ECAT Mathematics Chapter 20 Analytic Geometry Online Test With Answers

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ECAT Mathematics Chapter 20 Analytic Geometry Online Test

Sr. # Questions Answers Choice
1 If A(a,b) lies on 3x +2y =13 and point B(b,a) lies on x-y =5 then equation of AB is x- y= 5 x+ y+ =5 x+ y= -5 5x +5y =21
2 If line through (4,3) and (2,k) is perpendicular to y =2x +3, then k =_______ -1 1 -4 4
3 If k2x2 +2hxy- 4y2 =0 represents two perpendicular lines then k = 2 k = ±2 k = -2 k ≠0
4 The measure of the acute angle between the lines represented by x2 -xy -6y2 =0 is 120° 30° 130° 45°
5 The exterior angle of the interior angle C of he quadrilateral whose vertices are A(5,2),B(-2,3),C(-3,-4),D(4,-5) is 30° 60° 45° 90°
6 The points A(+1,-1),B(3,0),C(3,7),D(1,8) are vertices of Square Parallelogram Rectangle Trapezium
7 Area of the triangle whose vertices are (2,3),(0,1),(0,0) is 6 2 4 1
8 The equation of the line perpendicular to x- axis and passing through (-5,3) is y -3 =0 x+ 3 =0 y- 3 =∞ x +5 =0
9 The point P (5,8) and the origin lie on the side of the line 3x+ 7y+ 15 =0 Same side P above and origin below Opposite side P below and origin above
10 The points A(3,1),B(-2,-3),C(2,2) are vertices of an (an) Right triangle Equilateral triangle Isosceles triangle Scalene triangle
11 The line through the intersection of the lines x+ 2y+ 3= 0 : 3x +4y +7 =0 and making equal intercepts on the axes is x+ y+ 1= 0 x+ y- 2= 0 x+ y+ 2= 0 2x +y +2 =0
12 The straight lines represented by the equation ax2+ 2hxy +by2 =0 intersects at (1,1) (0,1) (1,0) (0,0)
13 The line l is horizontal if m is undefined m=0 m=1 m=0-1
14 The coordinates of a point P(x,y) referred to XY-system are (x+y,y+k) (x-h,y-k) (x,y) (x-h,y-k)
15 The point of concurrency of the medians of the ΔABC is called its Orthocenter Centriod Circumcentre Incentre
16 If the lines 2x-3y-1=0,3x-y-5=0 and 3x+py+8=0 meet at a unique point then p = -14 p = -1 p =0 p=12
17 If the points (a,2b):(c,a+b):(2c-a,h) lie on the same line then h=2a h=a+b h=ab h=ac
18 Area bounded between the curve xy=2 and the lines x=1 and x=2 ln2 square units ln√2 square units ln4 square units Square units
19 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
20 The center of the sphore which passes thro' (a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0) is
21 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
22 x-axis y-axis z-axis None of these
23 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
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25
26 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
27 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)
28 Parallel to the plane At right angles to the plane Lies in the plane Meet the plane obliquely
29 -10 10/7 -10/7 -7/10
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