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• ## The vectors (x1, y1) and (x2, y2) of V2 (F) are linearly

The vectors (x1, y1) and (x2, y2) of V2 (F) are linearly dependent if x1y2-x2y1= (a) x1y1 (b) x2y2 (c) …

Anurag Mishra Professor Asked on 28th May 2016 in
• 773 views
• ## Express the vector α =(1, -2, 5) as a linear combination of

Express the vector α =(1, -2, 5) as a linear combination of e1 =(1, 1, 1), e2 = (1, 2, …

Anurag Mishra Professor Asked on 28th May 2016 in
• 1816 views
• ## In the polynomial ring Z2 [x], 91+x0³=

In the polynomial ring Z2 [x], 91+x0³= (a) 1+x+x3 (b) 1+x+x2+x3 (c) 1+x2+x3 (d) x+x2+x3

Anurag Mishra Professor Asked on 28th May 2016 in
• 1930 views
• ## The zero’s of f(x) =2x+x²+3x³ +5 in Z5 [x] are

(a) 1,2 (b) 2, 3 (c) 0,2 (d) 0, 4

Anurag Mishra Professor Asked on 28th May 2016 in
• 1805 views
• ## In a ring R, u is a unit and x ϵ R such that ux is zero divisor, then

(a) x is nilpotent (b) x is an idempotent (c) x is a zero divisor (d) none

Anurag Mishra Professor Asked on 28th May 2016 in
• 1752 views
• ## The unit element of a quotient ring R/U is

(a) 1+U (b) 1 (c) 0+U (d) 1+R

Anurag Mishra Professor Asked on 28th May 2016 in
• 620 views
• ## Number of zero divisiors in a ring

Number of zero divisiors in a ring (Z12, +, .) is (a) 5 (b) 6 (c) 7 (d) 0

Anurag Mishra Professor Asked on 28th May 2016 in
• 611 views
• ## The ideals of a field F are

(a) {0}, {i} (b) {0}, {1} (c) {i}, {1} (d) None

Anurag Mishra Professor Asked on 28th May 2016 in
• 575 views
• ## Units in a ring Z (x) are

(a) 1, -1 (b) I, -i (c) 0, 1 (d) 1, i

Anurag Mishra Professor Asked on 28th May 2016 in
• 646 views
• ## If f(x)=3x²+5x+2 and g(x)=2x³+4x+1, then deg(f(x).g(x))=

(a) 3 (b) 4 (c) 0 (d) 6

Anurag Mishra Professor Asked on 28th May 2016 in
• 1775 views
• ## Number of units in the domain of Gaussian integers is

(a) 0 (b) 2 (c) 3 (d) 4

Anurag Mishra Professor Asked on 28th May 2016 in
• 648 views
• ## The characteristic of a ring with Unity is

(a) 0 (b) 1 (c) 2 (d) ¥

Anurag Mishra Professor Asked on 28th May 2016 in
• 594 views
• ## The idempotent elements of the ring

The idempotent elements of the ring(Z6 +, .) are (a) 1, 2 (c) 2, 3 (c) 3, 4 (d) 3, …

Anurag Mishra Professor Asked on 28th May 2016 in
• 636 views
• ## If f=(2 3 4 1) is a permutation of degree 5 then

If f=(2 3 4 1) is a permutation of degree 5 then f-1= (a) (1 2 3 4) (b) (1 …

Anurag Mishra Professor Asked on 28th May 2016 in
• 602 views
• ## The number of automorphisms of a cyclic group of order 9 is

(a) 6 (b) 8 (c) 9 (d) 7

Anurag Mishra Professor Asked on 28th May 2016 in
• 610 views
• ## The order of an identity element in a group is

(a) 0 (b) 1 (c) n (d) ≈

Anurag Mishra Professor Asked on 28th May 2016 in
• 578 views
• ## The number of generators of a cyclic group of order 15 is

(a) 2 (b) 8 (c) 5 (d) 14

Anurag Mishra Professor Asked on 28th May 2016 in
• 533 views
• ## Solution of x+5=3 in Z8 is

Solution of x+5=3 in Z8 is (a) x=-2 (b) x=8 (c) x=8 (d) x=1

Anurag Mishra Professor Asked on 28th May 2016 in
• 565 views
• ## G=({0, 1, 0, 2, 3, 4, 5}, +6) are

The generators of the cyclic group G=({0, 1, 0, 2, 3, 4, 5}, +6) are (a) 1, 2 (b) 1, …

Anurag Mishra Professor Asked on 28th May 2016 in
• 583 views