CONSTRUCTIONS Test

CONSTRUCTIONS

This is CONSTRUCTIONS Test-04 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
To draw a pair of tangents to a circle which are at right angles to each other, it is required to draw tangents at end points of the two radii of the circle, which are inclined at an angle of
  • A
    \({120^o}\)
  • B
    \({60^o}\)
  • C
    \({90^o}\)
    Correct
  • D
    \({45^o}\)
2
To draw a pair of tangents to a circle which are inclined to each other at an angle of \({45^o}\), it is required to draw tangents at the end points of the two radii of the circle, which are inclined at an angle of
  • A
    \({135^o}\)
    Correct
  • B
    \({105^o}\)
  • C
    \({130^o}\)
  • D
    \({135^o}\)
3
To draw a pair of tangents to a circle which are inclined to each other at angle \({x^o},\) it is required to draw tangents at the end points of those two radii of the circle, the angle between which is
  • A
    \({180^o} + {x^o}\)
  • B
    \({90^o} - {x^o}\)
  • C
    \({90^o} + {x^o}\)
  • D
    \({180^o} - {x^o}\)
    Correct
4
If you draw a pair of tangents to a circle C(O, r) from point P such that OP = 2r, then the angle between the two tangents is
  • A
    \({45^ \circ }\)
  • B
    \({30^ \circ }\)
  • C
    \({90^ \circ }\)
  • D
    \({60^ \circ }\)
    Correct
5
To draw tangents to each of the circle with radii 3 cm and 2 cm from the centre of the other circle, such that the distance between their centres A and B is 6 cm, a perpendicular bisector of AB is drawn intersecting AB at M. The next step is to draw
  • A
    a circle with MB as diameter
  • B
    extend AB to P such that BP = MB and draw a circle with MP as diameter
  • C
    a circle with AM as diameter
  • D
    a circle with AB as diameter
    Correct
6
To draw tangents to a circle of radius ‘p’ from a point on the concentric circle of radius ‘q’, the first step is to find
  • A
    midpoint of q – r
  • B
    midpoint of q
    Correct
  • C
    midpoint of p + q
  • D
    midpoint of p
7
To draw a tangent at point B to the circumcircle of an isosceles right \(\Delta ABC\)right angled at B, we need to draw through B
  • A
    a line inclined to \({60^ \circ }\)to AB
  • B
    a line perpendicular to AB
  • C
    a line perpendicular to BC
  • D
    a line parallel to AC.
    Correct
8
A pair of tangents can be constructed to a circle inclined at an angle of :
  • A
    \({185^ \circ }\)
  • B
    \({205^ \circ }\)
  • C
    \({195^ \circ }\)
  • D
    \({175^ \circ }\)
    Correct
9
A pair of tangents can be constructed to a circle from an external point, which are inclined each other at an angle \(\theta \)such that :
  • A
    \({90^o} < \theta < {270^o}\)
  • B
    \(0 < \theta < {360^o}\)
  • C
    \({180^o} < \theta < {360^o}\)
  • D
    \(0 < \theta < {180^o}\)
    Correct
10
To draw a pair of tangents to a circle which are inclined to each other at an angle of \({120^o}\), it is required to draw tangents at end points of those two radii of the circle, the angle between them should be :
  • A
    \({240^o}\)
  • B
    \({60^o}\)
    Correct
  • C
    \({90^o}\)
  • D
    \({120^o}\)
11
To draw a pair of tangents to a circle which are inclined to each other at an angle of \({35^o}\), it is required to draw tangents at the end points of those two radii of the circle, the angle between them should be:
  • A
    \({105^o}\)
  • B
    \({70^o}\)
  • C
    \({145^o}\)
    Correct
  • D
    \({140^o}\)
12
To draw a pair f tangents to a circle which are inclined to each other at an angle of \({60^o}\), it is required to draw tangents at end points of those two radii of the circle, the angle between them should be:
  • A
    \({60^o}\)
  • B
    \({120^o}\)
    Correct
  • C
    \({90^o}\)
  • D
    \({135^o}\)
13
Two distinct tangents can be constructed from a point P to a circle of radius 2r situated at a distance:
  • A
    less than 2r from the centre
  • B
    2r from the centre
  • C
    r from the centre
  • D
    more than 2r from the centre
    Correct
14
By geometrical construction, which of the following is possible to divide a line segment in the given ratio ?
  • A
    \(\sqrt 6 :2\)
  • B
    \((\sqrt 3 - 2):\left( {\sqrt 3 + 2} \right)\)
  • C
    \(\sqrt 5 :\frac{1}{{\sqrt 5 }}\)
    Correct
  • D
    \(\left( {2 + \sqrt 3 } \right):\left( {2 - \sqrt 3 } \right)\)
15
Two circles touch each other externally at C and AB is a common tangent to the circles. Then, \(\angle ACB = \)
  • A
    \({60^ \circ }\)
  • B
    \({45^ \circ }\)
  • C
    \({30^ \circ }\)
  • D
    \({90^ \circ }\)
    Correct