Math Chapter Wise

EnglishBihar (TRE 2.0)-2023

Q01.The length of the vector represented by the directed line segment with initial point P (2, - 3, 4) and terminal point Q (-2, 1, 1) is

A41 B32 C43 DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q02.In a right circular cone, the cross-section made by a plane parallel to the base is a:

Airustum of a cone Bsphere Chemisphere Dcircle

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EnglishKVS PGT 2023

Q03.The centre of a sphere which passes through the points (a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0), (where a, b, c ≠0) is:

Aa,0,0 2 Bc 0,0, 2 Cb 0,,0 2 Da b c,, 2 2 2

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EnglishNVS PGT 2022

Q04.The equation of a sphere circumscribing a tetrahedron whose faces are x = 0, y = 0, z = 0 and x y z + + = 1 a b c is:

Ax2 + y2 + z2 = a2 + b2 + c2 Bx2 + y2 + z2 + 2ax + 2by + 2cz = 0 Cx2 + y2 + z2 + ax + by + cz = 0 Dx2 + y2 + z2 − ax − by − cz = 0

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EnglishNVS PGT 2022

Q05.The radius of the smallest sphere passing through (1, 0, 0) (0, 1, 0) (0, 0, 1) is:

A2/3 B2/3 C3/2 D3/2

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EnglishNVS PGT 2022

Q06.The number of spheres that can be made to pass through the given three points (a, 0, 0), (0, a, 0) and (0, 0, a) is:

A1 B2 C3 DInfinite

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EnglishKVS PGT 2022

Q07.If line y = mx + c is tangent to the ellipse 2 2 x y 1 a b + =, then condition of tangency and point of contact (of tangent to the ellipse) are:

A2 2 2 2 2 2 a b c a m b,, c c = + B2 2 2 2 2 2 a m b c a m b,, c c = + − C2 2 2 2 2 2 a m b c a m b,, c c − = − − D2 2 2 2 2 2 a m b c a m b,, c c = − −

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EnglishRPSC PGT 2022

Q08.Equation of the axis of right circular cylinder, whose guiding curve is x2 + y2 + z2 = 4; x + y + z = 2, is-

Ax = 2y = 2z B2x = y = 2z C2x = 2y = z D2x = 2y = 2z

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EnglishRPSC PGT 2022

Q09.The condition that the cone ax2 + by2 +cz2 + 2ux + 2vy + 2wz + d = 0 may have three mutually perpendicular tangent planes, is -

Abc + ca + ab = f2 + g2 + h2 Bx2 + y2 = z2 2 tan θ Ca + b + c = 0 Dua + vb + wc + d = 0

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EnglishRPSC PGT 2022

Q10.The equation of the right circular cylinder whose axis is x-axis and radius is “r”, is-

Ay2 + z2 = r2 Bz2 + x2 = r2 Cx2 + y2 = r2 Dx2 + y2 + z2 = r2

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EnglishRPSC PGT 2022

Q11.If x = – y = z is one of the tree mutually perpendicular generators of the cone yz + 2zx – 2xy = 0, then equation of another generator of the cone is -

A2x = –2y = –z B2x = y = –2z C2x = –2y = –2z Dx = –2y = 2z

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EnglishRPSC PGT 2022

Q12.Equation λ S + λ S = 0 1 1 2 2, does not represent an equation of sphere, that passes through the intersection of two spheres S1 = 0, S2 = 0, if -

A1 1 λ = − B2 1 λ = − C1 2 λ = −λ D1 2 λ = λ

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EnglishRPSC PGT 2022

Q13.Equation of a cylinder whose generators are parallel to y-axis and which passes through the curve of intersection of surfaces: x2 + y2 + 2z2 = 12, x – y + z = 1, is-

A11x2 + 11y2 + 10z2 +24 (–xy + xz – yz) = 0 B2x2 + 3z2 + 2xz – 2x – 2z – 11= 0 C3x2 + 2z2 + 2xz – 2x – 2z – 11= 0 D2x2 + 3y2 – 2xz + 2x + 2z – 11= 0

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EnglishRPSC PGT 2022

Q14.Reciprocal cone of cone x2 + 2y2 + 3z2 = 0 is -

A6x2 + 3y2 + 2z2 = 0 B3x2 + 2y2 + z2 = 0 C2 2 x y 2 z 3 2 + + = 0 D6x2 + 2y2 + 3z2 = 0

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EnglishRPSC PGT 2022

Q15.Polar line of line x + 1 y -1 z + 1 = 1 -1 1 with respect to the sphere x2 + y2 + z2 = 2 is-

Ax – y + z = 0 –x + y + z + 2 = 0 Bx – y + z = 0 –x + y – z – 2 = 0 Cx – y + z = 0 –x + y – z + 2 = 0 Dx – y + z = 0 –x – y + z – 2 = 0

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EnglishDSE TGT 2022

Q16.Equation of the sphere having the points (2,1, − −3) and (1, − − −2,4) as the ends of the diameter is

Ax2 +y2 +z2 − −3x+y+z− − −12=0 Bx2 +y2 +z2 +3x+y− − −z− − −12=0 Cx2 +y2 +z2 − −3x− − −y− − −z− − −12=0 Dx2 +y2 +z2 − −3x+y− − −z− − −12= 0

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EnglishUPPSC GDC 2021

Q17.The spheres 2 2 2 x + y + z = 25 and 2 2 2 x + y + z – 24x – 40y –18z + 225 = 0

ADo not intersect BIntersect in two points CTouch internally DTouch externally

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EnglishUPPSC GDC 2021

Q18.Which of the following is a generator of the cone 2 2 2 2x – 3y + 4z = 0?

Ax y z 2 3 4 = Bx y z 1 1 2 = Cx y z 2 1 1 = − Dx y z 1 2 1 = −

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EnglishUPPSC GDC 2021 UPPCS (Pre) 1996, 2005

Q19.The plane ax + by + cz = 0 cuts the cone yz + zx +xy = 0 in perpendicular lines, if

Aa b c 0 + + = B1 1 1 0 a b c + + = C2 2 2 a b c 0 + + = D2 2 2 1 1 1 0 a b c + + =

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EnglishUPPSC GDC 2021

Q20.The maximum number of normal, which can be drawn from a given point to the paraboloid, 2 2 ax + by = 2cz is

A3 B4 C5 D6

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