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