x(t) = t + 1
c)
d) x(t) = 2et−1
66. Differentiate the following equation:
a)
b)
c)
d)
7 | P a g e Centre for Collaboration of Industry and Institutions (CCII) – www.cmju.in
67. Differentiate the following equation:
a)
b)
c)
d)
68. Differentiate the following equation:
a)
b)
c)
d)
69. Differentiate the following equation:
, where c and d are
constants.
a)
b)
c)
d)
70. Differentiate the following equation:
a)
b)
c)
d)
No comments:
Post a Comment