Math Chapter Wise

EnglishRajasthan TGT 2016

Q321.The number of ordered pairs of integers (x, y) satisfying the equation x2 +6x+y2 = 4 is

A8 B6 C4 D2

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EnglishRajasthan TGT 2016

Q322.If A={a,b,c} and relations R1, R2: A→ → →A are R1= {(a,b), (b,c), (c,a), (a,a), (b,b), (c,c)} and R2= {(a,b), (b,c), (c,a), (a,a)}, then

AR1 is equivalence relation but R2 is not BR1 is transitive but R2 in not CR1 and R2 both are equivalence DNone of these

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EnglishRajasthan TGT 2015

Q323.If x A x 0 x 10 2 = ∈ ≤ = ∈ ≤ = ∈ ≤ = ∈ ≤, B {x x is prime number of one digit} and x C x N,x 12 3 = ∈ ≤ = ∈ ≤ = ∈ ≤ = ∈ ≤ then A (B C) ∩ ∪ ∩ ∪ is equal to

A{2,6} B{3,6} C{2,6,12} D{3,6,12}

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EnglishRajasthan TGT 2015

Q324.A relation R is defined on set of integers where aRb is and only if a2 and b2 not prime to each other, then relation R does not satisfy the property–

AReflexive BSymmetric CTransitive DNone of these

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EnglishRajasthan TGT 2015

Q325.If A is the set of natural numbers less than 10 and B isthe set of prime numbers less than 9, then the number of relations defined from A to B is–

A216 B28 C27 D29/–1

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EnglishRajasthan TGT 2015

Q326.If function f: R R, → → defined as 2 f(x) x = then function f is

Aone-one but not onto Bonto but not one-one Cone-one and onto Dneither one-one nor onto

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EnglishRajasthan TGT 2015

Q327.If n n 0 1 n (1 x) c c x... c x + = + + + + = + + + + = + + + + = + + + then the value of 0 1 2 n c 2c 3c... (n 1)c + + + + + + + + + + + + + + + + + + + + is equal to–

An/n 2 Bn 1/n 2 − Cn n 1 n 2 n 2 − + Dn n 1 2 n 2 − +

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EnglishRajasthan TGT 2015

Q328.If O(a) m, = O(b) n, = where a anb b are elements of an abelian group G, then

AO(ab) m = BO(ab) mn = CO(ab) mn = DO(a,b) = L.C.M.{m,n}

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EnglishRajasthan TGT 2015

Q329.If H is a subgroup of a group G and a,b ∈G, then if

AHa = Hb iff ab-1 ∈G BHa = Hb iff ab-1 ∈H CaH = bH iff (ab)-1 ∈G DaH = Hb iff ab-1 ∈H

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EnglishRajasthan TGT 2015

Q330.Let G be a group and let H be any subgroup of G, If N be any normal subgroup of G, then

AHN H N (H N) ≡ ∩ BHN H H (H N) ≡ ∩ CHN N N (H N) ≡ ∩ DHN (H N) N H ∩ ≡

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EnglishRajasthan TGT 2015

Q331.Every subgroup of an abelian group is

ANon-abelian BCyclic CNormal DCoset

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EnglishRajasthan TGT 2015

Q332.If be a group homomorphism from a group (G,) + + to a group (G,) × ×, then for a,b G ∈

Af B+ = × Cf(a b) f Df(a b) f(a) f(b) + = +

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EnglishRajasthan TGT 2015

Q333.Which one of the following is correct?

AIn a ring if ab 0 = ⇒ either a 0 = or b 0 = BEvery finite ring is an intergral domain, CEvery finite integral domain is a field. DThe set of natural is a ring with respect to the usual addition and multiplication.

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EnglishRajasthan TGT 2015

Q334.Which of the following is not an integral domain?

A(N,.) + B(C,.) + C(Q,.) + D(R,.) +

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EnglishRajasthan TGT 2013

Q335.For a real numbers 'x' and 'y' if xRy ⇔ ⇔ ⇔ x–y+ 2 is an irrational number, then the relation R is-

Aonly reflexive Bonly symmetric Conly transitive Dequivalent

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EnglishRajasthan TGT 2013

Q336.If f(x) = 3x + 2 3,x 5x - 3 5 ≠ then

A() 1 1 (x), x 19 − = − f f B(fof) (x) = –x C() 1 (x) x − = − f f D() 1 (x) x − = f f

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EnglishRajasthan TGT 2013

Q337.Which of the following ring is not an integral domain-

A() E,, + i where E is the set of even integers including zero. B() C,, + i where C is the set of complex numbers. C{ } () a b 2, a,b I,, + ∈ + i where I is the set of whole numbers. D() Q,, + i where Q is set of rational numbers.

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EnglishRajasthan TGT 2013

Q338.Let G be a group of order 30. Let H and K be normal subgroups of order 3 and 6 respectively, then the order of the group G HK is-

A2 B3 C5 D10

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EnglishRajasthan TGT 2013

Q339.In the field () R,, ⊕ ⊕ ⊙ ⊙ ⊙ where R is set of real numbers and a ⊕ ⊕ ⊕ b = a + b –1, a ⊙ ⊙ ⊙ b = a + b – ab for all a, b ∈ R, then the additive inverse and multiplication inverse of 5 are respectively-

A–4, 1 B–3, 5 4 C–4, 5 4 D–3, 1

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EnglishRajasthan TGT 2013

Q340.If cancellation laws hold in finite ring R with unity and ∀ ∀ ∀a, b ∈ R, (ab)2 = a2 b2, then R is-

Aa field. Ba division ring but not a field. Can integral domain but not a field. Da non-commutative ring without zero divisions.

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