Math Chapter Wise

EnglishUP PGT-2016 (02-02-2019)

Q181.If G is a cyclic group of order 30, then total number of subgroups of G is

A6 B7 C8 D9

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EnglishUP PGT-2016 (02-02-2019)

Q182.If every element of a group G is its own inverse, then G is

Afinite Binfinite Cabelian Dnon-abelian

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EnglishUP PGT-2016 (02-02-2019)

Q183.In the group { { { } } { { } } 10 G 2,4,6,8. = the identity element is

A2 B4 C6 D8

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EnglishUP PGT-2016 (02-02-2019)

Q184.Let G be a group with binary operation *defined by a*b=a+b+1, ∀ ∀ ∀ a, b ∈ G. Inverse of element C of G is

A2+C B2–C C–2+C D–2–C

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EnglishUP PGT-2016 (02-02-2019)

Q185.Every subgroup of a cyclic group is

Anormal Bnormal only when order of subgroup is prime Cnon-normal Dnormal when order of group is prime

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EnglishUP PGT-2016 (02-02-2019)

Q186.Which one of the following is a subspace of vector space R3?

A() { } 3 a,b,c R:a b 0 ∈ + = B() { } 3 a,b,c R:a b 2 ∈ − = C() { } 3 a,b,c R:a b 1 ∈ + = D() { } 3 a,b,c R:a b 1 ∈ − =

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EnglishUP PGT-2016 (02-02-2019)

Q187.If H and K are subgroups of a group G and O(H)=3, O(K)=5, O(G) = 30 then O(H∩ ∩ ∩K) is

A1 B2 C3 D5

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EnglishUP PGT-2016 (02-02-2019)

Q188.If x, y are elements of a group G and O(y)=3, then O(xyx–1) is

A1 B2 C3 D6

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EnglishUP PGT-2016 (02-02-2019)

Q189.If f: G → → → G' is a group isomorphism then which of the following is true?

AO(a)<O(f(a)) BO(a)=O(f(a)) CO(a)>O(f(a)) DNone of the above

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q190.Let n > 1 be fixed and a, b, c, d be arbitrary integers. If a≡ ≡ ≡b (mod n) and c≡ ≡ ≡d (mod n). then:

Aa+c ≡ b+d(mod n) and ac ≡ bd (mod n) Ba+c ≠ b+d(mod n) and ac ≠ bd (mod n) Ca+c ≠ b+d(mod n) but ac ≡ bd (mod n) Da+c ≡ b+d(mod n) but ac ≠ bd (mod n)

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q191.Consider the linear congruence's 6x≡ ≡ ≡3 (mod 9). Then the incongruence's solutions modulo 9 of this congruence's are.

A0, 3,6 B1, 4 7 CNo solution D2, 5, 8

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q192.The system of linear congruence's: x ≡ ≡ ≡ 1 (mod 5) x ≡ ≡ ≡ 3 (mod 3) x ≡ ≡ ≡ 2 (mod 7)

Ahas a simultaneous solution, which is unique modulo 105. Bcannot be solved by Chinese Remainder theorem. Chas a simultaneous solution, which is not unique modulo 105. Dhas no simultaneous solution

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q193.If a is an Integer and a3 ≡ ≡x(mod 9), then is a possible value of x?

A5, 6, 7 B0, 1, 8 C2, 4, 6 D3, 5, 7

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q194.If p and q are distinct primes with ap ≡ ≡ a (mod q) and aq ≡ ≡ a (mod p) then

Aapq/≡ a (mod pq) Bapq/≡ 1 (mod pq) Capq/≡ –a (mod pq) Dapq/≡ 0 (mod pq)

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q195.If 27! x(mod29), ≡ ≡, then the value of x is:

A–1 B0 C27 D1

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EnglishLT 2018

Q196.The generator/generators of the cyclic group {a, a2, a3, a4 = e} is/are

Aa4 Ba2 Ca4, a2 Da, a3

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EnglishLT 2018/ PGT 2010, 2005

Q197.Let G be a group with identity element e. Let a, b∈G be such that a5 =e and aba–1 =b2. Then o(b) is

A17 B23 C29 D31

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EnglishLT 2018

Q198.A cyclic group having only one generator can have at most

A1 element B2 elements C3 elements D4 elements

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EnglishLT 2018

Q199.Every subgroup of an Abelian group is not

ACyclic BAbelian CNormal DNone of the above

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EnglishLT 2018

Q200.If f(x) = cos |x| and g(x)=sin|x|, then

Aboth f and g are even functions Bboth f and g are odd functions Cf is an even function and g is an odd function Df is an odd function and g is an even function f

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