Math Chapter Wise

EnglishBihar (TRE 1.0) -2023

Q01.Let D be a subset of real line. Consider the assertion: “Every infinite sequence in D has a subsequence which converges in D.” This assertion is true if

AD = [0, ∞) BD = [0,1] ∪ [3, 4] CD = [-1,1) ∪ (1,2] DMore than one of the above ENone of the above

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q02.The general solution of recurrence relation r r r 1 r 2 a 5a 6a 4,r 2 − − − + = ≥ − + = ≥ − + = ≥ − + = ≥ is:

Ar r r 1 2 A.5 A.6 8.4 + +, where A1 and A2 are arbitrary constants. Br r r 1 2 A.2 A.3 8.4 + +, where A1 and A2 are arbitrary constants. Cr r r 1 2 1 A.2 A.3.4 8 + −, where A1 and A2 are arbitrary constants. Dr r r 1 2 1 A.2 A.4.3 8 + −, where A1 and A2 are arbitrary constants.

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EnglishDSSSB 23 SEP 2018 (9 AM-11 AM)

Q03.If a1, a2...., an and b1, b2....., bn are non- negative real number such that a1> b1, a2>b2,...an>bn, then.

A1 2 n 1 2 n a a...a b b...b > but 1 2 n 1 2 n a a... a b b... b + + + < + + + B1 2 n 1 2 n a a... a b b... b + + + > + + + but 1 2 n 1 2 n a a...a b b...b < C1 2 n 1 2 n a a... a b b... b + + + < + + + and 1 2 n 1 2 n a a...a b b...b < D1 2 n 1 2 n a a... a b b... b + + + > + + + and 1 2 n 1 2 n a a...a b b...b >

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EnglishLT 2018

Q04.The value of n 1 1 1 lim..... n 1 n 2 6n →∞ + + is n 1 1 1 lim..... n 1 n 2 6n →∞ + +..

A0 Bloge2 Cloge3 Dloge6

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EnglishSECTION B PGT TIER-I 31.11.2014

Q05.The radius of convergence R of the series n n 0 (n 1)x is–

Ainfinite radius B1 C0 Dnone of these

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EnglishSECTION B PGT TIER-I 31.11.2014

Q06.The power series n n 0 2 (1) x 3 converges–

Aonly for x = 0 Bfor all x ℝ Conly for 1 x 1 Donly for 1 x 1

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

Q07.The value of 3 3 a b a b..... is–

A5 3/a b B5 3/ab Ca3/b DNone of these

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

Q08.The sum of the expression 1 1 1 2 2 3 1 1.... 3 4 80 81 + + is–

A7 B8 C9 D10

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

Q09.Let { { { } } } { { { } } n n a, b be sequences of real number satisfying n n a b ≤ for all n 1, ≥ then–

An a ∑ converges whenever n b ∑ converges Bn a ∑ converges absolutely whenever n b ∑ converges absolutely Cn b ∑ converges absolutely whenever n a ∑ converges Dnone of these

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

Q10.The series ((()) n n 1 1 2n 3 ∞ = − + ∑ ∑:

Aabsolutely convergent Bconditional convergent Cdivergent Dnone of these

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EnglishPGT 2000

Q11.The series 1/ 2 5 n 2n 1 + ∑ ∑ is:

ADivergent BConvergent CEllipse DNone of these

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EnglishRajasthan TGT 2016

Q12.The series 1 2 3...... 1.2 3.4 5.6 + + + + + + + + + + + + is

Adivergent Bconvergent Cconditionally convergent Doscillatory

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EnglishRajasthan TGT 2016

Q13.A set 1: n N n ∈ is

AClosed and bounded BOpen but bounded CNeither open nor closed but bounded DUnbounded

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EnglishRajasthan TGT 2015

Q14.If p and q are positive real numbers, then the series p p p q q q 2 3 4.... 1 2 3 + + + + + + + + + + + + is convergent if

Ap q 1/< − Bp q 1/< + Cp q 1/≥ − Dp q 1/≥ +

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EnglishRajasthan TGT 2013 UPPCS (PRE) 2002

Q15.The series 2 2 3 3 4 4 2 x 3 x 4 x x + + + + 2 3 4............. is convergent, if-

A1 0 x e < < B1 x e > C3 2 x e e < < D3 4 x e e < <

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EnglishRajasthan TGT 2011

Q16.Sequence 1 1 1 1 1 1,,,,,,..... 2 3 4 5 6 − − − − − − − − − − − − is

AMonotonic but not bounded BBounded but not monotonic CMonotonic and bounded DNeither monotonic nor bounded

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EnglishTGT 2011

Q17.The series p 1 n Σ is divergent if

Ap ≥ 1 Bp < 1 Cp ≤ 1 DNone of these

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EnglishTGT 2011

Q18.Series 2 n 1 2 2 2 1.................. 3 3 3 − + + + + + + + + + + + + + + + + + + + + is:

AConvergent BDivergent COscillatory DNone of these

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EnglishTGT 2011, 2009

Q19.The series n U ∑ ∑ of positive terms is convergent on divergent according as n n n 1 U lim 1 U →∞ →∞ + + > > or <1 then this test if known as-

AComparison test BRaabe's test CD' Alembert's test DCauchy's, condensation test

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EnglishTGT 2011

Q20.Every Cauchy sequence is:

AUnbounded BBounded CInfinite DNone of these

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