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A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green?

Given that Box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of... View Article

A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see Fig) . Find the cost of polishing the tiles at the rate of 50p per cm²

Answer: The plane closed figure, with three sides and three angles is called as a triangle. Area of a triangle Area = (1/2)... View Article

Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. (ii) 5 pencils and 7 pens together cost 50, whereas 7 pencils and 5 pens together cost 46. Find the cost of one pencil and that of one pen.

Let us assume that The numbr of girls as x number of girls and y number of boys. As per the... View Article

Which of the following arguments are correct and which are not correct? Give reasons for your Solution:. (i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 (ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2

(i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore,... View Article

In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees and so on till class XII. There are three sections of each class. How many trees will be planted by the students?

From the given data we come to know that the number of trees planted by the students is in an AP.... View Article

Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out (see Figure) ? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

Let us assume, AB is the height of the tip of the fishing rod from the water surface and BC... View Article

In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: F = (9/5) C + 32. (i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis. (ii) If the temperature is 30°C, what is the temperature in Fahrenheit? (iii) If the temperature is 95°F, what is the temperature in Celsius? (iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius? (v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Answer: Celsius and Fahrenheit are two scales used to measure temperature. The temperature in the centigrade scale will be expressed... View Article

A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite. (Assume π = 22/7)

Given Height of wood (and graphite) cylinder (h) = 14 cm = 140 mm Radius of pencil (R)= 7/2mm Radius of... View Article

Following are the car parking charges near a railway station upto: 4 hours Rs.60, 8 hours Rs.100, 12 hours Rs.140, 24 hours Rs.180. Check if the parking charges are in direct proportion to the parking time.

Solution We can tabulate the given data as Number of hours 04 08 12 24 Parking cost 60 100 140... View Article

ABCD is a trapezium in which AB || CD and AD = BC (see Fig.) . Show that (i) ∠A = ∠B (ii) ∠C = ∠D (iii) ΔABC ≅ ΔBAD (iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

The trapezium ABCD in which AB || CD and AD = BC. Extended AB and draw a line through C... View Article

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and π = 3.14.

Given For the cylinder part, Height (h) = 8 cm and Radius (R) = (2/2) cm = 1 cm For... View Article

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2.

The diameter of the cylinder = diameter of conical cavity = 1.4 cm The radius of the cylinder = radius of... View Article

To find out the concentration of SO2 in the air (in parts per million, i.e., ppm) , the data was collected for 30 localities in a certain city and is presented below. Find the mean concentration of SO2 in the air.

Concentration of SO2 ( in ppm) Frequency 0.00 – 0.04 4 0.04 – 0.08 9 0.08 – 0.12 9 0.12... View Article

Tick the correct Solution: in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is (A) 2 units (B) π units (C) 4 units (D) 7 units

The answer is Option (A) 2 units Solution Let the radius of the circle be r. Circumference of circle = 2πr... View Article

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?

Given π = c/d = 22/7 which is equal to 3.142… which is non-terminating non-recurring decimal. Therefore, π is irrational.... View Article

A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5cm and width 4cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7cm and height 10cm. Which container has greater capacity and by how much? (Assume π = 22/7)

Solution (i) tin can will be cuboidal in shape Length of can (l) = 5 cm Width of can (b)... View Article

The organisers of an essay competition decide that a winner in the competition gets a prize of Rs. 100 and a participant who does not win gets a prize of Rs. 25. The total prize money distributed is Rs. 3,000. Find the number of winners, if the total number of participants is 63.

Solution Let the numbers of winner be ‘W’ Then, the number of pWrticipWnt who didn’t win will be (63 –... View Article

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x. [Hint :S_x – 1 = S₄₉ – S_x ]

Given, Row houses are numbers from 1,2,3,4,5…….49. Thus we can see the houses numbered in a row are in the... View Article

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Let AB be the height of statue. D is the point on the ground from where the elevation is taken.... View Article

Daniel is paining the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m^2of area is painted. How many cans of paint will she need to paint the room?

Solution: Given Length of wall (l) = 15 m, Breadth of wall (b) = 10 m Height of wall, (h)... View Article

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