Page 54 - Ganit Kaushal

Ex 9. Which of the following has a definite length?
(a) A line (b) A ray (c) A line segment (d) None of these.

Sol. (c) A line segment
Ex 10. The number of points required to name a line is
(a) 1 (b) 2 (c) 3 (d) 4
Sol. (b) When we name a line, we use any two points on the line.
Ex 11. The number of lines that can be drawn through a given point is
(a) 1 (b) 2 (c) 3 (d) Infinitely many

Sol. (d) Infinitely many lines can be drawn through a given point.
Ex 12. The number of lines that can be drawn passing through two distinct points is
(a) 1 (b) 2 (c) 3 (d) Infinitely many
Sol. (a) Only one unique line can pass through two distinct points.
Ex 13. The maximum number of points of intersection of three lines drawn in a plane is
(a) 1 (b) 2 (c) 3 (d) Infinitely many
Sol. (c) A triangle has the maximum number of points of intersection of three lines, i.e. 3.

Ex 14. The minimum number of points of intersection of three lines drawn in a plane is
(a) 0 (b) 1 (c) 2 (d) 3
Sol. (a) 0; In this case, the lines are parallel to each other.
Ex 15. In the given figure, the number of line segments is (NCERT Exemplar)
(a) 5 (b) 10
(c) 12 (d) 15

Sol. (b) 10; The line segments are AB, AC, AD, AE, BC, BD, BE, CD, CE, DE.
Ex 16. The number of lines passing through five points such that no three of them are collinear is
(NCERT Exemplar)
(a) 10 (b) 5 (c) 20 (d) 8

Sol. (a) Total number of lines = 10.

Ex 17. Fill in the blanks.
(a) The number of common points in the two angles, marked in the given figure, is _______ .
(NCERT Exemplar)
(b) Half of a revolution is a/an _______ angle.

(c) One-fourth of a revolution is a/an _______ angle.
(d) More than half a revolution is a/an _______ angle.
(e) One complete rotation is a/an _______ angle.
(f) An angle whose measure is the sum of the measures of two right angles is _______ .
(g) When the sum of the measures of two angles is that of a right angle, then each of them is _______ .
(h) When the sum of the measures of two angles is that of a straight angle, and if one of them is acute,
then the other should be _______ .
(i) When the sum of the measures of two angles is that of a straight angle and if one angle is a right
angle, then the other angle is _______ .

52 Mathematics-6