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# Business Mathematics 1st Amity Solution

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Q1: Define a subgroup.
Q2: Define complete Graph with the help of examples.
Q3: Explain De Morgan’s Law with examples.
Q4: Explain Tautology with examples.
Q5: Consider the following sample of data.
7, -5, -8, 7, 9, 12, 0, 3, 11, 8, 6, -2, 4, 10

a. What are the mean and median for this dataset?
b. What are the standard deviation and variance?
c. What is the range?

Case Study
“In a survey of 200 students of a College it was found that 120 had laptop, 90 had calculator and 70 had mobile phone, 40 had laptop and calculator, 30 had calculator and mobile phone, 50 had mobile phone and laptop and 20 had none of these gadgets. On the basis of above information answer the following questions.
Q1. Find the number of students of calculator and mobile phone but not laptop.
Q2: Find the number of students of laptop and mobile phone but not calculator.
Q3: How many students have no laptop?

Assignment – C
QUESTION 1: The complement of the union of two sets is the intersection of their complements and the complement of the intersection of two sets is the union of their complements.These are called.
a. Union laws
b. De Morgan s laws
c. Associative laws
d. Commutative laws

QUESTION 2: Less than Ogive and more than Ogive intersect at
a. Mode
b. Mean
c. Median
d. Lower Quartile

QUESTION 3: A terminal node in a binary tree is called………..
a. Root
b. Leaf
c. Child
d. Branch

QUESTION 4: “The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set ___________.”
a. “{1,2}”
b. “{1,2,5}”
c. “{1,2,6}”
d. “{1,2,5,6}”

QUESTION 5: Mode of a distribution can be obtained from
a. Frequency polygon
b. Histogram
c. Less than type Ogives
d. More than type Ogives

QUESTION 6: Harmonic Mean is useful to find
a. Average speed
b. Average increment
c. Average height
d. None of these

QUESTION 7: The set of all real numbers under the usual multiplication operation is not a group since
a. multiplication is not a binary operation
b. zero has no inverse
c. multiplication is not associative
d. identity element does not exist

QUESTION 8: “Let p:7 is not greater than 4 and q : Paris is in France be two statements. Then, ~(p ? q) is the statement”
a. 7 is greater than 4 or Paris is in France
b. 7 is not greater than 4 and Paris is not in France
c. 7 is not greater than 4 and Paris is in France
d. 7 is greater than 4 and Paris is not in France

QUESTION 9: Binary trees with threads are called as …….
b. Pointer trees
c. Special trees
d. Special pointer trees

QUESTION 10: { – 3 n : n ? Z } IS an abelian group under
a. subtraction
b. division
c. multiplication

QUESTION 11: “If p: Sohan is tall, q: Sohan is handsome, then the statement Sohan is tall or he is short and handsome can be written symbolically as”
a. p ?(~p ?q)
b. p ?(~p ?q)
c. p ?(p ?~q)
d. ~p ?(~p ?~q)

QUESTION 12: Mode in a asymmetrical distribution is
a. Mode = 2Median-3Mean
b. Mode= Median-3Mean
c. Mode = 2Median-Mean
d. Mode = 3Median-2Mean

QUESTION 13: “Standard deviation of series 201,201,201,201,201 is”
a. 201
b. 101
c. 0
d. 1

QUESTION 14: Trees are said ………. if they are similar and have same contents at corresponding nodes.
a. Carbon copy
b. Replica
c. Copies
d. Duplicate

QUESTION 15: “If (G, .) is a group, such that (ab)2 = a2 b2 ? a, b ? G, then G is a/an”
a. commutative semi group
b. abelian group
c. non-abelian group
d. none of these

QUESTION 16: “A={A,S,S,A,S,S,I,N,A,T,I,O,N}, B={P,O,S,S,E,S,S,I,O,N} , Find A?B”
a. “S,S,S,S,I,O,N”
b. “S,S,S,I,O,N”
c. “I,O,N,I,S,S”
d. “S,S,S,I,I,O,N”

