Math Chapter Wise

EnglishBihar (TRE 1.0) -2023

Q01.Which of the following is the imaginary part of a possible value of ln () i?

Aπ B2/π C4/π DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q02.The principal value of ()() –2i/π –1 is

Ae2i Be2 Ce–2 DMore than one of the above ENone of the above

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EnglishUP PGT 2021

Q03.If sin (θ + iφ) = tanα + i secα then cos 2θ cosh 2φ is equal to –

A3 B2 C6 D4

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EnglishUP PGT 2021

Q04.If x = log (secθ + tanθ), then cosh x is equal to–

Atan θ Bcos θ Csin θ Dsec θ

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EnglishUP PGT 2021

Q05.Real part of sin2 (x + iy) is –

A[ ] 1 1 cos2 cosh 2y 2 + x B[ ] 1 1– cos2 cosh 2y 2 x C[ ] 1 1 sin 2 sinh 2y 2 + x D[ ] 1 1– sin 2 cosh 2y 2 x

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EnglishUP TGT 2021

Q06.For all () ∈ –1 x –1,1,tanh x is equal to

A() 2 log x x 1 + + B() 2 log x – x 1 + C1 1 x log 2 1– x + D1 x 1 log 2 x –1 +

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EnglishUP PGT 2021

Q07.sinh(x + iy) is equal to–

Asinx coshy + i coshx siny Bsinhx cosy + i coshx siny Csinx coshy – i coshx siny Dsinx coshy – i coshx siny

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EnglishUPPSC GIC 2021

Q08.If tan (θ + i φ) = cos α + i sin α, then the value of θ is

An 2 4 π − Bn 4 2 π + Cn 4 4 π − Dn 2 4 π +

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EnglishUP PGT 2021

Q09.The real part of e sin(x+iy) is

Ae sinx coshy [cos(cos x sinh y)] Be sinx coshy [sin(cos x sinh y)] Ce cosx sinhy [cos(cos x sinh y)] De cosx sinhy [sin(cos x sinh y)]

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EnglishUK SSSC LT 2020

Q10.Which of the following option is correct?

A2 3tan h x tan h3x 1 3tan h x = + B2 3tan h x tan h3x 1 3tan h x = − C3 2 3tan h x tan h x tan h3x 1 3tanh x − = − D3 2 3tan h x tanh x tan h3x 1 3tanh x + = +

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EnglishUP PGT 2021

Q11.Consider the following statements – I: d dx sech x= sech x tanh x II: d dx sinh–1 x = 2 1 x +1

Aonly I Bonly II CI and II both Dneither I nor II

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EnglishLT 2018

Q12.If cos(x+iy) = cosα + isinα, then the value of (cosh2y + cos2x) is?

A1 B2 C–2 D2

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EnglishDSSB TGT (SECTION-B) 28 DEC 2014

Q13.If x x e e y e e then dy dx is equal to–

A2/sech x B2/cosh x C2/sec h x D2/cosec h x

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EnglishUP TGT-2016 (08-03-2019)

Q14.If f(x) = cos hx + sin hx, then which one of the following is correct?

Af(x) f(y) = f(x)+f(y) Bf(x) f(y) = f(xy) Cf(x) f(y) = f(x+y) Dx f(x)f(y) f y =

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EnglishUP PGT-2016 (02-02-2019)

Q15.Which one of the following is correct?

A1 1 sinh x isin (ix) − − = B() 1 2 cosh x log x 1 x − = + − C() 1 1 cosh x icos ix − − = D() 1 1 tanh x itan ix − − =

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EnglishUP PGT-2016 (02-02-2019)

Q16.Value of x i ilog x i − + is

A1 2tan x − π + B1 2tan x 2 − π + C1 2tan x 2 − π − D1 2tan x − π −

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EnglishUP PGT-2016 (02-02-2019)

Q17.sin h–1 (cot x) is equal to

A() log cosx sin x + B−( )/log cosx sin x C() log cot x cosecx + D() log tan x cot x +

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EnglishPGT 2011

Q18.If sin (x+iy) = p+iq, then q=

Asinx cosy Bcosx siny Csinx coshy Dcosx sinhy

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EnglishPGT 2011

Q19.log (1+i) is equal to:

A1 log2 2 B1 log2 4 2 π + C1 log2 i 2 4 π + DNone of these

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EnglishPGT 2011

Q20.The value of log (–3) is:

Alog3 i/+ π Blog3 i/− π Clog3 2 i/+ π Dlog3 2 i/− π

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