Math Chapter Wise

EnglishRajasthan TGT 2015

Q81.If (X, d) be a metric space and let A,B∈X, then true statement is

AA is a open set. BA is closed if and only if is A A = CA B A B/∪ ≠ ∪ DA B A B/∪ ≠ ∩

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EnglishRajasthan TGT 2013

Q82.If A, B, C, D are any four points in space, and AB× CD+ BC×AD + CA×BD =λ (area of ∆ ∆ABC) then λ is equal to-

A4 B3 C2 D1

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EnglishRajasthan TGT 2013

Q83.The vector f is irrotational vector if-

Agrad f = 0 Bdiv f = 0 Ccurl f = 0 DNone of these

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EnglishRajasthan TGT 2013

Q84.If a is a differential vector point function, then div curl a =

A0 Bgrad a C2/a D2 a

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EnglishRajasthan TGT 2013

Q85.A vector field F is given by () () ˆ ˆ F= siny i +x 1+ cosy j then the ∫F.dr over a circular path given by x2 + y2 = a2, z = 0 is-

A2 2 a π B2 a π C2 1 a 2 π D2 1 a 4 π

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EnglishRajasthan TGT 2013

Q86.If F is a continuously differentiable vector point function in a region v enclosed by the closed surface s, then ˆ ∫v F.nds=

A() v F.dv ∇× ∫ Bv F.dv ∫ C() v F dv ∇× ∫ D() v.F dv ∇ ∫

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EnglishRajasthan TGT 2013

Q87.If c is the rectangle with vertices (0, 0), (π, 0), π, 2 and π 0,, 2 then () ∫ -x -x c e sinydx + e cosydy =

A() 2 e 2 −π − B() 2 e 2 −π + C() 2 e 1 −π − D() 2 e 1 −π +

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EnglishRajasthan TGT 2013

Q88.The set {1, 3, 2}, {1, –7, –8} and {2, 1, –1} of vectors in R3 is-

Alinearly dependent Blinearly independent Clinearly dependent and linearly independent DNone of these

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EnglishRajasthan TGT 2013

Q89.If 'h' is the difference of interval, then () 2 ∆ - x = ∇

Ah2 B2h2 C3h2 D6h2

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EnglishRajasthan TGT 2013

Q90.In difference table the first term of the series whose second and subsequence terms are 8, 3, 0, –1, 0 is-

A5 B10 C15 D20

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EnglishUP PCS (Pre) 2009

Q91.The vector equation 0 D.(r - r) = 0 represents (in 3D)

Aa straight line Ba plane Ca pair of lines DNone of the above

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English(GIC) PGT, 2015

Q92.If a and b are constant vectors, then × × div{(r a) b}is

A2(a.b) B2(a b)/− × C2a.b D0

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English(GIC) PGT, 2015

Q93.Which of the following identities is not correct?

Agrad(ψ) = grad ψ + ψ grad φ Bdiv(a) = div a + a grad φ Cdiv(a b) = b.curl a + a curl b × Dcurl(a) = curl a + (grad) a φ ×

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English(GIC) PGT, 2015

Q94.The vector n r r, where ˆ ˆ ˆ r = xi + yj+ zk and r = r is solenoidal if n is equal to

A–1 B–2 C1 D–3

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English(GIC) PGT, 2015

Q95.Which of the following vectors is not irrotational

Ar, r where ˆ ˆ ˆ r r,r xi yj zk B2 2 ˆ ˆ yi xj x y Ca r where a is a non-zero constant vector and ˆ ˆ r xi yj zk DNone of the above

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English(GIC) PGT, 2015

Q96.The value of the integral x c (e dx 2ydy dz) + − ∫ Where c is the curve x2 +y2 =1, z = 1 is equal to–

A2π Bπ C4π D0

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English(GIC) PGT, 2015

Q97.If div 5 r r A 5 r, then value of A–

A3 B5 C10 D8

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English(GIC) PGT, 2015

Q98.The value of 2 1 r where r r and ˆ ˆ ˆ r xi yj zk,is

A3 2 r B0 C3 2 r DNone of the above

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English(GIC) PGT, 2015

Q99.The work done in moving a particle in a force field– 2ˆ ˆ ˆ F 3x i (2xz y)j zk Along the line joining (0,0,0) to (2,1,3) is –

A16 B12 C18 D20

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English(GIC)PGT, 2015

Q100.If s is the surface of the sphere 2 2 2 2 x y z a, then the value of 2 S (xydydz y dzdx yzdxdy) is equal to–

A3/4 a B3 4 a 3 C3 16 a 3 D0

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