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Amity MSC IT Sem I Solved Assignment for Basic Mathematics

University  Amity blog
Service Type Blog
Course Assignment
Semester
Short Name or Subject Code Basic Mathematics
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Pattern Section A,B,C Wise
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BLOCK -1
                                                          Introduction to Set Theory
Q1. The set of integers is 
a) Infinite set
Q2. Compliment of a null set can be
Ans) infinite set 
                                                                       Set of theory
Q1. What can be the roaster form of the set A = {x : x is square number less than 30 }
Q2. if A= { 1,2 ,3 ,4 , 5 , 6} then , which of the following is true ?
Venn Diagrams and Set Operations

Q1. What amongst the following is represented by the Venn diagram?

Q2. Red shaded region in the Venn diagram represent .
A∩ B ∩C
                                                      Algebra of sets

Q1. If there is a list of thing including the items A,B,C,D,B,B,Q,F,D,Y then arranging these items in a set would define cardinality of_____
Q2. which amongst the following is true ?
                                                                SET THEORY – MULTISET 
Q1. Multiplicity is defined for _______
Q2. If A and B are multisets as A = {3.a , 2.b} and ={2.a , 3.b ,4.d },then
A- B =________
                                                                  Ordered Pairs
Q1. Which amongst  the following is a representation of an order pair ?
Q2.  order pair ( a, b) and ( b,a) in general are equal.
                                                                Cartesian Product
Q1 if A={ 1,2,3} and B={- 1,4,-3} then which amongst the following is true?
Q2. A U B * C =
                                                             Cartesian Product and Application
Q1. The three-dimensional space R*R*R =R3 includes all order .
Q2. The total number of subsets of the set A*B, when A = { -1,0}and B={ 1,2}is___
                                                                  Fuzzy logic
Q1. The sum of all the truth degrees associated with the difference in variables in a set has to equal to 1.
Q2 Is water is colourless ……The given statements generates _____type of set.
                                                               Fuzzy Set Theories – Basic operations
Q1.__________ consider the maximum of the given degree of  truth for the variable.
Q2. .__________ consider the minimum of the given degree of  truth for the variable.
                                                    Relation
Q1. The set of output values in relation is called ________
Q2. Domain set range set must be having equal number of element for having a relation defined \
                                                       Properties and Type of relations

Q1. If A= {1,2,3} then the relations  R__1 = {(1,1),(2,2),(3,3)(1,3)} is
Q2.If Z* be the set of all non-zero integers and R be the relation on Z * given by ( a,b)  E R if a is a factor of b . Then R is symmetric relation.
                                                                    Equivalence Classes
Q1. For two distinct element of a set their equivalence classes can never be the same
Ans- false 
Q2. if a,b E  A on which an equivalence relation R is defined then if b  E [a] =[b] =[a]
                                                            Equivalence Classes - Application
Q1. For any partition b_1,b_2, b_3 and b_4 of a set   A under an equivalence relation R,( B_1∩B_2) U ( B_3∩_4)
Q2. lf an equivalence relation R defined on the t A generates partitions {x1, x) and p ± (x3 , x}, hen number of elemenu will be there {x1, x) and p ± (x3 , x}, hen number of elemenu will be there
Q1. each element of the set generated by the relation is called_____
Ans- vertex
Q2. which of the following pair fo not belong to the relation represented by the diagram?
Q1. In general the composition RoS is same as SoR.
Q2. The composition RoS having the other pair ( a,c) a E A , c E c , where R be relation from set A to set B and s be relation from set b to C there exist an element  belonging to B called as ______
                                                          Functions-Introduction
Q1. Range of real valued function is always equal to its co – domain.
Q2. which of the following statement is not true?
                                                            Classification and Types of Function
Q1. if in a mapping of a function range set is the subset of co- domain then the function is_______function
Q2. if in a mapping of a function range set is the same set as the co- domain then the function is ______ function
                                              Composition of functions
Q1.  Associate law of function composition can be described as 
Ans-
Q2. If f: A – B and I A : A – A is an identify function , then ( f o I A) (x) = f [

SECTION -A

1. Define a subgroup.   
Ans- 

2. Define complete Graph with the help of examples. 
Ans- 
3. Explain De Morgan’s Law with examples. 
Ans
                                                                                                                                  
4. Explain Tautology with examples.    
ANS- 

                                                   
5.Consider the following sample of data.
  7, -5, -8, 7, 9, 12, 0, 3, 11, 8, 6, -2, 4 ,10
6.Answer the following questions.
a. What are the mean and median for this dataset?

b. What are the standard deviation and variance?

c. What is the range ?

