Bangalore University question papers B.Sc

Will you provide me the B. Sc 3rd semester Mathematics model question paper of Bangalore University?

As you want here I am giving model question paper of B. Sc (Mathematics) 3rd semester:

I. Answer any fifteen of the following 15x2=30
1. Show that O(a)=O(xax-1) in any group G.
2. Define center of a group.
3. Prove that a cyclic group is abelian.
4. How many elements of the cyclic group of order 6 can be used as generator of the group?
5. Let H be a subgroup of group G.Define K={xєG:xH=Hx}Prove that K is a subgroup of G.
2. Find the index of H={0,4} in G= (z8, +8).
3. Define convergence of sequence.
4. Find the limit of the sequence √2, √2 √2, √2√2√2..............
5. Verify Cauchy’s criterion for the sequence {n/n+1}
6. Show that a series of positive terms either converges or diverges.
7. Show that 1/1.2 + 1/2.3 + 1/3.4+.......... is convergent.
8. State Raabe’s test for convergence.
9. discuss the absolute convergence of 1-x2 +
∟2 x4 4! - x6 6!+......When x2=4
10. If a and b belongs to positive reals show that a-b a+b +1/3 [a-b a+b]3 +1/5 [a-b/a+b]5+.....
11. Name the type of discontinuity of (x)={3x+1, x>1
2s-1, x≤1}
12. State Rolle’s theorem.
13. Verify Cauchy’s Mean Value theorem for f(x)=log x and g(x)=1/x in {1, e]
14. Evaluate lim (cotx)sin 2x x→ 0
15. Find the Fourier coefficient a0 in the function foo = x, o ≤x <π
2π -x, π≤x≤2 π
16. Find the half range sine series of (x)=x over the interval (0, π).


II. Answer any three of the following 3x5=15
1. Prove that in a cyclic group (‹a) or order d, a (k 2. Show that {[1 0 [-1 0 [-1 1 [0 -1 [1 -1 form a cyclic group w.r.t. matrix multiplication.
0 1], 0 -1], -1 0], 1 -1], 0 0]}
3. Prove that if H is a subgroup of g then there exist a one-to-one correspondence between any two right cosets of H in G.
4. Find all the distinct cosets of the subgroup H= {1, 3,9} of a grouop G= {1,2,.....12} w.r.t multiplication mod 13.
5. If a is any integer p is a prime number then prove that ap=(amod p).

III. Answer any two of the following 2x5=10
1. Discuss the behavior of the sequence {(1+ 1/n)}n
2. If an=3n-4/4n+3 and |an - ¾/< 1/100, n> m find m using the definition of the limit.
3. Discuss the convergence of the following sequences whose nth term are (i) (n2-1)1/8 - (n+1)¼ (ii) [log(n+1)-log n]/tan (1/n)

IV. Answer any fifteen of the following 2x5=10
1. State and prove P-series test for convergence.
2. Discuss the convergence of the series 1.2/456 + 3.4/6.7.8 + 5.6/8.9.10+..........
3. Discuss the convergence of the series x2 2√1+x3 √3√2 + x4/4√3+........
4. Show that ∑ (-1)n is absolutely convergent if p›1 and conditionally convergent if p z 1
(n+1)p
5. Sum the series ∑(n+1)3/n!] xn

V. Answer any two of the following 2x5=10
1. If limx→a f(x)=L, lim x→a g(x)=m prove that lim x→a [ (x)+g (x)=1+m
2. State and prove Lagrange’s Mean Value theorem.
3. Obtain Maclaurin’s expansion for log (1+sin x)
4. Find the yalues of a, b, c such that lim x→a x(2+a cosx)-b sin x+c xo5 = 1/15
x5
VI. Answer any two of the following 2x5=10
1. Expand f(x)=x2 as a Fourier series in the interval (─)(ﻼ-π,-π) and hence Show that 1/12+1/22+1/32+..... π2/6
2. Find the cosine series of the function (x)= π-x in 0< x<_ π.
3. Find the half-range sine series for the function (x)=2x-1 in the interval (0.1)

Contact details:
Bangalore University
Mysore Rd, Jnana Bharathi,
Bengaluru,
Karnataka, 560056 ‎
080 2321 3172

Map:

will you please provide 5th sem physics paper 6 model question paper

i want model question papers in mathematics 5th semester...... pls help

hello.
Kindly share questions papers of physics-6 for 5th semester, bangalore university,
atomic, molecular and quantum physics.
Thank you.

Bangalore university bsc 5th sem previous year question papers in computer science

I would need chemistry model question paper for B.SC 4TH semester bangalore university