MTH202 Final Term Solved Subjective questions

Question: What is sequence and series?

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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.

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Question: What is conditional statement, converse, inverse and

contra-positive?

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Question: What is Euclidean algorithm?

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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?

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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?

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

k-combination and k-permutation.

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Question: What is meant by Discrete?

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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.

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Question: What are digital circuits?

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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?

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Answer: A statement which is always false is called an

absurdity.

Question: What is contingency?

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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?

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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?

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Question: What is recusion?

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Question: Different notations of conditional implication.

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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?

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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.

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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.

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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

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By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com