Math Chapter Wise

EnglishBihar (TRE 2.0)-2023

Q01.The value of ∑ n k n k k=0 3 C is

A4n Bn4 C4n DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 1.0) -2023

Q02.Let () [ ] ∈ ∞ 2 2 nx gn x =,x 0, 1+ n x Which of the following is true as n → → → ∞ ∞ ∞?

Agn → 0 pointwise but not uniformly Bgn → 0 uniformly Cgn (x) → x ∀x∈ [0, ∞] DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 1.0) -2023

Q03.If { xn } n is a convergent sequence in R and {yn } n is a bounded sequence in R, then we can conclude that

A{ } n n x y + is convergent B{ } n n x y + is bounded C{ } n n x y + has no convergent subsequence DMore than one of the above ENone of the above

Show answer

EnglishBihar (TRE 1.0) -2023

Q04.Define f(x) = 1 x for x > 0. Then f is uniformly continuous

Aon (0, ∞) Bon (r, ∞) for any r > 0 Con (0, r) for any r > 0 DMore than one of the above ENone of the above

Show answer

EnglishDSE TGT 2022

Q05.The sequence 2 2n 1 converges to

A2 B1 C0 D4

Show answer

EnglishDSE TGT 2022

Q06.The series whose nth term is sin (1/n)

AConverges Buniformly converges Coscillates Ddiverges

Show answer

EnglishDSE TGT 2022

Q07.The series 1+(1/2)+(1/4)+(1/8)+........+ ∞ ∞

AConverges BBecomes zero COscillates DDiverges

Show answer

EnglishDSE TGT 2022

Q08.The sequence n +1 n is

AIncreasing BDecreasing CUnbounded DOscillating

Show answer

EnglishDSE TGT 2022

Q09.Limiting value of the sequence {Sn}, where n 1 Sn = 1+ n

Alog 2 Be Ce2 D2e

Show answer

EnglishDSSSB PGT 2021

Q10.Let n be a fixed natural number. Thus, the series () ≥ ∑ m m n –1 m is–

AAbsolutely convergent if n > 100 BDivergent CConvergent DAbsolutely convergent

Show answer

EnglishJSSC PGT 2018

Q11.As n → → → ∞ ∞ ∞, the sequence s = (n3 + 4)/(10 + 6n3):

AIs undefined BConverges to 1/6 CConverges to 2/5 DDiverges

Show answer

EnglishOPSC PGT 2017

Q12.The series 1/ 3 1/ 3 (n 1) (n) is:

AConvergent BDivergent COscillatory DA power series

Show answer

EnglishUP TGT 2021

Q13.→∞ 2 2 2 2 3 n 1 + 2 + 3 +....+ n lim n is equal to

A0 B1/3 C2/3 DDoes not exist

Show answer

EnglishUP Higher Asst. Prof. 2021 UKPSC Lecturer (Mains) 2020 UP TGT 2009 UP PCS (Pre) 2006

Q14.Value of →∞ n 1 1 1 lim + +........+ n +1 n + 2 n + n is -

A1 log 2 Blog 1 Clog 2 Dlog 4

Show answer

EnglishUP TGT 2021

Q15.The sequence 1 log n is

AConvergent BDivergent to ∞ CDivergent to –∞ DNone of the above

Show answer

EnglishUPPSC GDC 2021

Q16.If f(x)= () →∞ n limf x, Where () () ≤ n f x = nx 1 – x,0 × < 1, then f(x) is equal to

Ax B0 Cx2 D1

Show answer

EnglishUP PGT 2021 LT -2018

Q17.Sum of the series 1 1+ 2 1+ 2 + 3 1+ 2 + 3 + 4 + + + +....... 2 3 4 5 is equal to

A2e Be Ce – 1 De/2

Show answer

EnglishUP PGT 2021

Q18.The sum of the series →∞ n 1 1 1 1 lim + + +........+ n n +1 n + 2 4n is equal to –

A0 B1 Clog 3 Dlog 4

Show answer

EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021 UP PGT 2013 UPPCS (Pre) 2003, 2000

Q19.The value of () →∞ ∑ n-1 n 2 2 r=0 1 lim n – r is

Aπ/4 Bπ/2 Cπ Dπ/3

Show answer

EnglishHaryana PGT 2020

Q20.n→∞ ∑ 2n 2 2 r=1 1 r lim = n n + r

A–1 + 2 B1 + 2 C–1 + 5 D1 + 5

Show answer