Math Chapter Wise

EnglishUPPSC Ashram Paddhati 2021

Q21.If S denotes the surface of the cube bounded by the planes x = 0, x = 1, y = 0, y = 1, z = 0, z = 1 then the value of normal surface integral of ˆ ˆ ˆ 3 2 F = (x – yz)i – 2x y j+ 2k over S is

A1 B1/3 C1/5 D1/6

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EnglishUPPSC Ashram Paddhati 2021

Q22.The unit normal to the surface x2 + 4y2 – 3z2 – 2 = 0 at the point (1, 1, 1) is

A1 ˆ ˆ ˆ (i + 4j– 3k) 26 Bˆ ˆ ˆ/i + 4j– 3k C1 ˆ ˆ ˆ (i + j+ k) 3 D1 ˆ ˆ ˆ (i – 3j – k) 11

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q23.What is the divergence of the vector field f = 6 x2 i+3xy2 j+xyz3 k at the point (2,3,4).

A124 B348 C106 D100

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EnglishHaryana PGT 2018

Q24.For c > 0, if ˆ ˆ ˆ ai +bj+ck is the unit normal vector at () 1, 1, 2 to the cone 2 2 z = x + y, then:

A2 2 2 a b c 0 + + = B2 2 2 a b c 0 + − = C2 2 2 a b c 0 − + = D2 2 2 a b c 0 − + + =

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male) Rajasthan TGT 2013

Q25.A vector field with a vanishing curl is known as__

AIrrotatioal BSolenoidal CCycloidal DRotational

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q26.What is the Green's value for the functions F = y2 and G = x2 for the region x =1 and y = 2 from origin.

A2 B–1 C1 D–2

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q27.Calculate the value of the integral ∫ 2 C (xydy – y dx) where C is the square, cut form the first quadrant by the lines x = 1 y = 1, will be? (Using Green's theorem)

A1/2 B3/2 C7/2 D5/2

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q28.Stokes theorem is used to convert the __ integrals to__ integrals

Aline to surface Bvolume to area Csurface to line Dline to area

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q29.Divergence and curl of a vector field are _____

AScalar & Scalar BScalar & Vector CVector & Scalar DVector & Vector

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EnglishUK SSSC LT 2020

Q30.The value of div 3 r is:

Ar B0 C1 D1/r

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English(GIC) PGT, 2015

Q31.If ˆ ˆ ˆ r xi yj zk and a is a constant vector, then curl r a

Aa B2a C3a DNone of above

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English(GIC) PGT, 2015

Q32.grad φ at a point to the surface φ (x,y,z) = const. is a vector–

Aparallel to a tangent to the surface Bnormal to the surface Cof constant magnitude Dhaving constant direction

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English(GIC) PGT, 2015

Q33.If ˆ ˆ ˆ F axi byj czk, then s ˆ F nds, = ∫∫ ∫∫ where S is the surface of 2 2 2 x y z 1 is equal to –

A(a b c) B4 (a b c) C4 (a b c) 3 D2 (a b c) 3

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English(GIC) PGT, 2015

Q34.If 2 2 2 ˆ ˆ ˆ F x yi y zj z xk, then value of curl F at the point is (1,2,3) –

Aˆ ˆ ˆ 4i 9j k − + − Bˆ ˆ ˆ/4i 9j k Cˆ ˆ ˆ/4i 9j k Dˆ ˆ ˆ/3i 4j k

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English(GIC) PGT, 2015

Q35.If ˆ ˆ r i cosnt jsinnt where n is a constant t is variable then the value of dr r. dt is–

A1 B–1 C2 DNone of the above

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EnglishTGT 2013

Q36.If a particle is being displaced on the operating equation x = e–t, y = 2cost, z = sint then what will be the velocity of the particle?

At ˆ ˆ ˆ e i 2sin t j cos t k − − − + Bt ˆ ˆ ˆ e i 2cos t j sin t k − − + + Ct ˆ ˆ ˆ e i 2sin t j cos t k − − + Dt ˆ ˆ ˆ e i 2sin t j cos t k − −

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EnglishNVS PGT 10-06-2019

Q37.The nature of singularity of the function tan (1/z):

Az=0 is a non –isolated essential singularity Bz = 0 is an isolated singularity Cz=0 is an isolated essential singularity Dz = 0 is a removable singularity

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EnglishUP PGT-2016 (02-02-2019)

Q38.For what value of m, the vector (m,3,1) is a linear combination of the vectors (3,2,1) and (2, 1, 0)?

A2 B3 C5 D1

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EnglishUP PGT-2016 (02-02-2019)

Q39.If 3 3 3 F grad(x y z 3xyz), = + + − = + + − = + + − = + + − then F is

Asolenoidal Birrotational Csolenoidal and irrotational both Dnone of the above

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EnglishUP PGT-2016 (02-02-2019)

Q40.A vector, which is normal to the surface 2 x xy yz 5 − + = − + = − + = − + = at the pint (1, 2, 3) is

Aˆ ˆ i 2j + Bˆ ˆ 2j 2k + Cˆ ˆ 2j k + Dˆ ˆ j 2k +

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