Math Chapter Wise

EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q41.Every homogeneous equation f(x,y,z) 0 represents–

ASphere with centre at origin BCone with vertex at origin CCylinder DNone of these

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q42.If volume of a sphere is 36π then its surface area will be–

A18π B6π C12π D36π

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EnglishTGT 1999

Q43.What will be the volume of the figure formed by rotating the ellipse 2 2 x y 1 a b + = + = around the major axis?

A2 ab 3 1 π B2 ab π C2 ab 4π D2 4 ab 3 π

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EnglishPGT 2013

Q44.It a tangent plane to the sphere x2 +y2 +z2 =r2 cuts distances a,b,c on the coordinate axes, then:

A1 1 1 r a b c + + = B2 2 2 2 1 1 1 1 + + = a b c r C4 4 4 4 1 1 1 1 + + = a b c r D1 1 1 1 a b c r + + =

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EnglishUPPCS(Pre) 2000 PGT 2013

Q45.The equation 2 2 2 2 2 2 0 ax by cz ux vy wz d + + + + + + = + + + + + + = + + + + + + = + + + + + + = one represents cone, if 2 2 2 + + u v w a b c is:

A1 Bd C2 D2d

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EnglishPGT 2013

Q46.The radius of the sphere x2 +y2 +z2 –2x–10y– 2z+2=0 will be:

A2 B3 C4 D5

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EnglishPGT 2009

Q47.The plane lx + my + nz = p touches the coincoid ax2 + by2 + cz2 = 1, if

Aal2 + bm2 + cn2 = p2 Ba2 l2 + b2 m2 + c2 n2 + p2 C2 2 2 2 m n p a b c + + = ℓ D2 2 2 2 2 2 2 m n p a b c + + = ℓ

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EnglishUPPCS(Pre) 1994 PGT 2005

Q48.The line x y z m n = l is a generator of the cone x2 –2y2 +3z2 = 0 if:

A2 2 2 1 2 3 0 − + = l m n B2 2 2 1 3 2 0 − + = l m n C2 2 2 2 3 0 − + = l m n D2 2 2 3 2 0 + + = l m n

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EnglishPGT 2005

Q49.The equation of the sphere through the circle x2 +y2 +z2 = 9, 2x+3y+4z = 5 and the origin is

A() () 2 2 2 5 9 2 3 4 0 + + − + + = x y z x y z B() () 2 2 2 9 5 2 3 4 0 + + − + + = x y z x y z C() () 2 2 2 9 5 2 3 4 0 + + + + + = x y z x y z D() () 2 2 2 5 9 2 3 4 0 + + + + + = x y z x y z

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EnglishPGT 2004

Q50.Central conicoid is represented by the following

A2 2 2 1 ax by cz + + = B2 2 2 1 ax by cz + − = C2 2 2 1 ax by cz − − = DAll of the above

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EnglishPGT 2004

Q51.The equation a(x2 + y2 + z2)+2(ux+vy+wz) +d=0 where a ≠ 0, always represents a sphere, provided?

Au2 + v2 + w2 – ad > 0 Bu2 + v2 + w2 + ad > 0 Cu2 + v2 + w2 – ad < 0 Du2 + v2 + w2 + ad < 0

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EnglishPGT 2004

Q52.The equation of normal to the sphere x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0 at (x1, y1, z1) is

A1 1 1 + + + = + + + x u y v z w x x y y z z B1 1 1 + + + = − − − x u y v z w x x y y z z C1 1 1 1 1 1 − − − = + + + x x y y z z x u y v z w D1 1 1 − − − = + + + x y y v z w x u y v z w

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EnglishRajasthan TGT 2016

Q53.The circumference of the base of a 9m. high wooden solid cone is 44m, then slant height of the cone is equal to.

A120m B130m C150m D7 5m

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EnglishRajasthan TGT 2016

Q54.A solid is hemispherical at the bottom and conical above it. If the surface areas of these two parts are equal, then the volumes of these two parts are in the ratio

A1: 3 B2: 3 C1: 2 D2: 3

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EnglishRajasthan TGT 2013

Q55.The equation of the right circular cylinder whose axis is z-axis, and radius r is-

Ax2 + y2 = r2 Bx2 + z2 = r2 Cy2 + z2 = r2 Dx2 + y2 + z2 = r2

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EnglishRajasthan TGT 2013

Q56.The semi vertical angle of right circular cone having a set of the three mutually perpendicualr tangent planes is-

A−1/tan 2 B−1/cot 2 C3/π D6/π

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EnglishTGT 2011

Q57.Three Cartesian axes and the lines x y z =, 1 -2 3 x y z = 3 -1 1, The equation of the cone passing through is-

Ayz–2zx+3xy=0 B3yz–zx+xy = 0 C3yz+16zx+15xy= 0 DNone of these

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EnglishUP PCS (Pre) 1998

Q58.If the cone x2 + y2 – z2 tan2 α = 0 has three mutually perpendicular generators, then α equals:

A3/π B4/π C() 1 tan 2 − Dnone of these

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EnglishUP PCS (Pre) 1994

Q59.For the surface 2 2 2 x 2y 3z 12 the equation of tangent plane at (1,2, 1) is–

Ax 4y 3z 12 Bx 4y 3z 12 Cx 4y 3z 12 Dx 4y 3z 12 0

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EnglishUP PCS (Pre) 1994

Q60.The radius of the circle 2 2 2 x y z 2y 4z 11, x 2y 2z 15 is–

A7 B5 C7 D5

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