Math Chapter Wise

EnglishDSE TGT 2022

Q21.The equation of the line passing through the point (1,–1,1) and parallel to the vector i-j+k is

Ax 2 y 1 z 1/1 2 1 Bx 1 y 1 z 1/1 1 1 Cx 1 y 1 z 1/1 2 1 Dx 6 y 1 z 1/1 1 2

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EnglishDSE TGT 2022

Q22.The equation of the plane passing through (- 10,5,4) and perpendicular to the line joining the points (4,–1,2) and (–3,2,3) is

Ax–3y–z+79=0 B7x–3y–z+89=0 C7x–y–z+9=0 Dx–y–z+89=0

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EnglishDSE TGT 2022

Q23.The equation of the plane passing through the points A= (1,1,1), B=(1,− − −1,1), C=(− − −7− − −3, − − −5) is

A3x− − −z+1=0 B3x− − −4z+1=0 Cx− − −4z+1=0 D3x− − −4z=0

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EnglishOAVS TGT 2021

Q24.If the points A (1, 6), B (3, 4) and C (k, 1) are collinear, then the value of k is:

A6 B4 C9 D8

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EnglishOAVS TGT 2019

Q25.How many plane can be made to pass through three distinct non-collinear points?

A3 B1 C2 DInfinite

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EnglishJSSC PGT 2018

Q26.Find the length of the arc of the circular helix with vector equations r (t) = ˆ ˆ ˆ Costi +sintj+ tk from (1,0,0) to (1, 0, 2π).

A2π B2 2π C1 Dπ

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EnglishJSSC PGT 2018

Q27.The Cartesian equation of the surface x = µ cosv, y = µ sin v, z = µ is:

Ax2 + z2 = y2 tan v Bx2 + y2 = z2 cot v Cx2 + y2 = z2 tan2 v Dx2 + z2 = y2 cot v

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EnglishUP PGT 2021 UPPCS (Pre) 2002

Q28.The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and 2lm + 2nl – mn = 0 is –

A45º B90º C120º DNone of the above

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EnglishUP PGT 2021

Q29.If the plane x + 2y + 3z = p touches the conicoid x2 – 2y2 + 3z2 = 2, then the value of p is–

A0 B1 C4 D2

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q30.The line x 2 y 3 z 5 3 4 5 − − + = − meets the plane x + 3y – 5z + 4 = 0 at the point-

A(–1, –1, 0) B(1, 1, 0) C(1, 0, 1) D(0, –1, –1)

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EnglishUPPSC GIC 2021

Q31.The distance between the planes 2x y z 1 + + = and 3x 6y 3z 2 + + = is-

A4/3 3 B1/3 6 C2/3 6 D5/2 6

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q32.A line lying in the yz - plane is inclined at an angle α with z - axis. Its direction cosines are-

A0, sinα, cosα B0, cosα, sinα Csinα, cosα, 0 Dcosα, sinα,0

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EnglishUPPSC Ashram Paddhati 2021

Q33.The lines 1 1 r = a + t b and 2 2 r = a +s b are coplanar, if

A1 2 a ×a = 0 B1 2 b ×b = 0 C() () 2 1 1 2 a – a b ×b = 0 ⋅ Dnone of the above

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EnglishUPPSC Ashram Paddhati 2021

Q34.A line makes angles α, β, γ, δ with the four diagonals of a cube, then the value of sin2 α + sin2 β + sin2 γ + sin2 δ is

A4/3 B3/4 C8/3 D3/8

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EnglishUPPSC Ashram Paddhati 2021 UPPCS GIC 2021 UKPSC Lecturer (Mains) 2020

Q35.The shortest distance between the lines x –1 y – 2 z – 3 = 2 3 4 and x – 2 y – 3 z – 4 = 3 4 5 is

A0 B1/6 C2/9 D5/6

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EnglishUKPSC Lecturer (Mains) 2020 UKPSC GIC 2018

Q36.If P(3,2,-4), Q(5,4,-6), R(9,8,-10) are collinear, then the ratio in which Q divides PR is:

A1:2 B1:4 C2:3 D2:1

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EnglishUKPSC Lecturer (Mains) 2020 UPPCS (Pre) 1996, 2000 UP TGT 2016 (08.03.2019)

Q37.The lines x = ay + b; z = cy + d and x= a' y + b', z = c' y + d' are perpendicular if

Aaa' + cc' + 1= 0 Baa' + bb' + cc' = 0 Caa' + bb' + dd' = 0 Dbb' + cc' + 1= 0

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EnglishUKPSC Lecturer (Mains) 2020

Q38.The two points (1,1,1) and (–3, 0, 1) with respect to the plane 3x + 4y – 12z + 13 = 0 lie on

Aopposite side and equidistant from it Bsame side and equidistant from it Cthe plane Dopposite side and not equidistant from it

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EnglishUKPSC Lecturer (Mains) 2020

Q39.Image of the point (1,-1,2) in the plane 2x–3y + z = 14 is:

A(3,3,4) B(–3,4,–3) C(3,–4,3) D(–3,–4,–3)

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EnglishUKPSC Lecturer (Mains) 2020

Q40.Consider the lines x +1 y + 2 z +1 = 3 1 2 and x – 2 y + 2 z – 3 = 1 2 3 Then the unit vector perpendicular to both the lines is:

A() 1 ˆ ˆ ˆ i 7j k 99 − + + B() 1 ˆ ˆ ˆ i 7j 5k 5 3 − − + C() 1 ˆ ˆ ˆ i 7j 5k 5 3 − + + DNone of these

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