BC0033 Basic Mathematics MQP
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Transcript of BC0033 Basic Mathematics MQP
Model Question Paper
Subject Code: BC0033
Subject Name – Basic Mathematics
Credits: 4 Marks: 140
Part-A – (1 mark questions)
1. A set is a collection of ………… ………….. objects
a) well taken
b) well defined
c) well selected
d) well arranged
2. A set containing no element is called as a ……. ………..
a) null set
b) singleton
c) superset
d) subset
3. The elements of the set are called as
a) numbers
b) objects
c) points
d) terminals
4. If the number of elements in a set is finite, then it is called a ……….. ………
a) infinite set
b) universal set
c) finite set
d) void set
5. The number of distinct elements in a set is called as the ………. ………. of that set
a) cardinal number
b) number
c) object
d) signature
6. The conjunction of two propositions p and q is the proposition ……….
a) pq
b) pq
c) pq
d) pq
7. The propositions which are constructed by combining two or more simple propositions with
the use of certain words is known as
a) molecules
b) connectives
c) connectors
d) contacts
8. The ……….. of a proposition is generally formed by introducing the word „not‟ at a proper
place in the proposition.
a) negation
b) truth value
c) contrapositive
d) converse
9. …………….. is a semigroup which satisfies the identity property.
a) Monoid
b) Ring
c) Group
d) Field
10. …………… is of importance in design of port address.
a) Ring theory
b) Group theory
c) Field theory
d) Commutative theory
11. Consider the operation ab = a + b where a, b Z, then is…………. On Z
a) a binary operation
b) not a binary operation
c) additive
d) commutative
12. A non-empty subset H of G is a subgroup of (G,) if and only if for any pair of elements
Hba ,
a) Hba
b) Hab
c) Hba 1
d) Hab 1
13. Let (G,) be a group and (H,) be a subgroup of (G,). Then for any a G, Ha is called
a) left coset of H in G
b) right coset of H in G
c) coset of H in G
d) subset of G
14. Intersection of any two subgroups of a group is again a ………..
a) ring
b) field
c) division group
d) subgroup
15. In a finite group (G,), the order of every subgroup (H,) ………. the order of (G,).
a) subtracts
b) adds to the
c) divides
d) is multiple of
16. A graph with p points and q lines is called a ………….. graph
a) (q, p) graph
b) pCq
c) qCp
d) (p, q) graph
17. A line joining a point to itself is called a ……………
a) parallel line
b) congruent lines
c) loop
d) triangle
18. If more than one line is joining two points, the resulting graph is called a
a) multiple graph
b) multi graph
c) parallel graph
d) join graph
19. A graph whose edge set is empty is called a …………. ……….
a) null graph
b) complete graph
c) equal graph
d) parallel graph
20. Collection of elements or cases for a particular purpose is called a ………..
a) general case
b) profile
c) data
d) sample space
21. Statistics is affected to a marked extent by a …………… of causes
a) group
b) variety
c) multiplicity
d) number
22. Data in statistics is collected in a systematic manner with a …………….. purpose
a) predetermined
b) fixed
c) varied
d) arranged
23. A man and a woman have to be selected from a group of 4 men and 5 women. In how many
ways can the selections be made?
a) 9 ways
b) 1 way
c) 12 ways
d) 20 ways
24. 34P
a) 24
b) 20
c) 25
d) 18
25. The product of first n natural numbers is called as …………..
a) factorial n
b) square of n
c) square root of n
d) multiple of n
26. If 5040nnP then n =
a) 6
b) 5
c) 4
d) 7
27. If the letters of the word FATE are arranged as in a dictionary. What is the rank of this word?
a) 12
b) 13
c) 14
d) 11
28.The number of permutations of the letters of the word „INSTITUTION‟ is
a) !3!2!3
!11
b) !2!3
!11
c) !2!2!3
!11
d) !2!2
!11
29. The experiment of “Tossing a coin” is a ……………. ………….
a) random variable
b) random experiment
c) experiment
d) light experiment
30. The set of all possible outcomes of a random experiment is the ………….. ………….
a) random space
b) sample space
c) random sample
d) sample space
31. …………. is a subset of a sample space.
a) event
b) experiment
c) sample space
d) random variable
32. An event which doesnot contain any outcome is a …………… ……….
a) complete event
b) regular event
c) null event
d) variable event
33. 22 cossin
a) – 1
b)1
c) 0
d) not defined
34. 4
sec
a) 2
1
b) 2
1
c) 2
d) 2
35. 3
cos
ec
a) 2
3
b) 3
2
c)1
d) 0
36. and …….. are called as complimentary angles
a) 90 –
b) 90 +
c) 90
d) – 90
37. If is any angle then …………… where n is any integer are called angles allied to .
a)
2n
b)
2n
c)
2
n
d)
2n
38. cot(–) =
a) – cot
b) cot
c) cot
1
d) cot
1
39.
43
123lim
2
23
1 xx
xxx
x=
a) 8
4
b) 8
3
c) 8
5
d) 8
7
40.
5
25lim
2
5 x
x
x
a) –10
b) 10
c) 20
d) 12
Part-B - 2 marks questions
41.
2
2lim
33
2 x
x
x
a) 323
2
b) 6
1
23
2
c) 2
3
23
2
d) 3
2
3
42.
3
2222 .....321lim
n
n
n
a) 3
1
b) 3
2
c) 3
7
d) 3
4
43.
n
n n
n2
1lim
a) 3
1
e
b) 4
1
e
c) 2
1
e
d) 7
1
e
44. f(x) is continuous at an interior point c if and only if
a) )(lim xfcx
b) )(lim cfcx
c) )()(lim cfxfcx
d) )()(lim afxfax
45. If „f‟ is finitely differentiable at every point c then „f‟ is …………. at c
a) not differentiable
b) continuous
c) not continuous
d) alternating
46. If 74)( xxxf then )(xf
a) xx 74 3
b) 53 74 xx
c) 63 74 xx
d) 53 7xx
47. If xxy sin then dx
dy
a)
2
sin sinlogcos
x
xxxx x
b)
x
xxx x sin
cossin
c)
x
xxxx x sin
logcossin
d)
x
xx x sinsin
48. If )cos(sin,)sin(cos ayax then 2
2
dx
yd is equal to
(a)
a
3sec
b) a
3sec
c)
2
3sec
a
d) sec
1
49. dxmxsinh
(a) x
mxcosh
b) x
mxsinh
c) m
mxcosh
d) x
mx2cosh
50. dxx2tan
a) cxx tan
b) cxx tan
c) cxx tan
d) cxx 2tan
51. dxxx cos
a) cxxx 2cossin
b) cxxx cossin
c) cxxx cossin
d) cxxx cossin
52.
dx
xx
x1
0
2 1
12
a) 4loge
b) 2loge
c) 3loge
d) 5loge
53. 1
0
dxxex
a) 1
b) 2
c) 3
4) 0
54. If n is a integer then ni )sin(cos
a) sincos i
b) nisincos
c) sincos in
d) nin sincos
55. If cos21
xx then
r
r
xx
1
a) 2
b) 0
c) cosr
d) 2cosr
56. Exponential form of x + iy =
a) ie
b) ire
c) ire
d) re
57. sinhx =
a) 2
xx ee
b) 2
xx ee
c) 2
xx ee
d) 2
2 xx ee
58. xxh 22 tanhsec
a) 2
b) 0
c) 1
d) 3
59. Cosh3x =
a) xx 23 cosh3cosh4
b) xx cosh3cosh4 2
c) xx cosh4cosh3 3
d) xx cosh3cosh4 3
60. If iei )tan( , then
a)
22tanlog
2
1
b)
24tanlog
c)
24tanlog
2
1
d)
22tanlog2
Part-C - 4 marks questions
61. The logarithm of a complex number has an infinite number of values and is therefore a
……….. ………… function.
a) single-valued
b) multi-valued
c) one-one function
d) onto function
62. The general solution of Log(–i) =
a)
2
12ni
b)
2
12n
c)
2
12 2ni
d)
4
12ni
63. If 0coscoscossinsinsin then 3sin3sin3sin
a) )2sin(3
b) )22sin(3
c) )sin(3
d) )sin(
64. A matrix in which number of rows equal to the number of columns is known as
a) Column matrix
b) Square matrix
c) Row matrix
d) Scalene matrix
65. If
200
121
031
A and
211
321
432
B then AB =
a)
422
411
1395
b)
432
411
1395
c)
422
411
1395
d)
422
411
1395
66. The inverse of the matrix
112
211
121
A is
a)
351
135
513
14
1
b)
351
135
513
14
1
c)
351
135
513
14
1
d)
351
135
513
14
1
67. The solution of the equations 3x + y + 2z = 3
2x – 3y – z = –3
x + 2y + z = 4 by Matrix method is
a) x = 1, y = 2, z = 1
b) x = 1, y = – 2, z = 1
c) x = 1, y = – 2, z = – 1
d) x = 1, y = 2, z = – 1
68. The rank of the matrix
562
241
321
A is
a) 1
b) 2
c) 3
d) 4
69. Consider the series ......43
1
32
1
21
1
, this series is
a) divergent
b) convergent
c) oscillating
d) neither (a) nor (b)
70. The series .....321 222
a) converges to 0
b) diverges to –
c) converges to –1
d) diverges to
71. The series ......1 2rr converges if
a) 1r
b) 1r
c) 1r
d) r = 0
72. The sum of .........15010050
33183
10050
183
50
3
a) 17
10 5
1
b) 17
10 5
1
c) 15
10 5
1
d) 17
12 5
1
73. The sum of to........!7
6
!5
4
!3
2is
a) e2
1
b) e3
1
c) e
1
d) e5
1
74. The probability that shooter A hits a target is 3
1. The probability that shooter B hits is
4
1. If
each of them shoot at the target, what is the probability that the target is hit by them?
(a) 0.5 (b) 0.3 (c) 0.6 (d) 0.7
75. The value of x from 26
sec4
tan4
sin3
cos)32( 22
22
xecx is
a) 3
5
b) 2
5
c) 4
5
d) 8
5
Subject Name: BC0033 – Mathematics(Bk id B0675)
Answer Keys -
Part - A Part - B Part - C
Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key Q. No. Ans. Key
1 B 21 C 41 B 61 B
2 A 22 A 42 A 62 A
3 B 23 A 43 C 63 C
4 C 24 A 44 C 64 B
5 A 25 A 45 B 65 D
6 A 26 D 46 C 66 A
7 B 27 C 47 C 67 D
8 A 28 A 48 A 68 B
9 A 29 B 49 C 69 B
10 B 30 D 50 C 70 D
11 A 31 A 51 B 71 B
12 C 32 C 52 C 72 A
13 B 33 B 53 A 73 C
14 D 34 C 54 D 74 A
15 C 35 B 55 D 75 C
16 D 36 A 56 C
17 C 37 D 57 A
18 B 38 A 58 C
19 A 39 C 59 D
20 C 40 A 60 C