Math Chapter Wise

EnglishBihar (TRE 1.0) -2023

Q01.For any positive integers a and 3, there exist unique integers q and r such that a = 3q + r, where r must satisfy

A1 < r < 3 B0 < r < 3 C0 ≤ r < 3 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q02.Consider the congruence xn ≡ ≡ 2(mod13). This congruence has a solution for x if

An = 8 Bn = 7 Cn = 6 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q03.Let a, b be positive integers with a > b and a + b = 24. Suppose that the following congruence's have a common integer solution: 2x ≡ ≡ ≡ 3a (mod5); x ≡ ≡ ≡ 4b (mod5) Which of the following statements is true?

Aa – b is divisible by 5 B3b > a > 2b Ca > 3b DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q04.The number of group homo-morphisms from Z10 to Z20 is

AZero Bone Cten DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q05.Let S7 denotes the group of permutations of the set {1,2,3, 4,5,6,7}. Which of the following is true?

AThere are no elements of order 6 in S7 BThere are no elements of order 8 in S7 CThere are no elements of order 7 in S7 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q06.Let p be a prime number. How many distinct sub-rings (with unity) of cardinality p does the field Fp2 have?

A0 B1 CP DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q07.Let p ≥ 5 be a prime. Then

AFP × Fp has at least five subgroups of order p Bevery subgroup of FP × FP is of the form H1 × H2 where H1, H2 are subgroups of FP Cevery subgroup of FP × FP an ideal of the ring FP × FP DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q08.Any group of order 25 is

Acyclic Bsimple CAbelian but not simple DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q09.If R is a ring with unity a, b ∈R such that ab = 1, then

Aba is an idempotent in R but (1- ba) is not Bboth ba and (1– ba) are idempotent elements in R Cneither ba nor (1- ba) is an idempotent element in R DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q10.Let G be a commutative group of order 202. Then the number of element(s) of order 2 in G is

A1 B2 C101 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q11.The class equation of a group of order 10 is

A1+1+ ---- +1(10times) = 10 B1+1+ 3+ 5 = 10 C1+ 2+ 2+ 5 = 10 DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q12.The value of 'a' for which one root of the quadratic equation (a2 – 5a + 3)x2 + (3a – 1) x + 2 = 0 is twice the other, is:

A1/3 B1 – 3 C2/3 D2 – 3

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EnglishEMRS TGT-2023

Q13.The number of real solutions of the equation 2 x – 3 x + 2 = 0, is:

A3 B2 C1 D4

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EnglishEMRS TGT-2023

Q14.Both the roots of the equation (x–a)(x–b) + (x– b)(x–c) + (x–c)(x–a) = 0 are always:

ANegative BReal CZero DPositive

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EnglishEMRS TGT-2023

Q15.If one of the zeroes of a cubic polynomial x3 + ax2 + bx + c is 1, then the product of other two zeroes is:

Aa – b + 1 Ba + b + 1 Ca + b – 1 Da – b – 1

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EnglishEMRS TGT-2023

Q16.If x+1 is a factor of 2x3 + ax2 + abx + 1, and 2a – 3b = 4, then the value of a + 2b is:

A12 B9 C14 D7

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EnglishEMRS TGT-2023

Q17.The solution of the pair of equations 2 2 b a x + y = a + b a b and x + y = 2ab is:

Ax = ab2, y =a2 b Bx = b, y = a Cx = ab, y = ab Da b x,y b a =

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EnglishEMRS TGT-2023

Q18.If (x1, y1) is the solution of pair of equations x y + –1 = 0 10 5 and x y + = 15 8 6 and y1 = λx1 + 5, then value of λ is:

A1/2 B1 – 2 C–2 D2

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EnglishRPSC PGT 2022

Q19.If R = ({0, 1, 2, 3, 4, 5}, + 6, × 6), then R is-

Aa field Ba division ring Ca ring with zero divisors Da ring without zero divisors

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EnglishRPSC PGT 2022

Q20.For algebraic structure (G = (0,1], • • •), correct statement is -

Ait is only semi group Bit is moniod Cit is group Dit is commutative group

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