CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
SMUAPR15
ASSESSMENT_CODE BCA1030_SMUAPR15
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID
QUESTION_TEXT
4984
a.Explain the concept of Venn diagram.
b.Let A = {1, 2, 3} and B = {4, 5}. Find A × B and B × A and show
that A × B ≠ B × A.
c.Discuss the convergence of the series
SCHEME OF
EVALUATION
a.Most of the relationship between sets can be represented by means
of diagrams. Figures representing sets in the form of enclosed region
in the planes are called Venn diagrams named after British logician
John Venn. The universal set U is represented by the interior of a
rectangle. Other sets are represented by the interior of circles.
b.A X B= {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}
And B X A={(4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (5, 3)}
Note that (1, 4) belongs to A X B but it does not belong to B X A.
Hence the proof.
c. The series is of the form:
1+(1/2)+(1/4)+(1/8)+…+[(1/2)]^(n-1)
Therefore the partial sums,
S1=1, S2=(3/2) S3=(7/4)…..
Here the sequence of partial sums converges. Hence the sequence
given also converges. (Using the principle of partial sums)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
4986
QUESTION_TEXT
Define a group and give one example.
SCHEME OF
EVALUATION
Definition of Group:
A non-empty set G is said to be a group with respect to the binary
operation * if the following axioms are satisfied:
a.Closure law: For every a, b in G, a*b belongs to G
b.Associative law: For every a, b, c in G,
a*(b*c)=(a*b)*c
c.Existence of identity element: There exists an element e in G such
that a*e=e*a=a for every a in G.
d.Existence of inverse: For every a in G, there exists an element b in
G such that,
a*b=b*a=e. here b is called the inverse of a.
a group G with respect to binary operation * is denoted by(G, *)
Example:
The set Z of integers is a group with respect to the usual addition as
the binary operation.
a.Closure law: We know that the sum of two integers is also an
integer. Hence for every m, n in Z, m+n belongs to Z.
b.Associative law: It is well known that the addition of integers is
associative
c.Existence of identity element: There exists 0 in Z such that,
m+0=0+m=m for every m in Z. Hence 0 is the additive identity.
d.Existence of inverse: For every m in Z, there exists –m in Z such
that m+(–m)=(–m)+m=0. Here –m is called the additive inverse of
m or simply the negative of m.
Therefore (Z, +) is a group.
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID
4987
a.Find the probability that at least one head appears in a throw of 3
unbiased coins.
b.An article consists of two parts A and B. The probabilities of
QUESTION_TEXT defects in A and B are 0.08 and 0.04. What is the probability that the
assembled part will not have any defect?
c.The mean of marks scored by 30 girls of a class is 44%. The mean
of 50 boys is 42%. Find the mean for the whole class.
SCHEME OF
EVALUATION
a.The possible outcomes are: HHH, HHT, THH, HTH, HTT, TTH,
THT, TTT
The probability that at least one head appears=7/8
b.Let x and y be the events that A and B do not have any defect
respectively.
P(x)=0.92 and P(y)=0.96
Assuming independence,
Probability that the assembled part will not have any
defect=P(x)*P(y)=0.92*0.96=0.8832
c.Here n1=30, n2=50
Mean marks of boys=42%
Mean marks of girls=44%
Therefore the mean for the whole class
=[(30*44)+(50+42)]/(30+50)=(1230+2100)/80=42.75%
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72349
QUESTION_TEXT
What is a matrix? Write four properties of determinants.
SCHEME OF
EVALUATION
A matrix is a rectangular array of numbers arranged as m
horizontal lists called rows, each list having n elements, the
vertical lists are called columns.
Four properties of determinants are:
(i) If two rows or columns of a determinant are interchanged then
the value of the determinant is unchanged but the sign is changed
(ii) If each element of any row or column of a determinant is a
multiple of K, the whole determinant is multiplied by K.
(iii) If two rows or two columns of a determinant are identical, the
value of the determinant is zero.
(iv) If any row or column of a determinant is the sum of two or
more terms, the determinant can be expressed as the sum of two
determinants.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72351
Define the following terms:
i. Null set
ii. Finite and infinite sets
QUESTION_TEXT
iii. Equal and equivalent sets
iv. Subsets
v. Universal set
SCHEME OF
EVALUATION
i. Null set: A set which does not contain any element is called the
empty set or null set.
ii. Finite and infinite sets: A set which is empty or consists of a
definite number of elements is called finite otherwise the set is
called infinite.
iii. Equal and equivalent sets: Given two sets of A and B . If every
element of A is also an element of B and if every element of B is also
an element of A, the sets A and B are said to be equal. Clearly, the
two sets have exactly the same elements. Two finite sets A and B are
said to be equivalent if they have the same number of elements.
iv. Subsets: If every element of a set A is also an element of a set
B, then A is called subset of B or A is contained in B.
v. Universal set: If in any particular context of sets, we find a set U
which contains all the sets under consideration as subsets of U, then
set U is called the universal set.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72353
QUESTION_TEXT
Briefly define the following :
i. Standard deviation
ii. Uses of standard deviation
iii. Variance
iv. Two merits of standard deviation
v. Two demerits of standard deviation
SCHEME OF
EVALUATION
(i) Standard deviation: Standard deviation is the root mean square
deviation of the value from their arithmetic mean. Standard
deviation is the positive square root of variance.
Uses of standard deviation : Standard deviation is the best absolute
measure of dispersion. It is a part of many statistical concepts such
as skewness, kurtosis, correlation, regression, estimation sampling,
test of significance and statistical quality control.
Variance: Variance is the mean square deviation of the values from
their arithmetic mean. Standard deviation is the positive square of
variance.
Two merits of standard deviation:
i. It is calculated on the basis of the magnitudes of all the items.
ii. The combined standard deviation can be calculated further.
Two demerits of standard deviation:
i. Compared with other absolute measures of dispersion, it is
difficult to understand.
ii. It gives more weightage to the items away from the mean that
those near the mean as the deviations are squared.