QUESTION 17: ” Range of 10,20,30,40,50.60 is ”
a. 40
b. 30
c. 20
d. 50

QUESTION 18: Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are respectively
a. “6,3”
b. ” 8,5″
c. “4,1”
d. ” 5,5″

QUESTION 19: “Median of 4,6,7,8,11 is”
a. 6
b. 7.5
c. 8
d. 7

QUESTION 20: A connected graph T without any cycles is called
a. free graph
b. circular graph
c. non cycle graph
d. none of these

QUESTION 21: The best measure of dispersion is
a. Range
b. Mean deviation
c. Standard deviation
d. Inter Quartile Range

QUESTION 22: Two sets are called disjoint if there _____________ is the empty set.
a. Union
b. Difference
c. Intersection
d. Complement

QUESTION 23: Mode of a distribution can be obtained from
a. Frequency polygon
b. Histogram
c. Less than type Ogives
d. More than type Ogives

QUESTION 24: Which of the following statements is a tautology
a. (~ q ?p) ?(p ?~p)
b. ((~q) ?p) ?q
c. (~q ?p) ?(p ?~p)
d. (p ?q) ?(~(p ?q))

QUESTION 25: Which of the following is a statement?
a. Open the door
c. Switch on the fan
d. Two plus two is four

QUESTION 26: “If a, b are the elements of a group G, then (ba)-1?”
a. a-1 b-1
b. b-1 a-1
c. a-1 b
d. b-1 a
amity solved assignments for mba and bba
QUESTION 27: Geometric Mean is useful to find
a. Average speed
b. Average increment
c. Average height
d. Average marks

QUESTION 28: ” Mean of 50,9,8,7,6, is”
a. 5
b. 16
c. 7
d. 6.5

QUESTION 29: Determine the total number of subsets of the following set:
a. 32
b. 64
c. 128
d. 14

QUESTION 30: A monoid is always a
a. A group
b. a commutative group
c. semi – group
d. a non abelian group

QUESTION 31: There are 8 students on the curling team and 12 students on the badminton team. What is the total number of students on the two teams if three students are on both teams:
a. 17
b. 20
c. 4
d. 14

QUESTION 32: “If A and B are any two sets,Then A ? (A ? B) is equal to.”
a. B
b. A
c. BC
d. AC

QUESTION 33: “1,2,3,4,5,6,7,y,9,9 ,10, 12,14,16. From above 14 observations we find that median is 8. The value of y is”
a. 7
b. 8
c. 8.5
d. 9

QUESTION 34: The set of intelligent students in a class is
a. Null set
b. Finite set
c. Not a well defined collection
d. Singleton set

QUESTION 35: Marks of a student is an example of
a. An attribute
b. A discrete variable
c. A continuous variable
d. None of these

QUESTION 36: ” Consider the statement, If n is divisible by 30 then n is divisible by 2 and by 3 and by 5. Which of the following statements is equivalent to this statement?”
a. (a) If n is not divisible by 30 then n is divisible by 2 or divisible by 3 or divisible by5
b. (b) If n is not divisible by 30 then n is not divisible by 2 or not divisible by 3 or not divisible by 5.
c. (c) If n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30
d. (d) If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30.

QUESTION 37: Semi Inter Quartile Range is
a. Q? +Q?
b. Q? – Q?
c. Q? /Q?
d. {Q? – Q?}/2

QUESTION 38: coefficient of Range is
a. {L+S/L-S}
b. {L-S / L+S}
c. {2L-S/S-2L}
d. None of these

QUESTION 39: “Standard deviation of 1,2,3,4,5,6,7 is”
a. 2
b. 3
c. 4
d. 5

QUESTION 40: Which of the following is not a measure of dispersion?
a. Range
b. Mode
c. Inter Quartile range
d. Standard deviation

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