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

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=(10ⁿ⁺¹-9n-10)/27.

Q7. If C₀,C₁,C₂,…….C_a are binomial coefficients in the expansion of (1+x)ⁿ, the prove that

C₀C₁+C₁C₂+C₂C₃+….+C_n-1C_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