mathes

Part C
4 Marks Questions


82) if A={ x/xN and x<3 } B={x/x2-16=0 and x<0}
find BXA where N is a set of natural nos
a) {(1,2),(1,4)} b) {(-4,1),(-4,2)}
c) {(1,-4),(2,-4)} d) {1,2,3,4}

83) Let A={1} B={2,3,4} c={3,4,5}
Which of the following bits are true
i) A(BUC)=(AB)U(AC) ii) AU(BC)=(AUB) (AUC)
iii) (A-B) B-C =A-(B-C) iv) None of these

a) i & ii b) ii & iii c) iii & ii d) None

84) U={a, b, c, d, e, f, g, h, k} A={a, b, c, g} B={d, e, f, g} C={a, e, f} D={f, g, h} Compute AUB ,AUBC ,A (BUC)
,(CD)c respectively
a) {a, b, c, d, e, f, g} {a, e, f}, {a, g} { a, b, c, d, e, g, h, k}
a) {a, e, f} {a, f} {a, b, c, d, e} {a}
b) {a, b, c, e, f, g} {a, g, d} {a, e} {b}
c) {a, b, c} { b, c, d}{ c, d, e} {f}

85) p : Two lines are perpendicular
q : they intersect at right angle
What is pq write truth table for the select any one of the below answer

i) pq: two lines one intersecting at the right angle if and only if those lines are perpendicular
ii. pq two lines are perpendicular if and only if they intersect at right angle
iii
P Q p->q q->p pq
T T T T T
T F F T F
F T T T F
F F T T t

iv
P Q p->q q->p pq
T T T T T
T F F T F
F T F F F
F F T T T

a) i & ii b) ii & iii c) i & iv

86) If x=3 then x2+x-12 = then given example can be symbolized follows
i. p: x=3
q: x2+x-12=-0 p->q

ii. p:x=3
q:x2+x-12=0
q->p

iii p: x=3
q: x2+x-12=0 (~p->~q)

then x<>3

iv. if x2+x-12<>0
then x<>3 (~q->~p)

a) i &ii b) i & iv c) iii & ii

87) Circuits for each of the following are 1
PV(Qr) p(pvp) pqv r


i p ii. p

q r q


iii. p
p p



iv. p q
r

a) i & ii & iii b) i & iii & iv c) i & iv

88) Find the identity element and inverse element in the expression a*b =a+b+3.for a
a)-3 ,6+a b) –3,-6-a c)3,6+a d) 6,3a

89) is a
a) Monoid b) semi group c) group d) none

90) For the corollary : In any graph G the no of pts of odd degree is even
a) Let V1,v2..vk denote pts of odd degree and w1,w2,…wm denote the pt of even degree in G k+m=p
We know that  deg vi =2p
i=1 k=1 m
Here  deg vi+ deg vi ++wi =2p which is even and further  deg vi is even and further m
 deg wi is even
i=1
Hence k
 deg iv is also even
i=1
K must be even

b) deg vi =2q where q is no of edges
i=1
k
hence deg vi +deg vi=2q even

further  deg wi is even
i=1
k
  deg vi is even
i=1
 k is even


c)  deg vi =3q where q is no. of edges
i=1 m
Hence deg vi+deg vi=3q
i=1 i=1
m
 deg wi is even
i=1

k
 vi also even
i=1

k is even

d) None



91) Let G be a K-regular bipartite graph with (v1,v2) and k>0 then
a) |v1|=|v2| b) |v1|<>|v2| c)|v1+v2|=| v1|-|v2| d) None

