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question_answer1)
If the sum of the squares of the distance of the point (x, y, z) from the points (a, 0, 0) and (-a, 0, 0) is \[2{{c}^{2}}\], then which one of the following is correct?
A)
\[{{x}^{2}}+{{a}^{2}}=2{{c}^{2}}-{{y}^{2}}-{{z}^{2}}\] done
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B)
\[{{x}^{2}}+{{a}^{2}}={{c}^{2}}-{{y}^{2}}-{{z}^{2}}\] done
clear
C)
\[{{x}^{2}}-{{a}^{2}}={{c}^{2}}-{{y}^{2}}-{{z}^{2}}\] done
clear
D)
\[{{x}^{2}}+{{a}^{2}}={{c}^{2}}+{{y}^{2}}+{{z}^{2}}\] done
clear
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question_answer2)
The ordered pair \[(\lambda ,\,\,\mu )\] such that the points \[(\lambda ,\mu ,-6),\] (3, 2, -4) and (9, 8, -10) become collinear is
A)
(3, 4) done
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B)
(5, 4) done
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C)
(4, 5) done
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D)
(4, 3) done
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question_answer3)
The co-ordinates of the point in which the line joining the points (3, 5, -7) and (-2, 1, 8) is intersected by the plane yz are given by
A)
\[\left( 0,\,\,\frac{13}{5},\,\,2 \right)\] done
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B)
\[\left( 0,-\frac{13}{5},-2 \right)\] done
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C)
\[\left( 0,-\frac{13}{5},\frac{2}{5} \right)\] done
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D)
\[\left( 0,\,\,\frac{13}{5},\,\,\frac{2}{5} \right)\] done
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question_answer4)
If P (3, 2, - 4), Q (5, 4, - 6) and R (9, 8, -10) are collinear, then R divides PQ in the ratio
A)
3 :2 internally done
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B)
3:2 externally done
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C)
2:1 internally done
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D)
2:1 externally done
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question_answer5)
Points ( -2, 4, 7), (3, -6, -8) and (1, -2, -2) are
A)
Collinear done
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B)
Vertices of an equilateral triangle done
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C)
Vertices of an isosceles triangle done
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D)
None of these done
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question_answer6)
Which of the following statement is true?
A)
The point A(0, -1), B(2, 1), C(0, 3) and D(-2, 1) are vertices of a rhombus. done
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B)
The points A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3) are vertices of a square. done
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C)
The points A(-2, -1), B(1, 0), C(4, 3) and D(1, 2) are vertices of a parallelogram. done
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D)
None of these done
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question_answer7)
Find the equation of set points P such that \[P{{A}^{2}}+P{{B}^{2}}=2{{K}^{2}},\] where A and B are the points (3, 4, 5) and (-1, 3, -7), respectively:
A)
\[{{K}^{2}}-109\] done
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B)
\[2{{K}^{2}}-109\] done
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C)
\[3{{K}^{2}}-109\] done
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D)
\[4{{K}^{2}}-10\] done
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question_answer8)
ABC is a triangle and AD is the median. If the coordinates of A are (4, 7, -8) and the coordinates of centroid of the triangle ABC are (1, 1, 1), what are the coordinates of D?
A)
\[\left( -\frac{1}{2},\,\,2,\,\,11 \right)\] done
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B)
\[\left( -\frac{1}{2},-2,\frac{11}{2} \right)\] done
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C)
\[(-1,2,11)\] done
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D)
\[(-5,-11,19)\] done
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question_answer9)
The equation of locus of a point whose distance from the y-axis is equal to its distance from the point (2, 1, -1) is
A)
\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=6\] done
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B)
\[{{x}^{2}}-4x+2z+6=0\] done
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C)
\[{{y}^{2}}-2y-4x+2z+6=0\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}-{{z}^{2}}=0\] done
clear
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question_answer10)
The ratio in which the join of points (1, -2, 3) and (4, 2, -1) is divided by XOY plane is
A)
1:3 done
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B)
3:1 done
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C)
-1:3 done
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D)
None of these done
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question_answer11)
Points (1, 1, 1), (-2, 4, 1), (-1, 5, 5) and (2, 2, 5) are the vertices of a
A)
Rectangle done
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B)
Square done
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C)
Parallelogram done
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D)
Trapezium done
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question_answer12)
If x co-ordinates of a point P of line joining the points Q (2, 2, 1) and R (5, 2, - 2) is 4, then the z-coordinates of P is
A)
-2 done
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B)
-1 done
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C)
1 done
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D)
2 done
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question_answer13)
A parallelopiped is formed by planes drawn through the points (2, 4, 5) and (5, 9, 7) parallel to the coordinate planes. The length of the diagonal of the parallelepiped is
A)
8 done
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B)
4 done
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C)
7 done
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D)
11 done
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question_answer14)
The co-ordinates of the points A and B are (2, 3, 4) and (-2, 5, -4) respectively. If a point P moves so that \[P{{A}^{2}}-P{{B}^{2}}=k\] where k is a constant, then the locus of P is
A)
\[-8x+4y-16z+16=k\] done
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B)
\[-8x-4y-16z-16=k\] done
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C)
\[-8x+4y-16z-16=k\] done
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D)
None of these done
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question_answer15)
What is the perpendicular distance of the point P(6,7, 8) from xy-plane?
A)
8 done
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B)
7 done
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C)
6 done
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D)
None of these done
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question_answer16)
P(a, b, c); Q(a+2, b+2, c - 2) and R (a + 6, b + 6, c - 6) are collinear.
Consider the following statements: |
1. R divides PQ internally in the ratio 3:2 |
2. R divides PQ externally in the ratio 3:2 |
3. Q divides PR internally in the ratio 1:2 |
Which of the statements given above is/are correct? |
A)
1 only done
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B)
2 only done
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C)
1 and 3 done
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D)
2 and 3 done
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question_answer17)
What is the locus of a point which is equidistant from the points (1, 2, 3) and (3, 2, - 1)?
A)
\[x+z=0\] done
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B)
\[x-3z=0\] done
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C)
\[x-z=0\] done
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D)
\[x-2z=0\] done
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question_answer18)
If x co-ordinates of a point P of line joining the points Q (2, 2, 1) and R (5, 2, - 2) is 4, then the z-coordinates of P is
A)
-2 done
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B)
-1 done
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C)
1 done
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D)
2 done
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question_answer19)
L is the foot of the perpendicular drawn from a point P(6, 7, 8) on the xy-plane. What are the coordinates of point L?
A)
(6, 0, 0) done
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B)
(6, 7, 0) done
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C)
(6, 0, 8) done
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D)
None of these done
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question_answer20)
If the origin is shifted (1, 2 -3) without changing the directions of the axis, then find the new coordinates of the point (0, 4, 5) with respect to new frame.
A)
(-1, 2, 8) done
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B)
(4, 5, 1) done
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C)
(3, -2, 4) done
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D)
(6, 0, 8) done
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question_answer21)
The ratio in which the line joining (2, 4, 5), (3, 5,- 4) is divided by the yz plane, is
A)
2 : 3 done
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B)
3 : 2 done
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C)
-2 : 3 done
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D)
4 : - 3 done
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question_answer22)
The points (5, 2, 4), (6, -1, 2) and (8, -7, k) are collinear if k is equal to
A)
-2 done
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B)
2 done
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C)
3 done
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D)
-1 done
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question_answer23)
What are coordinates of the point equidistant from the points (a, 0, 0), (0, a, 0), (0, 0, a) and (0, 0, 0)?
A)
\[\left( \frac{a}{3},\frac{a}{3},\frac{a}{3} \right)\] done
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B)
\[\left( \frac{a}{2},\frac{a}{2},\frac{a}{2} \right)\] done
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C)
\[(a,a,a)\] done
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D)
\[(2a,2a,2a)\] done
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question_answer24)
The xy-plane divides the line joining the points (-1, 3, 4) (2, -5, 6)
A)
Internally in the ratio 2:3 done
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B)
Externally in the ratio 2:3 done
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C)
Internally in the ratio 3:2 done
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D)
Externally in the ratio 3:2 done
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question_answer25)
Let A(4, 7, 8), B(2, 3, 4), C(2, 5, 7) be the vertices of a triangle ABC. The length of internal bisector of \[\angle A\] is
A)
\[\frac{\sqrt{34}}{2}\] done
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B)
\[\frac{3}{2}\sqrt{34}\] done
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C)
\[\frac{2}{3}\sqrt{34}\] done
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D)
\[\frac{\sqrt{34}}{3}\] done
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question_answer26)
A(3, 2, 0), B(5, 3, 2) and C(-9, 6, -3) are the vertices of a triangle ABC. If the bisector of \[\angle ABC\] meets BC at D, then coordinates of D are
A)
\[\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)\] done
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B)
\[\left( -\frac{19}{8},\frac{57}{16},\frac{17}{16} \right)\] done
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C)
\[\left( \frac{19}{8},\frac{57}{16},\frac{17}{16} \right)\] done
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D)
None of these done
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question_answer27)
The coordinates of point in xy-plane which is equidistant from three points A (2, 0, 3), B (0, 3, 2) and C (0, 0, 1) are
A)
(3, 2, 0) done
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B)
(3, 4, 0) done
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C)
(0, 0, 3) done
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D)
(2, 3, 0) done
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question_answer28)
Ratio in which the zx-plane divides the join of (1, 2 3) and (4, 2, 1).
A)
1:1 internally done
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B)
1:1 externally done
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C)
2:1 internally done
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D)
2: 1 externally done
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question_answer29)
The points (4, 7, 8), (2, 3, 4), (-1, -2, 1) and (1, 2, 5) are the vertices of a
A)
Parallelogram done
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B)
Rhombus done
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C)
Rectangle done
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D)
Square done
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question_answer30)
In \[\Delta ABC\] the mid-point of the sides AB, BC and CA are respectively (l, 0, 0), (0, m, 0) and (0, 0, n). Then, \[\frac{A{{B}^{2}}+B{{C}^{2}}+C{{A}^{2}}}{{{l}^{2}}+{{m}^{2}}+{{n}^{2}}}\] is equal to
A)
2 done
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B)
4 done
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C)
8 done
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D)
16 done
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