Math Chapter Wise

EnglishUP PCS (Pre) 2003

Q81.The equation of the sphere described on the join of (2, -3, 4) and (-5,6,-7) as diameter is–

A2 2 2/x y z 3(x y z) 56 0 B2 2 2/x y z 3(x y z) 56 0 C2 2 2/x y z 3(x y z) 56 0 D2 2 2/x y z 3(x y z) 56 0

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EnglishUP PCS (Pre) 2003

Q82.The equation of the sphere having the circle 2 2 2 x y z 9,x 2y 2z 3 as a great circle is–

A2 2 2 2(x y z) 3(x 2y 2z) 9 0 B2 2 2 2(x y z) 3(x 2y 2z) 27 0 C2 2 2 3(x y z) 2(x 2y 2z) 21 0 DNone of the above

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EnglishUP PCS (Pre) 2003

Q83.The plane 2x 2y z 0 touches the sphere 2 2 2 x y z 2x 4y 2z 3 0 if is equal to–

A6 B12 C18 D24

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EnglishUP PCS (Pre) 2003

Q84.The vertex of the cone xy 2yz 3zx 0 is the point:

A(1,2,2) B(1, 2, 2) C(8,4, 1) D(0,0,0)

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EnglishUP PCS (Pre) 2004

Q85.The pole of the plane x y 5z 3 with respect to the sphere 2 2 2 x y z 9 is–

A(1,2,2) B(3,0,0) C(2,4,1) D(3, 3,15)

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EnglishUP PCS (Pre) 2005

Q86.The radius of the smallest sphere passing through (1, 0, 0) (0, 1, 0) (0, 0, 1) is:

A2/3 B2/3 C3/2 Dnone of the above

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EnglishUP PCS (Pre) 2005

Q87.The pole of the plane 2x + 3y – 4z = 6 with respect to the sphere x2 + y2 + z2 + 2z–5 = 0 is:

A(2, 3/2, –2) B(2, 3, –2) C(3, 2, –2) DNone of the above

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EnglishUP PCS (Pre) 2006

Q88.The centre and radius of circle (())) ((()) 2 2 2 x 2 y 6 z 4,z 0 − + − + = − + − + = − + − + = − + − + = are respectively:

A(2,6,0) and 2 B(–2,–6,0) and 2 C(2, 6, 0)and 4 D(–2,–6,0) and 4

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EnglishUP PCS (Pre) 2006

Q89.The vertex of the cone (())) ((()))((())) ((()))((()) 2 x 1 y 3z 2y z x 1 4y 6z 0 − + − + − − + = − + − + − − + = − + − + − − + = − + − + − − + = is:

A(1,2,–3) B(–1,2,–3) C(–1,0,0) D(1,0,0)

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EnglishUP PCS (Pre) 2008

Q90.The number of spheres such that the number of their radical planes is equal to the number of their radical lines in

A5 B4 C3 Dnone of the above

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EnglishUP PCS (Pre) 2008

Q91.The number of independent constants to determine a cone with vertex origin is

A1 B2 C4 D5

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EnglishUP PCS (Pre) 2008

Q92.If the cone 2x2 +λy2 -5z2 = 0 has three mutually perpendicular tangent planes, then λ is equal to

A3 B−5/3 C−10/3 D–10

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EnglishUP PCS (Pre) 2008

Q93.Angle between conjugate lines of a sphere is

A90° B60° C30° D0°

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EnglishUP PCS (Pre) 2009

Q94.An ellipse cannot be obtained by an intersection of a plane with

Acylinder Bcone Chyperboloid Dsphere

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English

Q95.The angle between the radical plane of two spheres and the line joining their centers is

A00 B300 C450 D900

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English

Q96.If the plane lx + my + nz = p touches the sphere x2 + y2 + z2 = a2 then l2 + m2 + n2 is equal to

Ap2 Ba2 C2 p a D2 a p

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English

Q97.The maximum distance from the point (1, 2, 2) to the surface x2 +y2 +z2 =25 is

A10 B8 C6 D3

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EnglishUP PCS (Pre) 1997

Q98.The equation of the sphere of least radius, passing through the pints (a,0,0) (0,a,0) and (0,0,a) is:

A() () 2 2 2 2 2 x y z 3a x y z a 0 + + − + + + = B() () 2 2 2 2 3 x y z 2a x y z a 0 + + − + + − = C() () 2 2 2 2 3 x y z 2a x y z a 0 + + + + + + = D() () 2 2 2 2 x y z 2a x y z a 0 + + + + + − =

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EnglishUP PCS (Pre) 1997

Q99.The equation of the reciprocal cone to the cone fx gy hz 0 + + = + + = + + = + + = is:

Afxy+gyz+hzx=0 Bfyz+gzx+hxy = 0 Cfzx+gxy+hyz=0 Dfxy gyz hzx 0 + + =

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EnglishTGT 2010

Q100.The equation of the sphere which passes through the origin and the points of intersection of plane x y z 1 a b c + + = + + = + + = + + = with the coordinate axes, is

Ax2 + y2 + z2 – ax – by – cz = 0 Bx2 + y2 + z2 + ax + by + cz = 0 Cx2 + y2 + z2 – 2ax – 2by – 2cz = 0 Dx2 + y2 + z2 + 2ax + 2by + 2cz = 0

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