Math Chapter Wise

EnglishUP TGT-2016 (08-03-2019)

Q61.If a straight line makes angles α, β and γ with the co-ordinate axes, then sin2 α+sin2 β+sin2 γ is equal to

A0 B1 C2 DNone of these

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EnglishNVS PGT 10-06-2019

Q62.The lines x 1 y 4 z 5 k 2 1 − − − − − − − − − − − − = and x 2 y 3 z 4 1 1 k − − − − − − − − − − − − = − are coplanar if the value of k is:

A2 B–2 C1 D–3

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EnglishNVS PGT 10-06-2019

Q63.The equation of a plane passing through the point (1, –1, 2) and parallel to the plane 3x+4y– 5z=0 is:

A3x+4y–5z–1 = 0 B3x+4y–5z+11 = 0 C3x+4y–5z+1 = 0 D3x+4y–5z–11 = 0

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EnglishNVS PGT 10-06-2019

Q64.The angle between the planes 2x + y + z = 7 and x – y + 2z = 9 is:

A1200 B600 C300 D900

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EnglishKVS PGT 23-12-2018

Q65.The plane ax+by=0 is rotated through an angle α. The equation of plane in its new position is:

A2 2 ax by z a b tan 0 + + + α = B2 2 ax by z a b tan 0 + + − α = C2 2 ax by z a b cos 0 + + − α = D2 2 ax by z a b cos 0 + + + α =

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EnglishKVS PGT 23-12-2018

Q66.If the angle θ between the line x 1 y 1 z 2 1 2 2 + − − + − − + − − + − − = and plane 2x y z 4 0 − + λ + = − + λ + = − + λ + = − + λ + = is such that 1 sin 3 θ = θ =, then value of λ is:

A1/3 B2/3 C4/3 D5/3

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EnglishLT 2018

Q67.The coordinates of the point, where the line x 2 y 3 z 1 1 1 6 − + − − + − − + − − + − = − intersects the plane 2x+y+z=7, are

A(2, 1, –7) B(7, –1, 2) C(1, –2, 7) D(2, –7, 1)

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EnglishLT 2018 Rajashtan TGT 2016 PCS (Pre) 1997

Q68.If cosα, cosβ, cosγ are the direction cosines of a straight line, then (((()))) 2 2 2 sin sin sin α + β + γ α + β + γ α + β + γ α + β + γ is equal to

A0 B1 C3 D2

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EnglishLT 2018

Q69.The image of the point (3, 5, 7) in the plane 2x+y+z= 6 is

A(5,1,3) B(5,–1, 3) C(5,1,–3) D(–5, 1,3)

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EnglishLT 2018

Q70.The direction cosines of a line segment whose projections on the coordinate axes are –6, 3, 2 are

A6 3 2,, 7 7 7 − B6 3 2,, 7 7 7 C6 3 2,, 7 7 7 − DNone of the above

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EnglishLT 2018 Rajasthan TGT 2011, 2016

Q71.The length of perpendicular from (1, 2, 3) to the line x 6 y 7 z 7 3 2 2 − − − − − − − − − − − − = − is

A3 B17 C7 D20

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q72.The distance of the point (2,3,4) from the plane 3x 6y 2z 11 0 is–

A9 B7 C10 DNone of these

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EnglishSECTION B PGT TIER-I 31.11.2014

Q73.The locus of a point for which x = 0 is–

Axy-plane Byz-planeyz Czx-plane/zx Dnone of these

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EnglishSECTION B PGT TIER-I 31.11.2014

Q74.The perpendicular distance of the point P (6,7,8) from xy-plane is–

A8 B7 C6 DNone of these

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EnglishSECTION B PGT TIER-I 31.11.2014

Q75.If α,β,γ are the angles that a line makes with the positive direction of x,y,z axis respectively, then the direction cosines of the line are–

Asin α, sin β, sin γ Bcos α, cos β, cos γ Ctan α, tan β, tan γ Dcos2 α, cos2 β, cos2 γ

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EnglishSECTION B PGT TIER-I 31.11.2014

Q76.The reflection of the point (α,β,γ) in the xy- plane is–

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

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EnglishSECTION B PGT TIER-I 31.11.2014 UP PCS (Pre) 1998, 2000

Q77.A line makes equal angles with co-ordinate axis. Direction cosines of this line are–

A(1,1,1) B1 1 1,, 3 3 3 C1 1 1,, 3 3 3 D1 1 1,, 3 3 3

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015 PGT 2011

Q78.The distance of a point P(a,b,c) from x-axis is–

A2 2 a c + B2 2 a b + C2 2 b c + D2 2 b c +

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

Q79.The line x 2 y 3 z 4 3 4 5 − − − − − − − − − − − − = is parallel–

A2x + 3y + 4z = 0 B2x + y – 2z = 0 C3x + 4y + 5z = 7 Dx + y + z = 2

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

Q80.The angle between two diagonals of a cube is–

A1 1 cos 3 − B0/30 C1 1 cos 3 − D0/45

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