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CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
Jan2017
ASSESSMENT_CODE BC0033_Jan2017
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
2959
QUESTION_TEXT
What is a matrix? Explain six different types of matrices.
Matrix: A matrix is a rectangular array of numbers arranged in rows
and columns enclosed by a pair of brackets and subject to certain rules
of Presentation.
Six different types of matrices:
SCHEME OF
EVALUATION
i.
Square matrix: A matrix is said to be a square matrix if number of
rows is equal to number of columns.
ii. Column matrix: A matrix in which we have only one column is
said to be a column matrix.
iii. Row matrix: A matrix in which we have only one row is said to
be a row matrix.
iv. Diagonal matrix: A square matrix in which only the elements on
the main diagonal are nonzero is said to be diagonal matrix.
v. Identity matrix: A diagonal matrix in which all the diagonal
elements are all equal to one is called identity matrix.
vi. Scalar matrix: A diagonal matrix whose diagonal elements are
equal is called a scalar matrix.
vii. Null matrix: A matrix in which all the elements are zeroes, is
called a null matrix
viii. Upper Triangular matrix : A square matrix all of whose
elements below the leading diagonal are zero, is called an upper
triangular matrix
ix. Unit matrix : A unit matrix is a square matrix in which every
element in the principal diagonal is 1 and all the other elements are
zero
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
2962
QUESTION_TEXT
Define sample space. Explain equally likely events and mutually
exclusive events with an example.
SCHEME OF
EVALUATION
The set of all possible outcomes of a random experiment is the sample
space.(2 marks)
Equally likely events:(4 marks)
Two or more events are equally likely of they have equal chance of
occurrence. That is equally likely events are such that none of them has
greater chance of occurrence than the others.
Ex: while throwing a fair die, A = {2, 4, 6}, B = {1, 3, 5} and C = {1, 2,
3} are equally likely.
Mutually exclusive events:(4 marks)
Two or more events are mutually exclusive if only one of them can
occur at a time. That is the occurrence of any of these events totally
excludes the occurrence of the other events. Mutually exclusive events
cannot occur together.
Ex: While tossing a coin, the outcomes ‘Head’ and ‘Tail’ are mutually
exclusive because when the coin is tossed once the result cannot be
Head as well as Tail.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
2964
QUESTION_TEXT
Define Statistics. What are the basic characteristics of statistics?
SCHEME OF
EVALUATION
Statistics: When one refers to numerical descriptions of quantitative
aspects of things, it is called statistics. (1.25 marks)
Basic Characteristics of Statistics: (1.75 x 4 = 8.75 marks)
1. Statistics are aggregates of facts: statistics are a number of facts. A
single fact cannot be called a statistics. e.g. Enrollment in 1994 is not
astatistics but enrollment from 1985-1995 is a statistics.
2. Statistics are affected to a marked extent by a multiplicity of
causes:For example number of pass outs in a exam. will depend upon a
numberof factors viz., total enrollment, dropout quantity of level of
exam. etc.
3. Statistics must be estimated with a reasonable accuracy: For
example:number of trees in a orchad should not be in decimals or
figures0.297743 should not be written as 0.3 when it represents lakhs.
4. Data in statistics is collected in a systematic manner with a
predetermined purpose e.g. Blood pressure level of a patient before drug
administration,after I week and alter 2week of drug administration.
5. Statistics should be placed in relation to each other in point of time.
Space or condition putting all these characteristic together statistics
could be defined as : Aggregate of facts, affected to a marked extent by
multiplicity of causes, numerically expressed enumerated or estimated
according to a reasonable standard of accuracy, collected in a systematic
manner for a predetermined purpose and placed in relation to each other.
QUESTION_T
DESCRIPTIVE_QUESTION
YPE
QUESTION_ID 74105
a. There are two restaurants next to each other. One has a sign that says
“Good food is not cheap” and the other has a sign that says “cheap food is not
QUESTION_T
good”. Show that both signs are saying the same thing.
EXT
b. In how many ways the letters of the word MISSISSIPPI be arranged
such that 4S’s are not together?
a.
Let g: Food is Good
c: Food is cheap
The sign of first restaurant can be written as g→~c, and the sign of second be
written as c→~g.
SCHEME OF
EVALUATION
Hence the prove.
(5 marks)
b. 33810 ways (5 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
74107
QUESTION_TEXT
a. A bag contains 3 red and 4 green and 3 yellow marbles. Three
marbles are randomly drawn from the bag. What is the probability that
they are of
i. the same colour
ii. different colours
b. The probabilities of two students A and B solving a problem are
1/2 and 3/4 respectively. If both of them independently try , what is the
probability that the problem is solved?
SCHEME OF
EVALUATION
a.
i. 1/20
ii. 3/10 (3+3 marks)
b. 0.875 (4 marks)
QUESTION_TYPE DESCRIPTIVE_QUESTION
QUESTION_ID
104870
There are two book shelves. The first self has 8 Sanskrit books and 4
Kannada books. The Second self has 10 Sanskrit books and 15 Kannada
books. Once of the two shelves is selected at random. Two books are then
selected at random from the selected shelf. Find the probability that
QUESTION_TEXT
i.
Both the selected books are Kannada books
ii.
Both the selected books are Sanskrit books
iii.
One of them is a Kannada book and other is a Sanskrit book
The first shelf is selected
B- Both the selected books are Kannada books
C- Both the selected books are Sanskrit books
D- One of them is Kannada book and other is a Sanskrit book (1 mark)
A1 the second shelf is selected
SCHEME OF
EVALUATION
(3 MARKS)
i.
P [both Kannada books] =
ii.
p [both Sanskrit books] =
iii
P [ one Kannada and one Sanskrit] =
(2 M)
= 0.2205 (2 M)
= 0.2871 (2 M)
= 0.9848