Mathematics exemplar problems class 10 Solutions for Chapter 10 constructions

To divide a line segment AB in the ratio 3:8, first a ray AX is drawn so that BAX is an acute angle. Then, at equal distances, points are marked on the ray AX such that the minimum number of these points is

To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of two radii of the circle, the angle between them should be

To divide a line segment PQ in the ratio 2 : 5, draw a ray PX such that ∠QPX is an acute angle. Then, draw a ray QY parallel to PX. Mark the points P₁, P₂, and Q₁, Q₂, Q₃, Q₄, Q₅ at equal distances on ray PX and QY, respectively.

What is the next step in the construction?

To divide a line segment PQ in the ratio 3:7, draw a ray PX such that ∠QPX is an acute angle, then draw a ray QY parallel to PX. How many points at equal distances should we locate on each ray, PX and QY as the next step of the construction?

To construct a triangle similar to a given ΔABC with its sides 4/9 of the corresponding sides of ΔABC:

First, we draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. The next step in the construction is to locate ____ points on BX at equal distances.

To construct a triangle similar to a given ΔABC with its side 7/3 of the corresponding sides of ΔABC;

Draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC.

What is the minimum number of points to be located at equal distances on the ray BX?

To divide a line segment AB in the ratio 9:2, a ray AX is drawn first such that BAX is an acute angle. Then, points A₁, A₂, A₃,…. are located at equal distances on the ray AX. What should be next step in the construction?

To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that BAX is an acute angle and then points A₁, A₂, A₃,…. are located at equal distances on the ray AX and point B is joined to point

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A₁, A₂, A₃, … and B₁, B₂, B₃, … are located at equal distances on ray AX and BY, respectively. Then the points joined are

To construct a triangle similar to a given ΔABC with its side 8/5 of the corresponding sides of ΔABC;

Draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC.

What is the minimum number of points to be located at equal distances on the ray BX?

To construct a triangle similar to a given ΔABC with its sides 3/7 of the corresponding sides of ΔABC:

First, draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC.

Then, locate points B₁, B₂, B₃, … on BX at equal distances and next step is to join __________________

If a line segment AB of length 6 cm is divided internally by a point C in the ratio of 3 : 2, then the length of AC is ____.

State whether the following statment is true or false.

A pair of tangents can be constructed to a circle inclined at an angle of 170°.

State whether the following statment is true or false.

To construct a triangle similar to a given △ABC with its sides 7/3 of the corresponding sides of △ABC:

Draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC.

The points B1, B2, …., B7 are located at equal distances on BX

B₃ is joined to C and then a line segment B₆C’ is drawn parallel to B₃ where C‘ lies on BC produced. Finally, line segment A‘C‘ is drawn parallel to AC.

If two dices are rolled at the same time, what is the probability of getting the sum as 7 on two dice?

If two dices are rolled at the same time, what is the probability that the sum on the numbers on two dices is 5?

If two dices are rolled at the same time, what is the probability of getting tthe sum of numbers on the two dice as 10?

If two dices are rolled at same time, what is the probability of getting that the sum of the two numbers is 3?

If two dices are rolled at the same time, what is the probability that the sum of the numbers on two dices is 6?

If two dices are rolled at the same time, what is the probability that the sum of the two numbers is 4?

If two dices are rolled at the same time, what is the probability of getting 8 as the sum on two dice?

If two dices are rolled at the same time, what is the probability of getting the sum as 11 on the two dice?

If two dices are rolled at the same time, what is the probability of getting 12 as the sum of the numbers on the dice?

Point X is at a distance of 6 cm from the centre of a circle of radius 2 cm. How many tangents can be constructed to the circle from the point X?

State whether the following statment is true or false.

A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.

State whether the following statment is true or false.

A pair of tangents can be constructed from a point P at a distance of 8 cm from the centre of a circle of radius 5 cm.

State whether the following statment is true or false.

A pair of tangents can be constructed to a circle that are inclined to each other at an angle of 200°.

If two dices are rolled at the same time, what is the probability that the sum of numbers on two dices is 9?

State whether the following statment is true or false.

By geometrical construction, it is possible to divide a line segment in the ratio √3:(1/√3)