Math Chapter Wise

EnglishLT 2018

Q201.Let * be a binary operation defined on the set of positive rational number Q+ by the rule a*b ab, a,b Q 3 + = ∀ ∈ = ∀ ∈ = ∀ ∈ = ∀ ∈. Then the inverse of 4*6 is

A9/8 B2/3 C3/8 D3/2

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EnglishLT 2018/ PCS 2003

Q202.The least order of non-Abelian group is

A4 B5 C6 D8

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q203.If f(x) is an even function, then f '(x) is–

AAn even function BAn odd function CMay be even or odd DNothing can be said

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q204.If a (b c) and a (b c) where a,b,c N then

A2 2 2/a b (modc ) B2 2 2/c a (mod b ) C2 2 2/a c b D2 2 2/b c (moda )

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q205.If 2 f(x) sin (x) 3cosx 5, then f(x) is–

AAn even function BAn odd function CMonotonic DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q206.Let G be a finite group and Z ⊂ ⊂ ⊂ G be its center, Assume G/Z is cyclic, Then–

AG is abelian group BG is a cyclic group CG cannot be a cyclic group DG cannot be an abelian group

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q207.Let P be a prime number and G be a group of order 4 P Then–

AG always has an element of order exactly 4 P BG always has an element of order exactly 3 P CG always has an element of order exactly P DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q208.Every group of…………….order is cyclic–

Aodd Beven Cprime Dany

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q209.A group having no proper normal subgroup is–

ASimple group BNormal subgroup CAbelian subgroup DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q210.Let H be a subgroup of G and N be a normal subgroup of G then H ∩ ∩ ∩ N is–

ANormal subgroup BSimple group CAbelian subgroup DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q211.Let G be group of order 17. The total numbers of non-isomorphic subgroup of G is–

A1 B2 C3 D17

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q212.Let G be a cyclic group of order 24 then total number of group isomorphism of G onto itself is–

A7 B8 C17 D24

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q213.ln an integral domain R, which are the following holds?

AGiven any { } a,b R 0 ∈ − there is lways C R ∈ such that a.c b BNon- zero elements can never be a group under multiplication CThe equation 2 x a,a R always has a solution DFor { } a,b,c R 0,if ∈ − ac bc = then a b =

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q214.Let P be a permutation matrix then its inverse is–

AP BPt C1 DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q215.All the units in ring 8 Z of all integers modulo 8 are–

A2, 4, 6 B1, 3, 5, 7 C0, 1 DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q216.ln the multiplicative group {1,-1,i,–i} where 2 i 1, = − = − the inverse of 5 i is–

A1 Bi C-l D-i

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q217.Let G be the set of all positive rational numbers. lf * is a binary operation defined on G by a*b = ab a,b G 3 ∀ ∈ ∀ ∈ Then identity element of G is–/

A1 B2 C3 D4

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q218.If every element of a group G has its own inverse, then G is–

Afinite Binfinite Ccyclic Dabelian

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EnglishPGT 2013

Q219.The total number of subgroup of the group Z11 is

A2 B211/–11 C3 D7

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EnglishPGT 2013

Q220.The number of identical elements is a group will be

A1 B2 C3 DInfinite

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