List of practice Questions

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. 

1. 525 
2.  1750 
3.  252 
4.  1825
5.  6412

Why has the poet brought in the image of the merry children 'spilling out of their homes'?

What do you understand about the author’s literary inclinations from the account?

In a right triangle ABC, \(∠ B\) = 90°. 

1. If AB = 6 cm, BC = 8 cm, find AC 
2.  If AC = 13 cm, BC = 5 cm, find AB

How does the author describe the incongruity of an English poet addressing the audience at Gemini Studios ?

A gardener has \(1000\) plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

Notice the sentences in the text which are in ‘direct speech’. Why does the author use quotations in his narration?

The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

These are \(500\) children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

How do we know that ordinary people too contributed to the freedom movement?

Which of the following numbers are not perfect cubes: 

1. 216 
2. 128 
3.  1000 
4.  100 
5.  46656

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

1. 243
2. 256
3.  72
4.  675
5.  100

Parikshit makes a cuboid of plasticine of sides \(5\) \(cm\), \(2\) \(cm\), \(5\) \(cm.\) How many such cuboids will he need to form a cube?

The passing of time will no longer affect her, says the poet. Which lines of the poem say this?

“A slumber did my spirit seal,” says the poet. That is, a deep sleep ‘closed off’ his soul (or mind). How does the poet react to his loved one’s death? Does he feel bitter grief ? Or does he feel a great peace?

Now fill in the blanks with suitable words from the ones that you have formed.
(i) Mass literacy was possible only after the __of the printing machine.
(ii) Ramesh is unable to tackle the situation as he lacks__.
(iii) I could not resist the__ to open the letter.
(iv) Hardwork and __are the main keys to success.
(v) The children were almost fainting with__ after being made to stand in the sun.

The displacement equation of a spring block system is given by $y=a\,\sin\,\omega t$ in air. It is completely immersed in water if $A^|\,and\,\omega^|$ be new amplitude and angular frequency then

Find the square roots of the following numbers by the Prime Factorisation Method. 

1. 729 
2. 400 
3.  1764 
4.  4096 
5.  7744 
6.  9604 
7.  5929 
8.  9216 
9.  529 
10.  8100

Find the smallest square number that is divisible by each of the numbers \(8, 15\), and \(20\).

Find the smallest square number that is divisible by each of the numbers \(4, 9\), and \(10\).

\(2025\) 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.

The students of Class VIII of a school donated Rs \(2401\) in all, for Prime Minister's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Find the square roots of \(100\) and \(169\) by the method of repeated subtraction.

Without doing any calculation, find the numbers which are surely not perfect squares. 

1. 153 
2. 257 
3. 408 
4. 441