Math Chapter Wise

EnglishPGT 2009

Q61.If ˆ ˆ ˆ 2 F x yi xzj yzk = + + = + + = + + = + +, then the value of div curl F is?

A3 B2 C1 D0

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EnglishPGT 2009

Q62.The value of div () × × a r a where a is a constant vector is

A2/2a B2/a C2/3a DNone of these

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EnglishPGT 2009

Q63.Curl of gradient of.. () i e curl φ ∇φ ∇φ =

Ainfinite Bzero Cpositive DNone of these

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EnglishPGT 2005

Q64.If the vector ˆ ˆ ˆ (2x 3y)i (2y z)j (3x az)k + + − + + + + − + + + + − + + + + − + + is solenoidal, then the value of the constant 'a' will be

A–2 B–4 C2 D4

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EnglishPGT 2005

Q65.If φ is a scalar function of x, y, z then the value of ∇ ∇ ∇× × ×(∇ ∇ ∇φ) will be

Aφ B0 Cx+y+z DNone of these

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EnglishPGT 2004

Q66.If the vector (x + 3y) i + (y - 2z)j + (x + az) k is solenoidal then the value of the constant 'a' will be

A-1 B-2 C2 DNone of the above

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EnglishPGT 2004

Q67.The linear transformation T (x, y) = (a1x + b1y, a2x+b2y) defined on R2 invertible, if and only if

A1 2 2 1 0 − ≠ a b a b B1 2 1 2 0 − ≠ a a b b C1 1 2 2 0 − ≠ a b b b D1 2 1 1 0 − ≠ a b a b

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EnglishPGT 2003

Q68.2 3 ˆ ˆ ˆ 3 3 2 r ti t j t k = + + = + + = + + = + + Then 2 ˆ 2 ˆ r dr d dt dt × × is

A() 2 9 3 2 2 − + t i t j k B() 2 18 3 2 2 − + t i t j k C() 2 18 2 2 2 − + t i t j k D() 2 9 2 2 − + t i t j k

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EnglishPGT 2003

Q69.Find div F and curl F, When F = grad (x3 +y3 +z3 –3xyz)

A6(),0 + + x y z B2 2 2 2(),0 + + x y z C6(),2 3 + + + x y z xi j D2 2 2 6(),2 3 + + + x y z xi j

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EnglishPGT 2003

Q70.The derivative of a constant vector is

AA scalar Ba constant vector CZero vectors DNone of these

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EnglishPGT 2003

Q71.if F be a solenoidal vector, then curl curl curl F is

A4 F ∇ B3 F ∇ C2 F ∇ DNone of these

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EnglishPGT 2003

Q72.Find the co–ordinates of the centre of gravity of the arc of the asteroid 2 2 2 3 3 3 x y a + = + = which lies in the positive guard rant

A, 5 5 a a B2, 5 5 a a C2 2, 5 5 a a DNone of these

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EnglishPGT 2003

Q73.What is the dimension of the subspace W of IR3 where (()) { { } } 3,,. 2 0,2 3 0 W x y z IR x y z x y z = ∈ + + = + + = ∈ + + = + + = ∈ + + = + + = ∈ + + = + + =?

A1 B2 C3 D4

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EnglishPGT 2003

Q74.Which one of these statements is true for any two vectors α,β in Euclidean space?

A(), α β α β ≤ B(), α β α β = C(), α β α β > DNone of the above

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EnglishRajasthan TGT 2016

Q75.If f is a vector point function then grad (divf)=

Acurl (curl f)–∇2/f Bcurl (curl f)+∇2/f Ccurl (grad f) Dcurl (curl f)

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EnglishU.P.L.T. 2018 Rajasthan TGT 2016

Q76.Vector 3 r is

Aonly solenoidal Bonly irrotational Csolenoidal and irrotational both Dneither solenoidal nor irrotational

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EnglishRajasthan TGT 2016

Q77.If r (cosnt)a (sinnt)b, = + = + then dr r dt × =

A() n b a × B() n a b × C(cos nt+sin nt) () b a × D(cos nt+sin nt) () a b ×

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EnglishRajasthan TGT 2016

Q78.div (grad tan–1 y/x)=

A–1 B0 C1 D2

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EnglishRajasthan TGT 2015

Q79.If ˆ ˆ ˆ r xi yj zk = + + = + + = + + = + + and r r = then 1 grad r is equal to

A−2/r B3 2 r − C−3/r D2 1 r −

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EnglishRajasthan TGT 2015

Q80.If ˆ ˆ ˆ F (x y 1)i j (x y)k = + + + − + = + + + − + = + + + − + = + + + − + then

AF 0 ∇× = B. F 0 ∇ = C. F (F) 0 ∇× = DF 0 =

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