Math Chapter Wise

EnglishUP TGT 2021

Q141.The multiplicative group {1, –1, i, –i} is a cyclic group, its generators are

A1 and i B1 and –1 Ci and –i Donly i

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EnglishUP Higher Asst. Prof. 2021

Q142.Suppose that H, K are cyclic groups of order m, n respectively. Then H×K will be cyclic if

Am, n are even integers. Bm, n are odd integers Cm, n are odd prime numbers Dm, n are relatively prime numbers.

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EnglishUP Higher Asst. Prof. 2021

Q143.If G is an abelian group and the action of G on itself by conjugation is the trivial action g.a = a for all g, a∈G then for each a∈G the conjugacy class of a is,

A{a} B{G} Ca{G} DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q144.Suppose there exist 5 groups of order p2 q = 12 then

AOne of which is non-abelian. BTwo of which are non-abelian. CThree of which are non-abelian. DAll five are non-abelian.

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EnglishUP Higher Asst. Prof. 2021

Q145.Let the sets of rationals and reals numbers be denoted by Q and R respectively. Choose the correct answer.

AQ is both a subring and an ideal of R BQ is a subring but not an ideal of R CQ is an ideal but not a subring of R DQ is neither a subring nor an ideal of R

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EnglishUP Higher Asst. Prof. 2021

Q146.Let F be a field of integers modulo 11, then the polynomial x2 + x + 4

Ais reducible over F Bis irreducible over F Chas prime factor over F DNone of these

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EnglishUP Higher Asst. Prof. 2021 UPPSC GIC 2015 UP PGT 2010

Q147.Every Homomorphic of a group is isomorphic to

Acyclic group Bquotient group Cnormal subgroup Dnone of these

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EnglishUP Higher Asst. Prof. 2021

Q148.If G is a finite group and O(G) = pn, where p is prime number and n is positive integers, then

AZ(G) ≠{e} BZ(G) = {e} CZ(G) = G DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q149.If the prime p ≥ 7, then how many consecutive quadratic residues (mod p) will be

ATwo BThree CFour DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q150.If p is an odd prime and if g is a primitive root (mod p), then g r =

A–1 B1 C± 1 DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q151.If p is prime, then (a + b)p ≡

Aap + bp (mod p) Bap + bp (mod N) Cap – bp (mod p) Dap – bp (mod N)

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EnglishUP Higher Asst. Prof. 2021

Q152.A positive integer which has more divisors than any smaller positive integer is called

AHighly Composite Number BRamanujan Composite Number CHarshad Composite Number DHardy Composite Number

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EnglishUP Higher Asst. Prof. 2021

Q153.If a positive integer on a given base is divisible by the sum of its digits on the same base called

AA Ramanujan Number BA Harshad Number CA Hardy Number DNone of these

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021 UP TGT 2021

Q154.How many generators does a cyclic group of order 8 have?

A2 B3 C4 D6

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EnglishUK SSSC LT 2020

Q155.What is the solution of Boolean equation Y A B AB = + + = + + = + + = + +?

A1 BA.B CA.B DA B/+

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EnglishUKPSC Lecturer (Mains) 2020

Q156.Consider the group G = {1,5,7,11,13,17} under multiplication modulo 18. The inverse of 5 is:

A17 B13 C7 D11

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EnglishUKPSC Lecturer (Mains) 2020

Q157.Consider the following statements: I. Every subgroup of an abelian group is normal subgroup. II. The union of two normal subgroups is a normal subgroup. Which of the following options is correct?

AOnly I is true BOnly II is the CBoth I and II are true DNeither I nor II is true

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EnglishUKPSC Lecturer (Mains) 2020

Q158.The identity element of the group ({5, 15, 25, 35}, X40) is:

A15 B25 C35 D1

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EnglishUKPSC Lecturer (Mains) 2020

Q159.The unity element of the ring ({0,2,4,6,8}, +10, X10) is:

A2 B4 C6 DNone of these

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EnglishUKPSC Lecturer (Mains) 2020 UKPSC GIC 2018

Q160.The number of generators of a cyclic group of order 12, is:

A2 B3 C4 D5

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