**Roll No…….**

**Total No. of Questions: 13**

**Paper ID [A0202]**

**BCA (102) (S05) (O) (Sem.-1**

^{st})**BRIDGE COURSE IN MATHEMATICS**

**Time: 3 Hrs. Max. Marks:75**

**Instruction to Candidates:**

1.
Section-A is Compulsory.

2.
Attempt any Nine question
from Section-B.

**SECTION-A**

Q1.

(a) If A=[1,5], B=[1,5,6],C=[1,6,5]. Out 00 sets A and B which is a
proper subset of C.

(b) If A=[-3,0,1,2] and B=[1,2,3,4] then write A-B and A

(c) Prove
that AA=

(d) Draw
the Venn diagram is B is proper subset of A.

(e) Which
of the following are the partitions far sets S=[1,2,3,4]

(i)
[{1,2}, {3}, {4}]

(ii)
[{1,2}, {2,3}, {4}]

(iii)
[{1,2},{4}]

(iv)
[{1,2},{3,4}]

(f) Use Binomial theorem to find the value of (10.1)

^{5}
(g) Define Minor of a matrix with example.

(h) Write the differences between a matrix and determinant.

(i) Find A if A+B=A-B=

(j) Find
4

^{th}term in the expansion of^{9}.
(k) Find
the arithmetic mean of the following marks obtained by 10 students in
statistics:

52,40,70,75,43,40,35,65,48,62.

(l) Define mode and write formula to find mode.

(m)Define median and write formula to find median.

(n) Define pure and applied statistics.

(o) Define statistical Inference.

**SECTION-B**

Q2.
Prove that (AB)’= A’B’.

Q3. If R
be a relation in the set of integers Z defined by

R=[{x,y}:
x is divisible by 6)

Q4. Let
R= [{1,2},{2,3},{3,1}] and A={1,2,3}, find the reflexive, symmetric and
transitive closure of R using graphical representation of R.

Q5.
Prove that composition of any function with the identify function is the
function itself.

Q6. Show
by induction method

3+33+333+……+33……..3=(10

^{n+1}-9n-10)/27.
Q7. If C

_{0},C_{1},C_{2},…….C_{a}are binomial coefficients in the expansion of (1+x)^{n}, the prove that
C

_{0}C_{1}+C_{1}C_{2}+C_{2}C_{3}+….+C_{n-1}C_{n}=2n!(n-1)!(n+1)!
Q8.
Verify A(B+C)=AB+AC, when

A= B=C=

Q9. Find
the minor and co-factor of each element of 2

^{nd}and 3^{rd}row the determinant
Q10.
Marks obtained by 80 students are given below: Determine the value of the
median of distribution.

Marks: 0-1 10-20 20-30 30-40 40-50
50-60

No. of
Students: 3 9 15 30 18 5

Q11.
Find the mode for the following table:

Marks: 0-10 0-20 10-20 20-30
30-40 40-50

No. of
Students 3 9 5 3 2

Q12.
Write a note on the following.

(a) Graphical representation of discurbs

(b) Histogram

Q13. Calculate the mean for the following
frequency distribution:

Mark
Group: 5-10 10-15 20-25 25-30 30-35 35-40 40+45

No. of
Students: 5 6 15 10 5 4
2 2

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