Secondary School (English Medium) (5 to 8) Class 7 - CBSE Question Bank Solutions for Mathematics

A square tile of length 20 cm has four quarter circles at each corner as shown in the following figure (i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile [see figure (ii)]. If the circle touches all four sides of the square tile, find the area of the shaded portion. In which tile, area of shaded portion will be more? (Take π = 3.14)

(i)	(ii)

Calculate the area of shaded region in the following figure, where all of the short line segments are at right angles to each other and 1 cm long.

Architects design many types of buildings. They draw plans for houses, such as the plan shown in the following figure:

An architect wants to install a decorative moulding around the ceilings in all the rooms. The decorative moulding costs ₹ 500/metre.

1. Find how much moulding will be needed for each room.
   (i) family room
   (ii) living room
   (iii) dining room
   (iv) bedroom 1
   (v) bedroom 2
2. The carpet costs ₹ 200/m². Find the cost of carpeting each room.
3. What is the total cost of moulding for all the five rooms.

The side length of the top of square table is x. The expression for perimeter is ______.

The expression for the number of diagonals that we can make from one vertex of a n sided polygon is ______.

The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?

The speed of car is 55 km/hrs. The distance covered in y hours is ______.

Find the perimeter of the figure given below:

In a rectangular plot, 5 square flower beds of side (x + 2) metres each have been laid (see the figure). Find the total cost of fencing the flower beds at the cost of ₹ 50 per 100 metres:

A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:

1. How much wire is left?
2. If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?

The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 5 natural numbers.

The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of first 11 natural numbers.

The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of natural numbers from 11 to 30.

The sum of squares of first n natural numbers is given by `1/6n(n + 1)(2n + 1)` or `1/6(2n^3 + 3n^2 + n)`. Find the sum of squares of the first 10 natural numbers.

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 7.

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 10.

The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of table of 19.

If = 2x + 3,  = `3/2x + 7` and  = x – 3 then find the value of:

² + –

If = 2x + 3,  = `3/2x + 7` and  = x – 3 then find the value of:

^`1/2` + – 3