Mathematics ECAT Pre Engineering Chapter 18 Analytic Geometry Online Test With Answers

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Mathematics ECAT Pre Engineering Chapter 18 Analytic Geometry Online Test

Sr. # Questions Answers Choice
1 The equation of the sphere thro' the origin and making intercepts a, b, c on co-ordinate axes is x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>+ ax + by + cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>- 2ax - 2 by - 2 cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>= a + b + c x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2 </sup>- ax - by - cz =0
2 The center of the sphore which passes thro' (a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0) is
3 The equation of the sphere passing thro' (0, 0, 0), (a, 0, 0), (0, b, 0), (9, 0, c) is x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>+ 2 ax +2 by + 2cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>- 2ax - 2 by - 2cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>- ax - by - cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>+ ax + by + cz = 0
4 x-axis y-axis z-axis None of these
5 The intercepts of the plane 2x - 3y + 4z = 12 on the co-ordinate axes are given by 2, -3, 4 6, -4, -3 6, -4, 3 3, -2, 1.5
6
7
8 64.A point (x, y, z) moves parallel to xy plane. Which of the three variables x, y, z remain fixed? z x y x and y
9 The foot of perpendicular from (α,β,γ) only y-axis is (<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>α</i></span>, 0, 0) (0,<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>β</i></span>, 0) (0, 0, <span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>γ</i></span>) (0, 0, 0)
10 Parallel to the plane At right angles to the plane Lies in the plane Meet the plane obliquely
11 -10 10/7 -10/7 -7/10
12
13 The points (5, -4, 2),(4, -3, 1),(7, -6, 4),(8, -7, 5) are vertices of a Square Parallelogram Rectangle Rhombus
14 The points (5, 0, 2), (2, -6, 0), (4, -9, 6) and (7, -3, 8) are vertices of a Square Rhombus Rectangle Parallelogram
15 The equations of the line thro' the point (2, 3, -5) and equally inclined to the axis are
16 The lines l1and l2intersect. The shortest distance between them is Positive Negative Zero Infinity
17 The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is x + y + z - 15 = 0 x - y + z - 15 = 0 x - y - z - 15 = 0 x + y + z + 15 = 0
18 The distance of the plane 2x - 3y + 6z + 14 = 0 from the origin is 14 2 -2 11
19 The point which divides the line joining the points (2, 4, 5) and (3, 5, -4) in the ratio -2 : 3 lines on ZOX plane XOY plane YOZ plane None of these
20 0 2 4/3 5/3
21 The projections of a line segment on x, y, z axes are 12, 4, 3. The length and the direction cosines of the line segment are
22 The st. lines whose direction cosines satisfy al + bm + cn = 0, fmn + gnl + hlm=0 are perpendicular if
23 (3, 1, -2) (3, -2, 1) (2, -1, 3) (-1, -2, -3)
24 The distance of the points (3, 4, 5) from y-axis is
25 The direction cosines of any normal to the xy-plane are &lt;1, 0, 0&gt; &lt;0, 1, 0&gt; &lt;1, 1, 0&gt; &lt;0, 0, 1&gt;
26 The direction cosines of a line equally inclined with co-ordinate axes are
27 The points (5, 2, 4)(6, -1, 2) and (8, -7, k) are collinear if k is equal to -2 2 3 -1
28 If l, m, n are the d.c.'s of a line, then l2+ m2+ n2= 0 l2+ m2+ n2= 1 l + m + n = 1 l = m = n = 1
29 0 undefined
30 9 -9 0 1
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