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Saturday, February 26, 2011

Soved MCQ's MTH202 Final Term

1) If A and B are two disjoint (mutually exclusive) events
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
Then, It is not red but hot is denoted by ~ pU ~ q
3) If ( AUB ) = A, then ( AnB ) = B
Cannot be determined
How many integers from 1 through 1000 are neither multiple
of 3 nor multiple of 5?
The value of xfor -2.01 is
What is the expectation of the number of heads when three
fair coins are tossed?
Every relation is
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
The square root of every prime number is irrational
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
None of these
If r is a positive integer then gcd(r,0)=
None of these
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
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
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
The indirect proof of a statement pq 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
None of these
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.
None of these
The value of 0! Is
Cannot be determined
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
In the planar graph, the graph crossing number is
A matrix in which number of rows and columns are equal is called
Rectangular Matrix
Square Matrix pg296
Scalar Matrix
Changing rows of matrix into columns is called
Symmetric Matrix
Transpose of Matrix
Adjoint of Matrix
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
When 3k is even, then 3k+3k+3k is an odd.
When 5k is even, then 5k+5k+5k is odd.
The product of the positive integers from 1 to n is called
n factorial
Geometric sequence
The expectation m for the following table is
xi 1 3
f(xi) 0.4 0.1
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)
P(n) is called proposition or statement.
An integer n is odd if and only if n = 2k + 1 for some integer k.
Depends on the value of k

By ADEEL ABBAS, Bhakkar.

MTH202 Solved subjective

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.
Question: What is conditional probability with example?.
Question: Explain combinatorics.
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?
Answer: Tree diagrams are used in data structure, compiler
construction, in making algorithms, operating system
Question: Write detail of cards.
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?
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

By ADEEL ABBAS, Bhakkar.

MTH202 Final Term Solved Subjective questions

Question: What is sequence and series?
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.
Question: What is conditional statement, converse, inverse and
Question: What is Euclidean algorithm?
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?
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?
Question: Explain the difference between k-sample, k-selection,
k-combination and k-permutation.
Question: What is meant by Discrete?
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.
Question: What are digital circuits?
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?
Answer: A statement which is always false is called an
Question: What is contingency?
Answer: A statement which can be true or false depending upon
the truth values of the variables is called a
Question: Is there any particular rule to solve Inductive Step in
the mathematical Induction?
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
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
Now check this step in the examples of the
Lessons 23 and 24.
Question: What is Inclusion Exclusion Principle?
Question: What is recusion?
Question: Different notations of conditional implication.
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?
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.
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
Question: Explane venn diagram.
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

By ADEEL ABBAS, Bhakkar.