NCERT Exemplar Solutions - Mathematics - class 6 solutions for Chapter 2 Geometry

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

Number of lines passing through five points such that no three of them are collinear is

(A) 10

(B) 5

(C) 20

(D) 8

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

The number of diagonals in a heptagon is

(A) 21

(B) 42

(C) 7

(D) 14

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

Number of line segments in Fig. 2.5 is

(A) 5

(B) 10

(C) 15

(D) 20

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

Measures of the two angles between hour and minute hands of a clock at 9 O’ clock are

(A) 60°, 300°

(B) 270°, 90°

(C) 75°, 285°

(D) 30°, 330°

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is

(A) 5½

(B) 7½

(c) 2/11

(D) 2/15

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

In Fig. 2.6, ∠XYZ cannot be written as

(A) ∠Y

(B) ∠ZXY

(C) ∠ZYX

(D) ∠XYP

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

In Fig 2.7, if point A is shifted to point B along the ray PX such that PB = 2PA, then the measure of ∠BPY is

(A) greater than 45°

(B) 45°

(C) less than 45°

(D) 90°

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

The number of angles in Fig. 2.8 is

(A) 3

(B) 4

(C) 5

(D) 6

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

The number of obtuse angles in Fig. 2.9 is

(A) 2

(B) 3

(C) 4

(D) 5

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

The number of triangles in Fig. 2.10 is

(A) 10

(B) 12

(C) 13

(D) 14

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

If the sum of two angles is greater than 180°, then which of the following is not possible for the two angles?

(A) One obtuse angle and one acute angle

(B) One reflex angle and one acute angle

(C) Two obtuse angles

(D) Two right angles.

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?

(A) One obtuse angle and one acute angle.

(B) One right angle and one acute angle.

(C) Two acute angles.

(D) Two right angles.

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

A polygon has prime number of sides. Its number of sides is equal to the sum of the two least consecutive primes. The number of diagonals of the polygon is

(A) 4

(B) 5

(C) 7

(D) 10

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

In Fig. 2.11, AB = BC and AD = BD = DC. The number of isosceles triangles in the

figure is

(A) 1

(B) 2

(C) 3

(D) 4

In each of the questions 1 to 16, out of four options, only one is correct. Write the correct answer.

In Fig. 2.12, ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is

(A) 1

(B) 2

(C) 3

(D) 4

In each of the questions 1 to 16, out of four options only one is correct. Write the correct answer.

In Fig. 2.13, PQ ⊥ RQ, PQ = 5 cm and QR = 5 cm. Then ∆ PQR is

(A) a right triangle but not isosceles

(B) an isosceles right triangle

(C) isosceles but not a right triangle

(D) neither isosceles nor right triangle

In questions 17 to 31, fill in the blanks to make the statements true:

An angle greater than 180° and less than a complete angle is called ______.

In questions 17 to 31, fill in the blanks to make the statements true:

The number of diagonals in a hexagon is ________.

In questions 17 to 31, fill in the blanks to make the statements true:

A pair of opposite sides of a trapezium are ________.

In Fig. 2.14, points lying in the interior of the triangle PQR are ______, that in the exterior are ______ and that on the triangle itself are __.

In Fig. 2.15, points A, B, C, D and E are collinear such that AB = BC = CD = DE. Then

(a) AD = AB + ______

(b) AD = AC + ______

(c) mid point of AE is ______

(d) mid point of CE is ______

(e) AE = ______ × AB.

In Fig. 2.16,

(a) ∠AOD is a/an ______ angle

(b) ∠COA is a/an ______ angle

(c) ∠AOE is a/an ______ angle

The number of triangles in Fig. 2.17 is _. Their names are _____________________.

Number of angles less than 180° in Fig. 2.17 is __and their names are _______ .

The number of straight angles in Fig. 2.17 is __.

The number of right angles in a straight angle is ______ and that in a complete angle is ______.

The number of common points in the two angles marked in Fig. 2.18 is __.

The number of common points in the two angles marked in Fig. 2.19 is __.

The number of common points in the two angles marked in Fig. 2.20 ______ .

The number of common points in the two angles marked in Fig. 2.21 is ______.

The common part between the two angles BAC and DAB in Fig. 2.22 is __.

A horizontal line and a vertical line always intersect at right angles.

If the arms of an angle on the paper are increased, the angle increases.

If the arms of an angle on the paper are decreased, the angle decreases.

If line PQ || line m, then line segment PQ || m.

Two parallel lines meet each other at some point.

Measures of ∠ABC and ∠CBA in Fig. 2.23 are the same.

Two line segments may intersect at two points

Many lines can pass through two given points.

Only one line can pass through a given point.

Two angles can have exactly five points in common.

Ncert exemplar solutions mathematics class 6 Solutions for Chapter 2 geometry