List of practice Questions

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

What could be the possible 'one's' digits of the square root of each of the following numbers? 

1. 9801 
2. 99856 
3. 998001 
4. 657666025

Write a Pythagorean triplet whose one member is 

1. 6 
2. 14 
3.  16 
4.  18

Find the square of the following numbers 

1. 32 
2. 35 
3.  86 
4.  93 
5.  71 
6.  46

How many numbers lie between squares of the following numbers? 

1. \(12\) and \(13\) 
2.  \(25\) and \(26\) 
3.  \(99\) and \(100\)

How did Santosh begin to climb mountains?

Using the given pattern, find the missing numbers. 
\(1^ 2 + 2^2 + 2^2 = 3^2\)
\(2^ 2 + 3^2 + 6^2 = 7^2 \)
\(3^ 2 + 4^2 + 12^2 = 13^2 \)
\(4 ^2 + 5^2 + ....^2 = 21^2 \)
\(5^ 2 +....^2 + 30^2 = 31^2\) 
\(6^ 2 + 7^2 + ....^2 = ....^2\)

Observe the following pattern and supply the missing number. 
\(11^2 = 121\) 
\(101^2 = 10201\) 
\(10101^2 = 102030201\) 
\(1010101^2 = …\) 
\(...^2= 10203040504030201\)

Observe the following pattern and find the missing digits. 
\(11^2\) = \(121\) 
\(101^2\) = \(10201\) 
\(1001^2 = 1002001\) 
\(100001^2 = 1…2…1 \)
\(10000001^2 = …\)

The squares of which of the following would be odd numbers? 

1. 431 
2. 2826 
3. 7779 
4. 82004

What will be the unit digit of the squares of the following numbers? 

1. 81 
2. 272 
3.  799 
4.  3853 
5.  1234 
6.  26387 
7.  52698 
8.  99880 
9.  12796
10.  55555