JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank

done Sphere Total Questions - 18

• question_answer1)
  Equation \[a{{x}^{2}}+b{{y}^{2}}+c{{z}^{2}}+2fyz+2gxz+2hxy\] \[+2ux+2vy+2wz+d=0\]represents a sphere, if                                 [MP PET 1990]
  A)
             \[a=b=c\]                                   done clear
  B)
             \[f=g=h=0\] done clear
  C)
             \[v=u=w\]                                  done clear
  D)
             \[a=b=c\] and \[f=g=h=0\] done clear
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• question_answer2)
  A point moves so that the sum of its distances from the points (4, 0, 0) and (?4, 0, 0) remains 10. The locus of the point is         [MP PET 1988]
  A)
             \[9{{x}^{2}}-25{{y}^{2}}+25{{z}^{2}}=225\]                                  done clear
  B)
             \[9{{x}^{2}}+25{{y}^{2}}-25{{z}^{2}}=225\] done clear
  C)
             \[9{{x}^{2}}+25{{y}^{2}}+25{{z}^{2}}=225\]                                  done clear
  D)
             \[9{{x}^{2}}+25{{y}^{2}}+25{{z}^{2}}+225=0\] done clear
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• question_answer3)
  A point moves so that the sum of the squares of its distances from two given points remains constant. The locus of the point is
  A)
             A line done clear
  B)
             A plane done clear
  C)
             A sphere done clear
  D)
             None of these done clear
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• question_answer4)
  The equation \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=0\]represents
  A)
             (0, 0, 0) done clear
  B)
             A circle done clear
  C)
             A plane done clear
  D)
             None of these done clear
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• question_answer5)
  The locus of the equation \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+1=0\]is
  A)
             An empty set done clear
  B)
             A sphere done clear
  C)
             A degenerate set done clear
  D)
             A pair of planes done clear
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• question_answer6)
  The centre of sphere passes through four points (0, 0, 0),    (0, 2, 0), (1, 0, 0) and (0, 0, 4) is [MP PET 2002]
  A)
             \[\left( \frac{1}{2},\,1,\,2 \right)\] done clear
  B)
             \[\left( -\frac{1}{2},\,1,\,2 \right)\] done clear
  C)
             \[\left( \frac{1}{2},\,1,-\,2 \right)\] done clear
  D)
             \[\left( 1,\frac{1}{2},\,2 \right)\] done clear
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• question_answer7)
  The equation of the sphere touching  the three co-ordinate planes is [AMU 2002]
  A)
             \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2a(x+y+z)+2{{a}^{2}}=0\] done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2a(x+y+z)+2{{a}^{2}}=0\] done clear
  C)
             \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\pm 2a(x+y+z)+2{{a}^{2}}=0\] done clear
  D)
             None of these done clear
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• question_answer8)
  Let (3, 4, ?1) and (?1, 2, 3) are the end points of a diameter of sphere. Then the radius of the sphere is equal to                                                               [Orissa JEE 2003]
  A)
             1 done clear
  B)
             2 done clear
  C)
             3 done clear
  D)
             9 done clear
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• question_answer9)
  Co-ordinate of a point equidistant from the points (0,0,0), (a, 0, 0), (0, b, 0), (0, 0, c) is [RPET 2003]
  A)
             \[\left( \frac{a}{4},\frac{b}{4},\frac{c}{4} \right)\] done clear
  B)
             \[\left( \frac{a}{2},\frac{b}{4},\frac{c}{4} \right)\] done clear
  C)
             \[\left( \frac{a}{2},\frac{b}{2},\frac{c}{2} \right)\] done clear
  D)
             (a, b, c) done clear
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• question_answer10)
  How many different sphere of radius ?r? can be drawn which touches all the three co-ordinate axes
  A)
             4 done clear
  B)
             2 done clear
  C)
             6 done clear
  D)
             8 done clear
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• question_answer11)
  A plane passes through a fixed point \[(p,q,r)\] and cut the axes in A,B,C. Then the locus of the centre of the sphere \[OABC\] is 
  A)
             \[\frac{p}{x}+\frac{q}{y}+\frac{r}{z}=2\] done clear
  B)
             \[\frac{p}{x}+\frac{q}{y}+\frac{r}{z}=1\] done clear
  C)
             \[\frac{p}{x}+\frac{q}{y}+\frac{r}{z}=3\] done clear
  D)
             None of these done clear
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• question_answer12)
  The ratio in which the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=504\] divides the line segment  AB joining the points \[A\ (12,\ -4,\ 8)\] and \[(27,\ -9,\ 18)\] is given by
  A)
             \[2:3\] externally done clear
  B)
             \[2:3\] internally done clear
  C)
             \[1:2\] externally done clear
  D)
             None of these done clear
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• question_answer13)
  If two spheres of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] cut orthogonally, then the radius of the common circle is
  A)
             \[{{r}_{1}}{{r}_{2}}\] done clear
  B)
             \[\sqrt{(r_{1}^{2}+r_{2}^{2}})\] done clear
  C)
             \[{{r}_{1}}{{r}_{2}}\sqrt{(r_{1}^{2}+r_{2}^{2})}\] done clear
  D)
              \[\frac{{{r}_{1}}{{r}_{2}}}{\sqrt{(r_{1}^{2}+r_{2}^{2})}}\] done clear
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• question_answer14)
  If the plane \[2ax-3ay+4az+6=0\] passes through the midpoint of the line joining the centres of the spheres                   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13\]            and  \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8\],  then \[a\] equals [AIEEE 2005]           
  A)
             ? 2 done clear
  B)
             2      done clear
  C)
             ? 1 done clear
  D)
             1 done clear
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• question_answer15)
  The plane \[x+2y-z=4\] cuts the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] \[-x+z-2=0\] in a circle of radius [AIEEE 2005]
  A)
             2 done clear
  B)
             \[\sqrt{2}\] done clear
  C)
             3 done clear
  D)
             1 done clear
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• question_answer16)
  The radius of sphere \[x+2y+2z=15\]and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2y-4z=11\] is [AMU 2005]
  A)
  2 done clear
  B)
  \[\sqrt{7}\] done clear
  C)
  3 done clear
  D)
  \[\sqrt{5}\]                         done clear
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• question_answer17)
  The equation of the sphere concentric with the sphere \[2{{x}^{2}}+2{{y}^{2}}+2{{z}^{2}}-6x+2y-4z=1\]and double its radius is                                                               [Kerala (Engg.) 2005]
  A)
                     \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-x+y-z=1\] done clear
  B)
                     \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x+2y-4z=1\] done clear
  C)
                     \[2{{x}^{2}}+2{{y}^{2}}+2{{z}^{2}}-6x+2y-4z-15=0\] done clear
  D)
                     \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-3x+y-2z=1\] done clear
  E)
                     \[2{{x}^{2}}+2{{y}^{2}}+2{{z}^{2}}-6x+2y-4z-25=0\] done clear
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• question_answer18)
  If (2, 3, 5) is one end of a diameter of the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2z+20=0\]then co-ordinates of the other end of the diameter are              [Kerala (Engg.) 2005]
  A)
  (4, 3, 5) done clear
  B)
  (4, 9, -3) done clear
  C)
  (4, 9, 3) done clear
  D)
  (4, 3, -3) done clear
  E)
  (4, 9, 5) done clear
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