Math Chapter Wise

EnglishBihar (TRE 2.0)-2023

Q01.The value of loge 2 is

A1+ 1 1 1...... 2! 3! 4! + + + B0 C1- 1 1 1...... 2 3 4 + − + DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q02.The sum of the infinite series 1- 2 3 1 1 1 + - +...... 2 2 2 is

A1 B1/2 C2/3 DMore than one of the above ENone of the above

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EnglishKVS PGT 2022

Q03.If tanθ + secθ = ex, then cosθ is equal to:

Ax x 2 e e− + Bx x e e 2 − Cx x e e 2 − + Dx x 2 e e− −

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EnglishRPSC PGT 2022

Q04.If x2 y – 2x + y = 0; x 1, < than 3 5 3 5 y y x x y + +........... / x + + +......... 3 5 3 5 is equal to -

A4 B2 C1/2 D1/4

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EnglishRPSC PGT 2022

Q05.3 5 7 9........... 1 3 5 7 + + + + is equal to -

Ae B1 3e e 2 − C1 3e e 2 − + D3e/2

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EnglishDSE TGT 2022

Q06.Series expansion at origin is called

ALogarithmic Bexponential CMaclaurins DTaylors

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EnglishDSE TGT 2019

Q07.The sum value of the series sin p + x sin (p+q) + [(x2)/2!] sin (p+2q) +........ is

Ae(x cos q)/[sin (p + x sin q)] Be(x cos q) C0 De(x cos q)/[cos (p + x sin q)]

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EnglishOAVS TGT 2018

Q08.If n n n d I (x log x) dx and n n 1 I nI (n 1)!, then which of the following is correct?

An 1 1 1 1 I (n 1) log x 1... 2 3 n 1 n Bn 1 1 1 1 I n! log x 1... 2 3 n 1 n Cn 1 1 1 1 I (n 1) log x 1... 2 3 n 1 n Dn 1 1 1 1 1 I log x 1... n! 2 3 n 1 n

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015 UPTGT 2005

Q09.If N n!(n! 1.2....n) = where n 2 > > is a natural number then the value of 2 3 n 1 1 1.... log N log N log N + + + + + + + + + + + + is equal to–

A1 B0 Cn! DNone of these

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

Q10.log tan1 logtan 2...logtan89 is equal to–

A1 B0 Ctan 1n Dtan 89n

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EnglishPGT 2011

Q11.Expansion of x e 1 e + by Maclaurin's theorem is:

A2 1 1 1 x x........ 2 4 48 + − + B2 1 1 1 x........ 3 4 x + − + C2 2 1 1 1 x x........ 2 4 36 + + + DNone of these

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EnglishPGT 2013

Q12.The third term in expansion of power of (x–2) in x4 –3x3 is-

A12(x–2)2 B5 (x–3)2 C6(x–2)2 D5(x–2)3

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EnglishPGT 2010

Q13.The sum of the series 2 2 2 2 2 2 1.2 2.3 3.4... 1! 2! 3! + + + + + + + + + + + + is

A27e B24e C28e DNone of these

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EnglishPGT 2010

Q14.The sum of the series 2 3 4 5 1 2 3 4 x x x x........ 2 3 4 5 + + + + + + + + + + + + + + + + is (where |x| <1)

A() log 1 1 x + + + B() log 1 1 + − − x C() log 1 1 x − + + + DNone of these

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EnglishPGT 2010

Q15.Expansion by Maclaurin's theorem of ex cos x will be

A3 2 4 2 5 2 2 2 1.... 3! 4! 5! x x x x − − + + + + B3 2 4 2 5 2 2 2 1.... 3! 4! 5! x x x x + − − − + C3 2 4 2 5 2 2 2 1.... 3! 4! 5! x x x x − − − − − + D3 2 4 2 5 2 2 2 1.... 3! 4! 5! x x x x + + + + +

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EnglishPGT 2009

Q16.The value of the series... 2 2 3 3 1 1 1 1 1 1 1 1 1 2 2 3 4 6 2 3 2 3 + − + + + − + − + + + − + − + + + − + − + + + − is

Alog 2/e Blog 3/e Clog 2/e Dlog 3/e

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EnglishPGT 2009

Q17..... 3 5 1 1 3 5 m n m n m n m n m n m n − − − − − − − − − − − − + + + + ∞ + + + + ∞ + + + + ∞ + + + + ∞ + + + + + + + + + + + + =

Alog e m n Blog e n m Clog − + e m n D1 log 2 e m n

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EnglishPGT 2009

Q18.Sum of the series 13 + 23 + 33 +…n3 is

A2 (1) 2 + n n B(1)(2) 2 + + n n n C2 (1) 2 + n n DNone of these

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EnglishPGT 2009

Q19.The value of 3.6 + 6.9 + 9.12 +….3n. (3n + 3) is

A3 (1)(2) + + n n n B3 (1) + n n C3 (2) + n n DNone of these

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EnglishPGT 2005

Q20.If |x|<1, the sum of the infinite series 2 3 4 1! 1 2! 1 3! 1.... 2! 3! 4! + + + + + + + + + + + + + + + + + + + + + + + + + + + + x x x x is

A() log 1 x e e x − − B() log 1 1 x e e x + − − C() log 1 1 x e e x − − − D() log 1 x e e x + −

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