Soved MCQ's MTH202 Final Term

http://www.allvupastpapers.blogspot.com/  

1) If A and B are two disjoint (mutually exclusive) events

then

P(AUB) =

► P(A) + P(B) + P(ACB)

► P(A) + P(B) + P(AUB)

► P(A) + P(B) - P(ACB)

► P(A) + P(B) - P(ACB)

► P(A) + P(B)

2) If p=It is red,

q=It is hot

http://www.allvupastpapers.blogspot.com/  

Then, It is not red but hot is denoted by ~ pU ~ q

► True

► False

3) If ( AUB ) = A, then ( AnB ) = B

► True

► False

► Cannot be determined

http://www.allvupastpapers.blogspot.com/  

How many integers from 1 through 1000 are neither multiple

of 3 nor multiple of 5?

► 333

► 467

► 533

► 497

The value of xfor -2.01 is

► -3

► 1

► -2

http://www.allvupastpapers.blogspot.com/  

What is the expectation of the number of heads when three

fair coins are tossed?

► 1

► 1.34

► 2

► 1.5

http://www.allvupastpapers.blogspot.com/  

Every relation is

► function

► may or may not function

► bijective mapping

► Cartesian product set

The statement p . q o (p Rq)U(q Rp) describes

► Commutative Law

► Implication Laws

► Exportation Law

► Equivalence

http://www.allvupastpapers.blogspot.com/  

The square root of every prime number is irrational

► True

► False

► Depends on the prime number given

A predicate is a sentence that contains a finite number of

variables and becomes a statement when specific values are

substituted for the variables

► True

► False

► None of these

http://www.allvupastpapers.blogspot.com/  

If r is a positive integer then gcd(r,0)=

► r

► 0

► 1

► None of these

http://www.allvupastpapers.blogspot.com/  

Associative law of union for three sets is

► A E (B E C) = (A E B) E C

► A C (B C C) = (A C B) C C

► A E (B C C) = (A E B) C (A E B)

► None of these

http://www.allvupastpapers.blogspot.com/  

Values of X and Y, if the following order pairs are equal.

(4X-1, 4Y+5)= (3,5) will be

► (x,y) = (3,5)

► (x,y) = (1.5,2.5)

► (x,y) = (1,0)

► None of these

http://www.allvupastpapers.blogspot.com/  

The expectation of x is equal to

► Sum of all terms

► Sum of all terms divided by number of terms

► axf (x)

A line segment joining pair of vertices is called

► Loop

► Edge

► Node

http://www.allvupastpapers.blogspot.com/  

The indirect proof of a statement pq involves

► Considering ~q and then try to reach ~p

► Considering p and ~q and try to reach contradiction

► Considering p and then try to reach q

► Both 2 and 3 above

The greatest common divisor of 5 and 10 is

► 5

► 0

► 1

► None of these

http://www.allvupastpapers.blogspot.com/  

Suppose that there are eight runners in a race first will get

gold medal the second will get siver and third will get bronze.

How many different ways are there to award these medals if

all possible outcomes of race can occur and there is no tie.

► P(8,3)

► P(100,97)

► P(97,3)

► None of these

The value of 0! Is

► 0

► 1

► Cannot be determined

http://www.allvupastpapers.blogspot.com/  

A sub graph of a graph G that contains every vertex of G and

is a tree is called

► Trivial tree

► empty tree

► Spanning tree

http://www.allvupastpapers.blogspot.com/  

In the planar graph, the graph crossing number is

► 0

► 1

► 2

► 3

A matrix in which number of rows and columns are equal is called

► Rectangular Matrix

► Square Matrix pg296

► Scalar Matrix

http://www.allvupastpapers.blogspot.com/  

Changing rows of matrix into columns is called

► Symmetric Matrix

► Transpose of Matrix

► Adjoint of Matrix

http://www.allvupastpapers.blogspot.com/  

If A and B are finite (overlapping) sets, then which of the

following must be true

► n(AUB) = n(A) + n(B)

► n(AEB) = n(A) + n(B) - n(ACB)

► n(AEB)= o

► None of these

http://www.allvupastpapers.blogspot.com/  

When 3k is even, then 3k+3k+3k is an odd.

► True

► False

When 5k is even, then 5k+5k+5k is odd.

