Math Chapter Wise

EnglishUKPSC Lecturer (Mains) 2020 TGT 2005

Q41.The distance of the point P(3,8,2) from the line x –1 y – 3 z – 2 = 2 4 3 measured parallel to the plane 3x + 2y –2z + 17 = 0 is:

A6 B18 C7 D5

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EnglishUKPSC Lecturer (Mains) 2020

Q42.The direction cosines of the line which is perpendicular to the lines with direction ratios 1,–2, –2 and 0, 2, 1 are:

A2 1 2,, 3 3 3 − B2 1 2,, 3 3 3 − C1 2 2,, 3 3 3 − D2 2 1,, 3 3 3

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EnglishUKPSC Lecturer (Mains) 2020

Q43.The equation 3 4 5 + + = 0 y – z z – x x – y represents:

Aplane Bstraight line Cpair of planes Dpair of straight lines

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EnglishUKPSC Lecturer (Mains) 2020

Q44.The lines x + y – z = 5; 9x– 5y + z = 4 and 6x – 8y + 4z = 3; x+ 8y –6z+7 = 0 are

AParallel BCoincident CPerpendicular DMaking an angle 450/with each other

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EnglishRajasthan TGT 2011 UKPSC Lecturer (Mains) 2020

Q45.The perpendicular distance of (1, 2, 3) from the line 6 y 7 z 7 3 2 2 − − − = − x is:

A6 B7 C8 D9

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EnglishUKPSC Lecturer (Mains) 2020

Q46.If, x,y,z are three positive real numbers, then minimum value of y z z y y z + + + + + x x x is:

A1 B2 C3 D6

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EnglishHaryana PGT 2019

Q47.If the line x - 3 y + 2 z + 4 = 2 -1 3 is contained in the plane px + qy – z = 9, then the value of p2 + q2 is:

A26 B18 C5 D2

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EnglishHaryana PGT 2019

Q48.If plane x y z + + = 1 2 3 6 intersect co-ordinate axes in A, B and C respectively, then area of ∆ ∆ABC is:

A18 B30 C3 14 D13 14

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EnglishHaryana PGT 2019

Q49.If the lines x –1 y – 2 z – 3 = k 2 3 and x – 2 y – 3 z –1 = 3 k 2 intersect in a point, than the integral value of k is:

A–2 B–5 C5 D2

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EnglishUK SSSC LT 2020

Q50.A line makes angle α, β, γ with coordinate axes then the value of cos 2α + cos 2β + cos 2γ will be:

A0 B1 C2 D–1

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EnglishUK SSSC LT 2020

Q51.The plane 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are:

AMutually perpendicular BParallel CIntersect at y-axis DPasses through 5 0,0, 4

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EnglishUK SSSC LT 2020

Q52.The acute angle between two lines, whose direction ratio are 2, 3, 6 and 1, 2, 2 is:

Acos–1/(20/21) Bcos–1/(18/21) Ccos–1/(17/21) DNone of the above

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EnglishHaryana PGT 2020

Q53.Which of the following planes is parallel to the line x- 2 y - 3 z -4 =? 3 4 5

A2x + 3y + 4z = 29 B3x + 4y + 5z = 5 2 C2x + y – 2z = 3 D2x – y + 2z = 3

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EnglishHaryana PGT 2020

Q54.A plane passes through the fixed point (a, b, c) and cuts the coordinates axes respectively in A, B and C. The locus of the centre of the sphere passing through origin and A, B and C will be:

Ax y z 1 a b c + + = Bx y z 2 a b c + + = Ca b c 1 x y z + + = Da b c 2 x y z + + =

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EnglishHaryana PGT 2020

Q55.If coordinates of points A, B, C and D are respectively (3, 5, –3), (2, 3, –1), (1, 2, 3) and (3, 5, 7), then:

AAB CD/⊥ BAB CD CAngle between AB and CD is 3 π DAngle between AB and CD is 6 π

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EnglishUKPSC GIC 2018

Q56.A line () ()ˆ ˆ r = 3 + 2λ i + 4 - 2λ j + (1 + λ)k crosses the plane x – 2y – 5z = 2 at the point P. The distance between points P and Q = (3, 4, 1) is

A3 B9 C12 D36

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EnglishUKPSC GIC 2018

Q57.Shortest distance between the pairs of straight lines () () () ˆ ˆ ˆ − − − r = 1 t i + t 2 j+ 3 2t k () () () ˆ ˆ ˆ − − r = S +1 i + 2S 1 j 2S +1 k is

A8/29 B8/3 6 C18/29 D16/29

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EnglishUKPSC GIC 2018

Q58.The angle between the lines whose direction cosines are given by the equation 3 ℓ + m + 5n = 0 and 6mn –2n ℓ + 5 ℓ m = 0 is

Aθ = cos–1 4 6 B6 π θ = C1 1 cos 6 − θ = Dθ = cos–1 2 3

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EnglishUKPSC GIC 2018

Q59.The distance between the parallel planes 2x – y + 2z +3 = 0 and 4x –2y + 4z + 5 = 0 is

A1/6 B5/6 C1/3 D2/3

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EnglishUKPSC GIC 2018

Q60.How many unrelated conditions are required to determine a plane?

A4 B3 C2 D1

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