English Medium Class 9 - CBSE Question Bank Solutions

In ∆ABC, D is the mid-point of AB and P is any point on BC. If CQ || PD meets AB in Q (Figure), then prove that ar (BPQ) = `1/2` ar (∆ABC).

O is any point on the diagonal PR of a parallelogram PQRS (Figure). Prove that ar (PSO) = ar (PQO).

A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that ar (ADF) = ar (ABFC)

The medians BE and CF of a triangle ABC intersect at G. Prove that the area of ∆GBC = area of the quadrilateral AFGE.

In the following figure, CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY).

In ∆ABC, if L and M are the points on AB and AC, respectively such that LM || BC. Prove that ar (LOB) = ar (MOC)

In the following figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (APQ)

If the medians of a ∆ABC intersect at G, show that ar (AGB) = ar (AGC) = ar (BGC) = `1/3` ar (ABC)

In the following figure, X and Y are the mid-points of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Prove that ar (ABP) = ar (ACQ).

Through three collinear points a circle can be drawn.

ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that ∠CBD + ∠CDB = `1/2` ∠BAD

The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.

The frequency distribution has been represented graphically as follows:

Do you think this representation is correct? Why?

In a diagnostic test in mathematics given to students, the following marks (out of 100) are recorded:

46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44

Which ‘average’ will be a good representative of the above data and why?

Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement.

The expenditure of a family on different heads in a month is given below:

Draw a bar graph to represent the data above.

Expenditure on Education of a country during a five year period (2002-2006), in crores of rupees, is given below:

Represent the information above by a bar graph.

The following table gives the frequencies of most commonly used letters a, e, i, o, r, t, u from a page of a book:

Represent the information above by a bar graph.

In the following figure, there is a histogram depicting daily wages of workers in a factory. Construct the frequency distribution table.

Draw a histogram of the following distribution: