Math Chapter Wise

EnglishUP PGT-2016 (02-02-2019)

Q41.Which one of the following is not correct for a common catenary

Ax /c y s ce + = B2 ds csec d = ψ ψ Cy/c sec tan e ψ + ψ = Dx s csinh c =

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EnglishUP PGT-2016 (02-02-2019)

Q42.If (((()))) n div r r 0 = then n is equal to

A–3 B1 C2 D–1

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EnglishUP PGT-2016 (02-02-2019)

Q43.The directional derivative of xy yz zx φ = + + φ = + + φ = + + φ = + + at (1,1,1) in the direction of the vector ˆ ˆ ˆ i 2j 2k − + is

A1/3 B2/3 C5/3 D7/3

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EnglishLT 2018

Q44.If a,b,c are non-coplanar unit vectors such that (((()))) b c a b c, 2 + × × = × × = × × = × × = then the angle between a and b is

A3 4 π B4/π C2/π Dπ

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EnglishLT 2018

Q45.div ((()) r a, × × where a is a constant vector, is equal to

A0 Ba Cr Da.r

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EnglishLT 2018

Q46.If vectors A and B are irrotational, then

AA B/× is irrotational BA B/× is solenoidal CA B/− is rotational DNone of the above

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EnglishPGT 2005 LT 2018

Q47.If a and b are constant vectors, then (((()))) r ab ∇ is equal to

A0 B( )/a.b r Ca b/× D() a b r ×

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EnglishSECTION B PGT TIER-I 31.11.2014

Q48.Let V be the vector space of functions on the interval [0,1]. Then the functions x3, sin x and cos x are–

ALinearly dependent BLinearly independent CData are insufficient DNone of the above

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

Q49.The following set of 3 vectors 1 x 2, 6 1 x and 3 4 2 in 3 IR are linearly dependent when x is equal to-

A0 B1 C2 D3

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

Q50.Two vectors u and v are orthogonal if –

Au.v 0/≠ Bu.v 0 = Cu.v 1 = DNone of these

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

Q51.The value of (((()))) div(curlF)i.e.. F ∇ ∇ × ∇ ∇ × ∇ ∇ × ∇ ∇ × equal to–

A0 B1 C2/V F Dnone of these

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

Q52.Divergence of the vector 2 2 ˆ ˆ ˆ x zi xyj yz k + − + − at (1, 1,1) − − is–

A0 B3 C5 D6

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EnglishPGT 2013

Q53.The unit vector normal at the point (–1, –1, 2) on the surface xy3 z2 =4 is?

A4 12 4 i j K − − + B() 1 11 i j k − + − C() 1 3 11 i j k − + − Di j k/+ −

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EnglishPGT 2013

Q54.If (((()))) ((()) 2 2 2 = + + − + = + + − + = + + − + = + + − + F x ay x i xy y j is a irrotational vector then the value of a will be:

A2 B–1 C0 D–2

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EnglishPGT 2013

Q55.What will be the directional derivative of (())) 2 3,, f x y z xy yz = + = + at the point (2, –1, 1) in the direction of the vector ˆ ˆ ˆ 2 2 i j k + + + +?

A−11/2 B8/3 C5 D−11/3

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EnglishPGT 2010

Q56.If the vector ((())) ((()))ˆ ˆ F x,y,z x 2y az i xk = + + + = + + + = + + + = + + + is irrotational then the value of a is

A2 B1 C0 DNone of these

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EnglishPGT 2009

Q57.If C is the curve x2 + y2 = 1, z = y2, then by Stokes theorem the value of c (yz dx zx dy xy dz) + + ∫ ∫ is

A3 B0 C5 DNone of these

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EnglishPGT 2009

Q58.Value of 2 2 r. r ∇ ∇ is equal to

A3 3 − r B2 2 − r C4 2 − r D4 4 − r

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EnglishPGT 2009

Q59.For the catenary y = c cosh x c

As = c sin x c By = c tan ψ Cs = c sin h x c Ds = c sec ψ

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EnglishPGT 2009

Q60.If = r a − + t t e be ω, where, a b are constant vectors, then d r r dt ω − 2 is equal to

A0 B1 C2 D3

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