Quantitative Aptitude
GEOMETRY MCQs
Coordinate Geometry, Coordinate Geometry (10th Grade), Three Dimensional Geometry (10th Grade)
Total Questions : 133
| Page 14 of 14 pages
Answer: Option D. -> 16p2
:
D
Let equation of plane is
lx+my+nz=p
or x(pl)+y(pm)+z(pn)=1
Coordinates of A, B, C are (pl,0,0)(0,pm,0) and
(0,0,pn) respectively.
∴ Centroid of OABC is (p4l,p4m,p4n)
x1=p4l,y1=p4m,z1=p4n∵l2+m2+n2=1⇒p216x21+p216y21+p216z21=1
or x21y21+y21z21+z21x21=16/p2x21y21z21
∴ Locus is x2y2+y2z2+z2x2=16p2x2y2z2
∴k=16p2
:
D
Let equation of plane is
lx+my+nz=p
or x(pl)+y(pm)+z(pn)=1
Coordinates of A, B, C are (pl,0,0)(0,pm,0) and
(0,0,pn) respectively.
∴ Centroid of OABC is (p4l,p4m,p4n)
x1=p4l,y1=p4m,z1=p4n∵l2+m2+n2=1⇒p216x21+p216y21+p216z21=1
or x21y21+y21z21+z21x21=16/p2x21y21z21
∴ Locus is x2y2+y2z2+z2x2=16p2x2y2z2
∴k=16p2
Answer: Option B. -> -1
:
B
cos2α+cos2β+cos2γ=2cos2α−1+2cos2β−1+2cos2γ−1=2(cos2α+cos2β+cos2γ)−3=2−3=−1
:
B
cos2α+cos2β+cos2γ=2cos2α−1+2cos2β−1+2cos2γ−1=2(cos2α+cos2β+cos2γ)−3=2−3=−1
Answer: Option B. -> 13
:
B
The centre of the sphere is (-2, 1, 3) and its radius is √4+1+9+155=13.
Length of the perpendicular from the centre of the sphere on the plane is ∣∣∣−24+4+9−327√144+16+9∣∣∣=33813=26
So the plane is outside the sphere and the required distance is equal to 26 - 13 = 13.
:
B
The centre of the sphere is (-2, 1, 3) and its radius is √4+1+9+155=13.
Length of the perpendicular from the centre of the sphere on the plane is ∣∣∣−24+4+9−327√144+16+9∣∣∣=33813=26
So the plane is outside the sphere and the required distance is equal to 26 - 13 = 13.
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