## Bridge Course in Mathematics, Question Paper of BCA (D) 1st Semester, Download Question Paper 1

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Roll No…….
Total No. of Questions: 13
Paper ID [A0202]
BCA (102) (S05) (O) (Sem.-1st)
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 A A= (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 4th 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 (A B)’= 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=(10n+1-9n-10)/27.
Q7. If C0,C1,C2,…….Ca are binomial coefficients in the expansion of (1+x)n, the prove that
C0C1+C1C2+C2C3+….+Cn-1Cn=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 2nd and 3rd 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