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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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