Math Chapter Wise

EnglishUP PGT 2021

Q21.The equation of a right circular cone with vertex at the origin the axis the z-axis and semi vertical angle 4 π is–

Ax2 + z2 = y2 By2 + x2 = z2 Cz2 + y2 = x2 Dxy = z2

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EnglishUP PGT 2021

Q22.The radius of sphere x2 + y2 + z2 + x + y + z = 4 is –

A3 B4 C19/4 D19/2

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EnglishUP PGT 2021

Q23.The equation of the sphere passing through the origin and making intercepts 1, 3, 5 with the three coordinate axes is:

Ax2 + y2 + z2 + x + 3y + 5z = 0 Bx2 + y2 + z2 – x + 3y – 5z = 0 Cx2 + y2 + z2 + x – 3y + 5z = 0 Dx2 + y2 + z2 – x – 3y – 5z = 0

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EnglishUP PGT 2021

Q24.The equation of the director sphere of the central conicoid 2 2 2 2 2 2 x y z + + = 1 a b c is

Ax2 + y2 + z2 = a2 + b2 + c2 Bx2 + y2 + z2 = 2 2 2 1 1 1 a b c + + Cax2 + by2 + cz2 = a2 + b2 + c2 Dx2 + y2 + z2 = 1

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q25.The radius of the circle x2 + y2 + z2 – 8x + 4y + 8z – 45 = 0, x – 2y + 2z = 3 is-

A4 B5 C4 5 D2 5

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021 Rajasthan TGT 2011

Q26.The equation of the right circular cone, whose vertex is the origin, the axis is the z axis and semi- vertical angle is α, is-

Ax2 + y2 = z2 sin2 α Bx2 + y2 = z2 cos2 α Cx2 + y2 = z2 tan2 α Dx2 + y2 = z2 cot2 α

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EnglishUP TGT 2021

Q27.The equation of the sphere on the join of (2, –3, 1) and (3, –1, 2) as diameter is

Ax2 + y2 + z2 – 5x + 4y + 3z – 11 = 0 Bx2 + y2 + z2 + 5x – 4y + 3z – 11 = 0 Cx2 + y2 + z2 + 11 = 0 Dx2 + y2 + z2 – 5x + 4y – 3z + 11 = 0

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EnglishUP TGT 2021 UPPCS (Pre) 1997

Q28.The general equation to the cone of second degree which passes through the axes, is

A2 2 2 x y z 0 a b c + + = Bfyz + gzx + hxy = 0 Cax2 + by2 + cz2 = 0 Dfx gy hz 0 + + =

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EnglishUP TGT 2021

Q29.Find the equation of the cone with vertex at the origin and direction cosines of its generators satisfy the equation l2 + 2m2 – 3n2 = 0

Ax2 + y2 – z2 = 0 Bx2 + 2y2 – 3z2 = 0 Cx2 – 2y2 + 3z2 = 0 Dxy + yz + zx = 0

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EnglishUPPSC Ashram Paddhati 2021 Rajasthan TGT 2015

Q30.Two spheres of radii r1 and r2 intersect each other orthogonally. The radius of the common circle is

A2 2 1 2 r + r B1 2 2 2 1 2 r + r r + r C1 2 2 2 1 2 r r r + r Dnone of the above

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EnglishUK SSSC LT 2020

Q31.The equation x2 – 2y2 + 3z2 – 4xy + 5yz – 6zx + 8x – 19y – 2z – 20 = 0 represents a:

ASphere BCylinder CCone DNone of the above

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EnglishUK SSSC LT 2020

Q32.If the plane 2x – 2y + z = 9 touches the sphere x2 + y2 + z2 = r2, then the value of 'r' will be:

A1 B2 C3 D9

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EnglishHaryana PGT 2018

Q33.A sphere 2 2 2 x + y + z = 9 is cut by the plane x + y + z = 3The radius of the circle so formed is:

A5 B6 C3 D3

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EnglishNVS PGT 10-06-2019

Q34.The radius of a sphere whose centre is (4, 4, –2) and which passes through the origin is:

A4 B1 C6 D5

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EnglishNVS PGT 10-06-2019

Q35.The equation of a sphere on the line joining the pints (1, 5, 6) and (–2, 1, 1) as diameter is:

Ax2 + y2 + z2 + 2x – 4y – 7z – 9 = 0 Bx2 + y2 + z2 + 6x – y – 4z + 5 = 0 Cx2 + y2 + z2 – x + 6y + 7z – 9 = 0 Dx2 + y2 + z2 + x – 6y – 7z + 9 = 0

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EnglishKVS PGT 23-12-2018

Q36.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:

A2 2 2 2 2 2 x y z a b c + + = + + B2 2 2 x y z 2ax 2by 2cz 0 + + + + + = C2 2 2 x y z ax by cz 0 + + + + + = D2 2 2 x y z ax by cz 0 + + − − − =

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EnglishUP PGT-2016 (02-02-2019)

Q37.Equation of a cone, whose vertex is at origin and base is the curve z= k, f(x,y)=0 is

Axk yk f, 0 z z = B() f k,kyz 0 = C() f ky,kxz 0 = DNone of the above

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EnglishUP PGT-2016 (02-02-2019)

Q38.If 2x–y+z+4=0 is a tangent plane to the sphere whose centre is (1, 0, 1), then radius of sphere is

A7 B7/6 C5/6 D5

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EnglishUP PGT-2016 (02-02-2019)

Q39.In three dimensional geometry equation x2 +y2 =r2 represents a

Acircle Bsphere Ccylinder Dcone

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EnglishLT 2018

Q40.The radius of the sphere x2 +y2 +z2 –x – y– z=0 is

A3/2 B3/2 C3/2 D3

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