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It is given that XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ZYP, find XYQ and reflex QYP.

It is given that XYZ = 64° and XY is produced to point P. Let us draw a figure from the given information. If ray YQ bisects ZYP, we need to... View Article

The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder. (Assume π = 22/7)

Given Height of cylinder(h)=14 cm Curved Surface Area of cylinder=88 cm2 Find out We have to find the diameter of the base of the cylinder... View Article

In Figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that : (i) AC2 = AD2 + BC.DM + 2 (BC/2) 2 (ii) AB2 = AD2 – BC.DM + 2 (BC/2) 2 (iii) AC2 + AB2 = 2 AD2 + 1/2 BC2

Given: In ∆ABC, AD is a median, AM ⊥ BC. To Prove (i) AC2 = AD2 + BC.DM + (BC/2)2 (ii) AB2 = AD2 – BC.DM +... View Article

In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.

From the figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1). Find distance between points using distance... View Article

A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?

Solution Let the number of days be x. Total number of animals = 20+10 = 30 The number of days and animals are inversly proportional Therefore,... View Article

The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Given Length of the cuboidal tank, l = 8 m Height of cuboidal tank, h = 3m The volume of the cuboidal tank = 50000 litres Find out... View Article

The first and the last term of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Given that First term, a = 17 Last term, l = 350 Common difference, d = 9 Find out We have to find out the number of terms and their sum Solution... View Article

ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Considering ∆ABD We observe that P and S are the mid points of side AB and AD respectively. [Given] We know the theorem: The line segment... View Article

On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig.) . Find the area of the remaining portion of the handkerchief.

Given Number of circular designs = 9 Radius of the circular design = 7 cm There are three circles in one side of square handkerchief. Find out... View Article

The following numbers are obviously not perfect squares. Give reason. i) 1057 ii) 23453 iii) 7928 iv) 222222 v) 64000 vi) 89722 vii) 222000 viii) 505050

Solution If a number ends with 2 (or) 3 (or) 7 (or) 8 at units place then we can tell it is not a perfect square. i. 1057 = Ends with 7 ii.... View Article

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth.

Let the breadth of mango grove be l. Length of mango grove will be 2l. Area of mango grove = (2l) (l)= 2l2 2l2 = 800 l2 = 800/2 =... View Article

The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.

Daily expenditure(in c) 100-150 150-200 200-250 250-300 300-350 Number of households 4 5 12 2 2 Solution To determine the midpoint... View Article

The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find the mean, median and mode of these scores.

Given The number of goals was scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3, 3, 4, 3 Find out We have to find out the... View Article

A wooden bookshelf has external dimensions as follows: Height = 110cm, Depth = 25cm, Breadth = 85cm (see fig) . The thickness of the plank is 5cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.

Given Length of bookshelf (l) = 85cm Breadth of bookshelf (b) = 25 cm Height of bookshelf (h) = 110cm Find out We have to find out... View Article

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60° Give the justification of the construction

To construct a tangent from given conditions 1. Let us draw a circle of radius 5 cm and with the centre as O. 2. Considering a point Q... View Article

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days 0-6 6-10 10-14 14-20 20-28 28-38 38-40 Number of students 11 10 7 4 4 3 1 Solution Class interval Frequency (fi)... View Article

A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5cm. Find the outer curved surface of the bowl. (Assume π = 22/7)

Given hemispherical bowl made of brass has inner diameter 10.5cm Find out We have to find the cost of tin-plating it on the inside at the rate of... View Article

In Fig., two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that: (i) ∆ PAC ~ ∆ PDB (ii) PA . PB = PC . PD.

In ΔPAC and ΔPDB, ∠P=∠P[Common]∠PAC=∠PDB [Exterior angle of cyclic... View Article

A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank.

Given The radius of a cylindrical tank, r = 1.5 m Height of cylindrical tank, h = 7 m Find out We have to find out the the quantity... View Article

A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

Trapezium area can be calculated by using the below formula: Area = (1/2) h (a+b) where, a and b are the length of parallel sides/bases... View Article