Section B - Case Study


Case 
 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.
Ans- 
Q3. How many students have no laptop?
Ans – 

SECTION-C MCQ

1."If (G, .) is a group, such that (ab)^2 = a^2 . b^2  ∀ a, b ∈ G, then G is a/an"
a)  none of these 
 b) commutative semi group 
 c) non-abelian group 
d)  abelian group

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

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

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

5. Formula for obtaining Median in discrete type of data is ____
a) Both (a) & (b) 
 b) (n+(n+1))/2 
 c) l + (h/f) (n/2 - c)
d)  (n+1)/2 
6. Marks of a student is an example of
 a) None of these 
  b)A discrete variable 
  c)An attribute 
  d)A continuous variable

7. "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) 8 
 b) 7 
 c) 8.5 
  d)9

8. { - 3 n : n ε Z } IS an abelian group under
 a) subtraction 
 b) multiplication 
  c)division 
 d) addition

9. A monoid is always a
a)  a non-abelian group 
b)  semi - group 
 c) a commutative group 
  d)A group

10. The best measure of dispersion is
 a) Mean deviation 
  b)Range 
  c)Standard deviation 
  d)Inter Quartile Range
11. Semi Inter Quartile Range is
 a) {Q₃ - Q₁}/2 
  b)Q₃ - Q₁ 
 c)Q₃ +Q₁ 
 d)Q₃ /Q₁

12. 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)  Commutative laws 
b)  Union laws 
 c) De Morgan s laws 
 d) Associative laws

13. "The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set ___________."
  a)"{1,2,6}"
  b)"{1,2}"
  c)"{1,2,5,6}" 
  d)"{1,2,5}"

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

15. The empty set  is the subset of ________
a)  Only power set 
  b)No set 
  c)Every set 
  d)Only universal set

16. If A = {x/x is a real number, LaTeX: x^2=16\:and\:2x\:=\:6 x 2 = 16 a n d 2 x = 6  }
, then the element(/s) of A can be written as _____
a)  {4,3} 
 b) {φ} 
  c){4} 
  d){3}

17. If A = { 2n/ n is an integer} , B = {3m/ m is an integer} , then the set A LaTeX: \cap ∩  B= ___________
a) {6r / r is a natural number} 
  b) None of the above 
  c){6r / r is an integer} 
  d){∅}

18. A connected graph T without any cycles is called
  a)free graph 
  b)circular graph 
  c)non-cycle graph 
  d)none of these

19. "If A and B are any two sets, Then A ∪ (A ∩ B)  is equal to."
a)  BC 
 b) A 
  c)B 
  d)AC
20. 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"
21. Determine the total number of subsets of the following set:
{1,2,3,4,5,6,7}
a)  14 
b) 32 
c) 64
d) 128
22. Coefficient of Range is
 a) None of these 
  b){L+S/L-S} 
  c){L-S / L+S} 
  d){2L-S/S-2L
23. "If a, b are the elements of a group G, then (ba)^(-1)?"
 a) a^(-1). b 
  b)b^(-1). a 
  c)a^(-1). b^(-1) 
  d)b^(-1). a^(-1)
24. Which of the following is a statement?
 a) Do your homework 
  b)Two plus two is four 
  c)Open the door 
  d)Switch on the fan
25. "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
26. "Let p:7 is not greater than 4 and q : Paris is in France, be two statements. Then, ~(p V 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 in France 
  c)7 is not greater than 4 and Paris is not in France 
  d) 7 is greater than 4 and Paris is not in France
27 Which of the following statements is a tautology
a)  (~q ∧p) ∧(p ∧~p) 
  b) (~ q ∧p) ∨(p ∨~p) 
  c) ((~q) ∧p) ∧q 
  d) (p ∧q) ∧(~(p ∧q)) 
28. Harmonic Mean is useful to find
 a) Average increment 
  b)None of these 
  c)Average height 
  d)Average speed
29. Geometric Mean is useful to find
  a) Average speed 
  b) Average marks 
  c) Average increment
  d) Average height
30. "Standard deviation of series 201,201,201,201,201 is"
  a)1 
  b)0 
  c)101 
  d)201
31. Mode in a asymmetrical distribution is
 a) Mode = 2Median-Mean 
  b)Mode= Median-3Mean 
  c)Mode = 2Median-3Mean 
  d)Mode = 3Median-2Mean
32. "Median of 4,6,7,8,11 is"
 a) 8 
  b)7.5 
  c)7 
  d)6
33. " Mean of 50,9,8,7,6, is"
 a) 16 
  b)5 
  c)6.5 
  d)7
34. "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 Latex:  \cap ∩ B"
a) "S,S,S,I,O,N"
  b)"I,O,N,I,S,S" 
  c)"S,S,S,I,I,O,N" 
  d)"S,S,S,S,I,O,N"
35. " 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)  If n is not divisible by 30 then n is not divisible by 2 or not divisible by 3 or not divisible by 5.
b)  If n is not divisible by 2 or not divisible by 3 or not divisible by 5then n is not divisible by 30.
 c) If n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30
 d) If n is not divisible by 30 then n is divisible by 2 or divisible by 3 or divisible by5
36. 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)14 
  d)4
37. " Standard deviation of 1,2,3,4,5,6,7 is"
 a) 5 
  b)3 
  c)4 
  d)2
38. " Range of 10,20,30,40,50.60 is "
a)  20 
  b)30 
  c)50 
  d)40
39. The set of all real numbers under the usual multiplication operation is not a group since
a) zero has no inverse 
 b) identity element does not exist 
  c)multiplication is not associative 
  d)multiplication is not a binary operation
40. The set of intelligent students in a class is
 a) Not a well-defined collection 
  b)Singleton set 
  c)Null set 
  d)Finite set