English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:-

1. Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
2. Is there any other suitable graphical representation for the same data?
3. Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

The following table gives the life times of 400 neon lamps:-

1. Represent the given information with the help of a histogram.
2. How many lamps have a life time of more than 700 hours?

The following table gives the distribution of students of two sections according to the mark obtained by them:-

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

Represent the data of both the teams on the same graph by frequency polygons.

[Hint: First make the class intervals continuous.]

A random survey of the number of children of various age groups playing in a park was found as follows:

Draw a histogram to represent the data above.

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

1. Draw a histogram to depict the given information.
2. Write the class interval in which the maximum number of surnames lie.

Represent `sqrt6,` `sqrt7,` `sqrt8` on the number line.

Represent `sqrt3.5,` `sqrt9.4,` `sqrt10.5` on the real number line.

Visualise 2.665 on the number line, using successive magnification.

Visualise the representation of `5.3bar7` on the number line upto 5 decimal places, that is upto 5.37777.

In a ΔABC, if ∠A=l20° and AB = AC. Find ∠B and ∠C. 

In Figure AB = AC and ∠ACD =105°, find ∠BAC.  

Find the measure of each exterior angle of an equilateral triangle. 

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other. 

In figure, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD 

Determine the measure of each of the equal angles of a right-angled isosceles triangle.

AB is a line seg P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B (See Fig. 10.26). Show that the line PQ is perpendicular bisector of AB. 

In Fig. 10.40, it is given that RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT 

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that
(i) PT = QT (ii) ∠TQR = 15°