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For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag. (b) The height of competitors in an athletics meet. (c) The number cassettes produced by 5 companies. (d) The number of passengers boarding trains from 7.00 a.m. to 7.00 p.m. at a station. Give reason for each.

Solution Histogram is a graphical representation of data if the data represented using class- interval. (b) The height of competitors in an... View Article

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1 4 m and a tread of 1 2 m. (see Fig.) . Calculate the total volume of concrete required to build the terrace. [Hint : Volume of concrete required to build the first step = 1/4 ×1/2 ×50 m3.]

From the given figure, The first step is ½ m wide, 2nd step is 1m wide and 3rd step is 3/2m wide. Thus we know that the width... View Article

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m2? [If required you can split the tiles in whatever way you want to fill up the corners]

Answer Given Base of flooring tile = 24 cm = 0.24 m Corresponding height of a flooring tile = 10 cm = 0.10 m Find out The number of tiles... View Article

The following frequency distribution gives the monthly consumption of an electricity of 68 consumers in a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption(in units) No. of customers 65-85 4 85-105 5 105-125 13 125-145 20 145-165 14 165-185 8 185-205 4... View Article

Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig.) . Prove that ∠ ACP = ∠ QCD.

Solution To prove: ∠ACP=∠QCD∠ACP=∠QCD —— [angles in the same segment are equal] ∠ DCQ=∠ QBD... View Article

Form the pair of linear equations for the following problems and find their solution by substitution method (i) The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat and each ball. (ii) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

(i) The coach of a cricket team buys 7 bats and 6 balls for Rs.3800. Later, she buys 3 bats and 5 balls for Rs.1750. Find the cost of each bat... View Article

The weekly wages (in Rs.) of 30 workers in a factory are: 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840. Using tally marks, make a frequency table with intervals as 800 – 810, 810 – 820 and so on.

Solution The frequency table with intervals as 800 – 810, 810 – 820 and so on, using tally marks is given below:... View Article

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

Let AB be the tower. C and D be the two points with distance 4 m and 9 m from the base respectively. As per the given data... View Article

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Let us asume The age of one friend be x years. Then, the age of the other friend will be (20 – x) years. Four years ago, Age of First... View Article

The paint in a certain container is sufficient to paint an area equal to 9.375 m². How many bricks of dimensions 22.5 cm×10 cm×7.5 cm can be painted out of this container?

Given Bricks of dimensions 22.5 cm×10 cm×7.5 cm Find out We have to find the number of bricks that can be painted out of this... View Article

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90°-(1/2) A, 90°-(1/2) B and 90°-(1/2) C.

Given: ∆ABC and it circum-circle AD,BE and CF are bisectors of ∠A,∠B and ∠C Respectively. To prove:∠ D=90°-1/2∠A ,... View Article

Draw a triangle ABC with side BC = 7 cm, ∠ B = 45°, ∠ A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ∆ ABC. Give the justification of the construction

Let us first find the measure of ∠C ∠B = 45°, ∠A = 105° We know that, The Sum of all interior angles in a triangle... View Article

In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60 Find the mean, median and mode of this data.

Given A mathematics test given to 15 students, the following marks (out of 100) are recorded: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40,... View Article

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that: (i) ar (PRQ) = 1/2 ar (ARC) (ii) ar (RQC) = (3/8) ar (ABC) (iii) ar (PBQ) = ar (ARC)

Solution Given: From ∆ABC, P is midpoint of AB, Q is midpoint of BC, R is midpoint of AP To Prove ar (PRQ) = 12 ar (ARC)... View Article

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle. Give the justification of the construction

To construct a tangent from given conditions 1. Let us draw a circle with the help of a bangle. 2. Now draw two non-parallel... View Article

Write the answer of each of the following questions: (i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane? (ii) What is the name of each part of the plane formed by these two lines? (iii) Write the name of the point where these two lines intersect.

(i) Name of the horizontal and vertical lines are: The horizontal line drawn on the Cartesian plane is known as the x-axis. The vertical... View Article

A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m×15 m×6 m. For how many days will the water of this tank last?

Given Length of the tank, l = 20 m The breadth of the tank,b= 15m Height of tank, h = 6 m Total population of a village = 4000... View Article

2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

Solution Let as assume number of rows be, R So, Each row has number of plants = R Therefore, Total number of plants = R x... View Article

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

Given that In a group of 3 students, the probability of 2 students not having the same birthday is 0.992 Find out The probability that the 2... View Article

Water is pouring into a cuboidal reservoir at the rate of 60 liters per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.

Given The volume of reservoir = 108 m3 Rate of pouring water into cuboidal reservoir = 60 litres/minute Find out We have to find out... View Article