Download CUSTOMER_CODE SMUDE DIVISION_CODE SMUDE

CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
APR2016
ASSESSMENT_CODE BCA1030_APR2016
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
4985
QUESTION_TEXT
Show that ~(p ∧ q) is logically equivalent to (~p) ∨ (~q).
Truth table for ~(p ^ q)
pqp^q~(p^q)
TTTF
TFFT
FTFT
FFFT
SCHEME OF
EVALUATION
Truth table for (~p)V(~q)
pq~p~q(~p)V(~q)
TTFFF
TFFTT
FTTFT
FFTTT
Now observe that the entries in the last column of both the tables are
same. Hence, the statements are logically equivalent.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
4987
QUESTION_TEXT
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 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
4989
QUESTION_TEXT
i.Mention any 6 qualities of an ideal measure of tendency.
ii.Write any 4 merits of Arithmetic mean.
SCHEME OF
EVALUATION
6 qualities of an ideal measure of tendency:
1.It should be easy to understand. Its computation procedure should
be simple.
2.It should be rigidly defined.
3.It should be based on all the vales.
4.It should be capable of further algebraic treatments.
5.It should not be affected by extreme values.
6.It should be stable. That is the measure should be such that
sampling variation in the value of the measure should be least.
4 merits of Arithmetic mean:
1.It is rigidly defined.
2.The logic behind the computation is easy to understand.
3.It can be easily adopted for further statistical analysis.
4.It is based on all the values.
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
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.
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
72354
QUESTION_TEXT
Define convergence and divergence of the series and explain 3 general
properties of series.
SCHEME OF
EVALUATION
A series is called convergent if the sequence of its partial sums has a
finite limit; this limit is termed as the sum of the convergent series.
If a sequence of its partial derivatives has no finite limit, then the series
is called divergent. A divergent series has no sum.
General properties of series:
1. The converge or diverge of an infinite series remains unaffected by
addition of removal of a finite number of terms; for the sum of these
terms belong the finite quantity addition of removal does not change
the nature of its sum.
2. If as series in which all the terms are positive is convergent, the
series remains convergent even when some or all of its terms are
negative; for the sum is clearly the greatest when all the terms are
positive.
3. The convergence or divergence of an infinite series remains
unaffected by multiplying each term by a finite number.