92) Which f the following rules are necessary group data for drawing histograms
i The internals should be equal size
ii. The number of internals should be between 5&15
iii. The internals can never overlap each other if an internal each width a no then the following internal begin
with the next number
iv. Any score to be tallied can fall into one and only one internal

a) i & ii b) i, ii & iii c) i , ii, iii & iv d) None

93) Calculate the mean of the marks obtained by 13 students
marks 0-10 10-20 20-30 30-40 40-50
no of students 2 10 12 18 4

a) 27 b) 27.61 c) 20 d) 26.71

94) Obtain the median for the following distribution of error committed by computer operators
no of errors 0-10 10-20 20-30 30-40 40-50
no of operators 8 78 12 10 2

a) 19.44 b) 18.44 c) 17.44 d) 16.44

95) A fancy match was played to raise the fund for cancer patients .in Indian sample of 200 tickets solo, following
observations were found tickets of which denomination were sold in the largest quantity
cost of tickets 1 3 5 10 25 50
no of tickets 24 26 50 70 20 10

a) 50 b) 70 c) 10 d) 25

96) The income of 80 families are given below
income 400-600 600-800 800-1000 1000-1200
families 10 15 35 20

a) 800 b) 914 c) 914 d) 944

97) The probability that a regular scheduled flight depart on time is 0.83 the probability that is arrives on time is 0.82 and
the probability that it departs and arrives on time is 0.78
Find the probability that a plane
i. Arrives on time
ii. Depart on time given that it has arrived on time
a) 0.78,0.94 b) 0.68,0.84 c) 0.8 , 0.9 d) 1,0.94

98) An office has 4 secretaries handling respectively 20% 60% 15% 5% of the files of all govt reports the probability that
they must fill such reports are respectively 0.05,
0. 1 ,0.1 0.05

Find the probability that a misfiled report can be placed on the first secretary
a) 0.1122 b) 0.11 c) 0.1143 d) None

99) The factories produces identical clocks the product of the first factory consists of 10000 clocks of which 100 are
defective .The second factory produces 20,00 clocks of which 300 are defective .What is the probability that a
particular defective clock was produced by the first factory
a) 1.5 b).25 c) 0.50 d) None



100) A lot consist of 10 good articles 4 with minor defects and 2 with major defects one article is chosen at random find
the probability that
i. It has no defects
ii It has no major defects
iii. It is either good or has major defects

a) 10/116 b) 14/16 c) 12/16 d) None
i) a & b ii) a & b & c iii) b & c, d

101) Two dice are thrown find the probability that the sum of the number is 10 ,given that the first die shows 6
a) 1/6 b) 1/10 c) 1/3 d) 1/2


1 2 3 1 2 3 1 2 3 1 2 3
102) Set of permutation p= 1 2 3 p2= 1 3 2 p3= 3 2 1 p4= 2 1 3


1 2 3 1 2 3
p5 = 2 3 1 p6 = 3 1 2




is a
a) A group b) An abelian group c) Only a monoid d) Only semi group

103) A (p, q) graph has t pts of degree m and all other pts are of degree n then 2q=?

a) qn+(m-n)t b) pm+(m-n)t
c) pn+(m-n)t d) p+(m-n)t



104) Calculate mean, median class and modal class the data relating to weight of 120 articles of
weight in gm 0-10 10-20 20-30 30-40 40-50 50-60
no of articles 14 17 22 26 23 18

a) 39.5, 40-50, 30-40, 16.66666667
b) 29.5, 20-30, 40-50, 15.66667
c) 29 20-30 40-50 15.66667
d) None



Key for Mathematics



Part – A
1 A 2 D 3 C 4 A 5 B 6 B 7 C
8 D 9 A 10 C 11 A 12 D 13 D 14 B
15 C 16 A 17 C 18 D 19 A 20 A 21 A
22 B 23 C 24 C 25 D 26 D 27 A 28 C
29 B 30 C 31 B 32 A 33 C 34 A 35 A
36 B 37 C 38 B 39 B 40 B 41 A 42 A
43 B 44 4 45 C 46 B 47 B 48 B 49 B
50 B 51 B 52 C 53 C

Part –B
54 D 55 A 56 B 57 A 58 A 59 A 60 B
61 B 62 A 63 C 64 B 65 C 66 A 67 C
68 C 69 B 70 C 71 A 72 B 73 D 74 C
75 A 76 C 77 B 78 A 79 D 80 B 81 A

Part -C
82 B 83 I 84 A 85 I 86 II 87 III 88 B
89 C 90 B 91 A 92 III 92 B 94 A 95 C
96 B 97 A 98 C 99 B 100 II 101 A 102 A 103 C 104 A