Sail E0 Webinar

Quantitative Aptitude

MENSURATION MCQs

Regular Polygons, Triangles, Circles

Total Questions : 254 | Page 5 of 26 pages
Question 41. There are only ___ ways in which a circle and line can interact.
 Discuss Question

:
Circle and line can interact in maximum three ways:

  1. When a line is neither touching or cutting a circle.

  2. When a line is touching a circle.

  3. When a line is cutting a circle.

Question 42. The diameter of a circle passes through the ____ of a circle.
  1.    point
  2.    circumference
  3.    centre
  4.    chord
 Discuss Question
Answer: Option C. -> centre
:
C
The diameter of the circle is the longest chord that passes through the centre of the circle.
The Diameter Of A Circle Passes Through The ____ Of A Circle...
Here, O is the centre of the circle and AB is its diameter.
Question 43. The diameter divides the circle into two equal parts, each part is ____.
  1.    Semi-circle
  2.    Radius
  3.    Circle
  4.    Circumference
 Discuss Question
Answer: Option A. -> Semi-circle
:
A
The diameter is the longest chord that divides the circle into exactly two halves. Each part is called as Semi-Circle.
The Diameter Divides The Circle Into Two Equal Parts, Each P...
Question 44. The distance around the circle is called ____.
  1.    radius
  2.    diameter
  3.    centre
  4.    circumference
 Discuss Question
Answer: Option D. -> circumference
:
D
The length of the boundary or the distance around a circle is known as the circumference.
The Distance Around The Circle Is Called ____.
Question 45. If A and B are two points on the circle, then the line joining A and B is called as the ____.
  1.    point
  2.    circumference
  3.    centre
  4.    chord
 Discuss Question
Answer: Option D. -> chord
:
D
If A And B Are Two Points On The Circle, Then The Line Joini...
A and B are two points on the circle. The line joining A and B is calledchord.
Question 46. Part of a circumference is _____.
  1.    Radius
  2.    Diameter
  3.    Center
  4.    Arc
 Discuss Question
Answer: Option D. -> Arc
:
D
Part Of A Circumference Is _____.
Circumference is the length of the boundary of a circle. A part of it is called an arc.
Question 47. Consider a family of circles which are passing through the point (–1, 1) and are tangent to x-axis. (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval
  1.    −12≤k≤12
  2.    k≤12
  3.    < k < 12
  4.    k≥12
 Discuss Question
Answer: Option D. -> k≥12
:
D
Since, circles are passing through the point (–1, 1) and touching X-axis, the equationof circles can be written as -
(h+1)2+(K1)2=K2
h2+2h+22K=0
If h is real the Δ0
4- 4.1. (2 – 2K) 0
= 4 - 8 + 8k0
=8k4
=k12
Question 48. If the line x + 2by + 7 = 0 is diameter of the circle x2+y26x+2y=0, then b =
  1.    3
  2.    -5
  3.    -1
  4.    5
 Discuss Question
Answer: Option D. -> 5
:
D
Here the centre of circle (3, -1) must lie on the line x + 2by + 7 = 0
Therefore, 3 - 2b + 7 = 0 b = 5
Question 49. The locus of the centre of a circle which touch the circles x2+y26x6y+14=0 externally and also the Y - axis is given by
  1.    x2−6y−7y+14=0
  2.    x2−10x−6y+14=0
  3.    y2−6x−10y+14=0
  4.    y2−10x−6y+14=0
 Discuss Question
Answer: Option D. -> y2−10x−6y+14=0
:
D
Let (x, y) be centre ofcircle which touch y - axis and given circle.
At any point, the radius of this circle will be equal to 'x' units. Since this circle is touching the given circle which has a radius of two units,
Distance between centres of the two circles= 2 + x
(x3)2+(y3)2=2+x
y210x6y+14=0
Question 50. If a straight line through C(8,8) making an angle 135 with the x-axis cuts the circle x=5cosθ,y=5sinθ in points A and B, then length of segment AB is
  1.    5
  2.    10
  3.    15
  4.    15√2
 Discuss Question
Answer: Option B. -> 10
:
B
Inclination of the line AB is 135Slope=tan135=1
Equation of AB is y8=1(x+8)x+y=0
x + y = 0 passes through the centre of the circle x2+y2=25
Length of the chord AB = Diameter of the circle =2×5=10

Latest Videos

Latest Test Papers