► True

► False

http://www.allvupastpapers.blogspot.com/  

The product of the positive integers from 1 to n is called

► Multiplication

► n factorial

► Geometric sequence

The expectation m for the following table is

xi 1 3

f(xi) 0.4 0.1

► 0.5

► 3.4

► 0.3

► 0.7

http://www.allvupastpapers.blogspot.com/  

If p= A Pentium 4 computer,

q= attached with ups.

The given graph is

► Simple graph

► Complete graph

► Bipartite graph

► Both (i) and (ii)

► Both (i) and (iii)

http://www.allvupastpapers.blogspot.com/  

P(n) is called proposition or statement.

► True

► False

An integer n is odd if and only if n = 2k + 1 for some integer k.

► True

► False

► Depends on the value of k

http://www.allvupastpapers.blogspot.com/  

By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com

MTH202 Solved subjective

http://www.allvupastpapers.blogspot.com/  

Question: Write the types of functions.

Answer: Types of function:- Following are the types of function

1. One to one function 2. Onto function 3. Into

function 4. Bijective function (one to one and onto

function) One to one function:- A function f : A to B is

said to be one to one if there is no repetition in the

second element of any two ordered pairs. Onto

function:- A function f : A to B is said to be onto if

Range of f is equal to set B (co-domain). Into

function:- A function f : A to B is said to be into

function of Range of f is the subset of set B (co

domain) Bijective function: Bijective function:- A

function is said to be Bijective if it is both one to one

and onto.

Question: Explain the pigeonhole principle.

http://www.allvupastpapers.blogspot.com/  

Question: What is conditional probability with example?.

http://www.allvupastpapers.blogspot.com/  

Question: Explain combinatorics.

http://www.allvupastpapers.blogspot.com/  

Answer: Branch of mathematics concerned with the selection,

arrangement, and combination of objects chosen from

a finite set.

The number of possible bridge hands is a simple

example; more complex problems include scheduling

classes in classrooms at a large university and

designing a routing system for telephone signals. No

standard algebraic procedures apply to all

combinatorial problems; a separate logical analysis may

be required for each problem.

Question: How the tree diagram use in our real computer life?

http://www.allvupastpapers.blogspot.com/  

Answer: Tree diagrams are used in data structure, compiler

construction, in making algorithms, operating system

etc.

Question: Write detail of cards.

http://www.allvupastpapers.blogspot.com/  

Answer: Diamond Club Heart Spade A A A A 1 1 1 1 2 2 2 2 3 3

3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10

10 10 10 J J J J Q Q Q Q K K K K Where 26 cards are

black & 26 are red. Also ‘A’ stands for ‘ace’ ‘J’ stands

for ‘jack’ ‘Q’ stands for ‘queen’ ‘K’ stands for ‘king’

Question: what is the purpose of permutations?

http://www.allvupastpapers.blogspot.com/  

Answer: Definition:- Possible arrangements of a set of objects

in which the order of the arrangement makes a

difference. For example, determining all the different

ways five books can be arranged in order on a shelf. In

mathematics, especially in abstract algebra and

related areas, a permutation is a bijection, from a

finite set X onto itself. Purpose of permutation is to

establish significance without assumptions

http://www.allvupastpapers.blogspot.com/  

By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com

MTH202 Final Term Solved Subjective questions

Question: What is sequence and series?

http://www.allvupastpapers.blogspot.com/  

Answer: Sequence A sequence of numbers is a function defined

on the set of positive integer. The numbers in the

sequence are called terms. Another way, the sequence

is a set of quantities u1, u2, u3... stated in a definite

order and each term formed according to a fixed

pattern. U r =f(r) In example: 1,3,5,7,... 2,4,6,8,... 1 2 ,−

2 2 ,3 2 ,− 4 2 ,... Infinite sequence:- This kind of

sequence is unending sequence like all natural numbers:

1, 2, 3, ... Finite sequence:- This kind of sequence

contains only a finite number of terms. One of good

examples are the page numbers. Series:- The sum of a

finite or infinite sequence of expressions. 1+3+5+7+...

Question: Differntiate contigency and contradiction.

http://www.allvupastpapers.blogspot.com/  

Question: What is conditional statement, converse, inverse and

contra-positive?

http://www.allvupastpapers.blogspot.com/  

Question: What is Euclidean algorithm?

http://www.allvupastpapers.blogspot.com/  

Answer: In number theory, the Euclidean algorithm (also called

Euclid's algorithm) is an algorithm to determine the

greatest common divisor (GCD) of two integers.

