Math Chapter Wise

EnglishEMRS PGT-2023

Q01.The shortest distance between the lines 1 x +1 y + 2 z +1 L: = 3 1 2 and 2 x - 2 y + 2 z - 3 L: = 1 2 3 is:

A17/3 B41/4 3 C17/5 3 D0

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EnglishEMRS PGT-2023

Q02.The angle between the lines 2x = 3y = -z and 6x = -y = -4z is:

A30º B45º C90º D0º

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EnglishEMRS PGT-2023

Q03.Which of the following points lies on the line passing through the point (2, -3, 5) and parallel to vector ˆ ˆ ˆ i + 3j- 4k?

A(2, 3, 5) B(0, 1, 2) C(3, 0, 1) D(-2, 3, -5)

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EnglishBihar (TRE 1.0) -2023

Q04.Find the shortest distance between the lines x - 8 y + 9 z -10 = 3 -16 7 and x -15 y - 29 z - 5 = 3 8 -5

A16 B14 C15 DMore than one of the above ENone of the above

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EnglishKVS PGT 2023

Q05.The Position vector of the point which divides the join of points 4 a + b and a - 2 b externally in the ratio 2: 3 is:

A() 1 14a b 5 − B() 1 11a 4b 5 − C5a 8b/+ D10a 7b/+

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EnglishKVS PGT 2023

Q06.The projection of AB i 2j 4k = − + on CD i 2j 2k = − + + is:

A14/3 B1 C4 D5/3

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EnglishKVS PGT 2023

Q07.The angle between the two lines x 2 y 1 z 3 2 7 3 − + − + = − − and x 2 2y 8 z 5 1 4 4 + − − = − is:

A30° B60° C45° D90°

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EnglishKVS PGT 2023

Q08.Coordinates of a point/ the points on a line x 2 y 1 z 3 3 2 2 + + − = Which is/are at a distance of 5 units from a point P (1, 3, 3) is /are:

A(−2, −1, 3) and (4, 3, 7) B(− 2, −1, 3) C(−2, 3, −1) and (4, 7, 3) D(4, 7, 3)

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EnglishKVS PGT 2023

Q09.The value of λ for which the vector a 4i 6j 2k = + +, b i 4j 3k = − − and c i j 3k = λ + − are coplanar is:

A− 4 B0 C8 D4

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EnglishKVS PGT 2023

Q10.The image of point (− − −1, 3, 4) in the plane x − − −2y = 0 is:

A17 19,,4 3 3 − − B() 15,11,4 C17 19,,1 3 3 − − D9 13,,4 5 5 −

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EnglishNVS PGT 2022

Q11.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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EnglishNVS PGT 2022

Q12.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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EnglishKVS PGT 2022

Q13.The position vector of the point which divides the join of points 3a 2band a b − + internally in the ratio 3: 1 is:

A6a b 4 + B−10a 5b/4 C10a 5b 4 + D−6a b/4

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EnglishKVS PGT 2022

Q14.The distance of a point (5, 2, –4) from the plane () r. 3i 2j 3k 4 − + = is:

A9/29 B15/29 C5/29 D9/50

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EnglishKVS PGT 2022

Q15.If lines x - 5 2- y 1- z = 5λ + 2 5 -1 and x 2y +1 1- z = 1 4λ -3 are perpendicular to each other, then the value of λ is:

A–1 B0 C1 D1/3

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EnglishRPSC PGT 2022

Q16.Equation of Tangent line at point λ = 1 to the curve r = (1+ λ, – λ2, 1+ λ3) is -

Ax 2 y 1 z 2 1 1 3 − − − = Bx 2 y 1 z 2 2 2 3 − + − = − Cx 2 y 1 z 2 1 2 3 − + − = − Dx–1 = –2 (y+1) = 3(Z–2)

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EnglishRPSC PGT 2022

Q17.Shortest distance between lines ˆ ˆ ˆ ˆ r = -3λk andr = (1- t)i + 2tj is -

A1/2 B2/5 C1/5 D0

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EnglishRPSC PGT 2022

Q18.If line x - 3 y - 4 z - 5 = 2 3 4 lies in the plane 4x + cy + 4z – d = 0, then values of c and d are respectively -

A5, 3 B2, –8 C–8, 0 D8, 0

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EnglishRPSC PGT 2022

Q19.The sum of the coordinates of a point lying in the yz – plane is 8. If its distance from xz – plane is thrice to its distance from xy – plane, then its coordinates are-

A(6, 2, 0) B(0, 6, 2) C(0, 2, 6) D(2, 0, 6)

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EnglishRPSC PGT 2022

Q20.The three straight lines 3x + 4y + 6 = 0, 4x + 7y + 8 = 0, x + 3 2 y + 2 = 0 are-

AParallel BSides of a triangle CSides of isosceles triangle DConcurrent

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