English Medium कक्षा ९ - CBSE Question Bank Solutions

Draw a histogram to represent the following grouped frequency distribution:

The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table:

Draw a histogram to represent the data above.

The marks obtained (out of 100) by a class of 80 students are given below:

Construct a histogram to represent the data above.

Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:

Draw a histogram and frequency polygon representing the data above.

Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:

Draw the frequency polygon representing the above data without drawing the histogram.

Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.

Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?

Classify the following numbers as rational or irrational:

`2-sqrt5`

Simplify the following expression:

`(3+sqrt3)(2+sqrt2)`

Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = `c/d`. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Represent `sqrt9.3`  on the number line.

Rationalise the denominator of the following:

`1/sqrt7`

Give the geometric representations of y = 3 as an equation in one variable.

Give the geometric representations of y = 3 as an equation in two variables.

Give the geometric representations of 2x + 9 = 0 as an equation in one variable.

Give the geometric representations of 2x + 9 = 0 as an equation in two variables.

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that

1. ΔABD ≅ ΔACD
2. ΔABP ≅ ΔACP
3. AP bisects ∠A as well as ∠D.
4. AP is the perpendicular bisector of BC.

AD is an altitude of an isosceles triangles ABC in which AB = AC. Show that

1. AD bisects BC
2. AD bisects ∠A

Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see the given figure). Show that:

1. ΔABM ≅ ΔPQN
2. ΔABC ≅ ΔPQR

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.