Its major significance is that it does not require

factoring the two integers, and it is also significant in

that it is one of the oldest algorithms known, dating

back to the ancient Greeks.

Question: what is the circle definition?

http://www.allvupastpapers.blogspot.com/  

Answer: A circle is the locus of all points in a plane which are

equidistant from a fixed point. The fixed point is

called centre of that circle and the distance is called

radius of that circle

Question: What is bi-conditional statement?

http://www.allvupastpapers.blogspot.com/  

Question: Explain the difference between k-sample, k-selection,

k-combination and k-permutation.

http://www.allvupastpapers.blogspot.com/  

Question: What is meant by Discrete?

http://www.allvupastpapers.blogspot.com/  

Answer:

A type of data is discrete if there are only a finite

number of values possible. Discrete data usually occurs

in a case where there are only a certain number of

values, or when we are counting something (using whole

numbers). For example, 5 students, 10 trees etc.

Question: Explain D'Morgan Law.

http://www.allvupastpapers.blogspot.com/  

Question: What are digital circuits?

http://www.allvupastpapers.blogspot.com/  

Answer: Digital circuits are electric circuits based on a number

of discrete voltage levels.

In most cases there are two voltage levels: one near to

zero volts and one at a higher level depending on the

supply voltage in use. These two levels are often

represented as L and H.

Question: What is absurdity or contradiction?

http://www.allvupastpapers.blogspot.com/  

Answer: A statement which is always false is called an

absurdity.

Question: What is contingency?

http://www.allvupastpapers.blogspot.com/  

Answer: A statement which can be true or false depending upon

the truth values of the variables is called a

contingency.

Question: Is there any particular rule to solve Inductive Step in

the mathematical Induction?

http://www.allvupastpapers.blogspot.com/  

Answer: In the Inductive Step, we suppose that the result is

also true for other integral values k. If the result is

true for n = k, then it must be true for other integer

value k +1 otherwise the statement cannot be true.

In proving the result for n = k +1, the procedure

changes, as it depends on the shape of the given

statement.

Following steps are main:

1) You should simply replace n by k+1 in the left

side of the statement.

2) Use the supposition of n = k in it.

3) Then you have to simplify it to get right side

of the statement. This is the step,

where students usually feel difficulty.

Here sometimes, you have to open the brackets,

or add or subtract some terms

or take some term common etc. This step of

simplification to get right side of the given

statement for n = n + 1 changes from question to

question.

Now check this step in the examples of the

Lessons 23 and 24.

Question: What is Inclusion Exclusion Principle?

http://www.allvupastpapers.blogspot.com/  

Question: What is recusion?

http://www.allvupastpapers.blogspot.com/  

Question: Different notations of conditional implication.

http://www.allvupastpapers.blogspot.com/  

Answer: If p than q. P implies q. If p , q. P only if q. P is

sufficient for q.

Question: What is cartesion product?

http://www.allvupastpapers.blogspot.com/  

Answer: Cartesian product of sets:- Let A and B be sets. The

Cartesian product of A and B, denoted A x B (read “A

cross B”) is the set of all ordered pairs (a, b), where a

is in A and b is in B. For example: A = {1, 2, 3, 4, 5, 6} B

= {a} A x B = {(1,a), (2,a), (3,a), (4,a), (5,a)}

Question: Define fraction and decimal expansion.

http://www.allvupastpapers.blogspot.com/  

Answer: Fraction:- A number expressed in the form a/b where

a is called the numerator and b is called the

denominator. Decimal expansion:- The decimal

expansion of a number is its representation in base 10

The number 3.22 3 is its integer part and 22 is its

decimal part The number on the left of decimal point is

integer part of the number and the number on the

right of the decimal point is decimal part of the

number.

Question: Explane venn diagram.

http://www.allvupastpapers.blogspot.com/  

Answer: Venn diagram is a pictorial representation of sets.

Venn diagram can sometime be used to determine

whether or not an argument is valid. Real life problems

can easily be illustrate through Venn diagram if you

first convert them into set form and then in Venn

diagram form. Venn diagram enables students to

organize similarities and differences visually or

graphically. A Venn diagram is an illustration of the

relationships between and among sets, groups of

objects that share something in common

http://www.allvupastpapers.blogspot.com/  

By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com