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

What will be the units digit of the square of the following number? 

 12796

What will be the units digit of the square of the following number? 

55555

What will be the units digit of the square of the following number?

 53924

From the pattern, we can say that the sum of the first n positive odd numbers is equal to the square of the n-th positive number. Putting that into formula:
1 + 3 + 5 + 7 + ...  n =  n², where the left hand side consists of n terms. 

Observe the following pattern 

2² − 1² = 2 + 1
3² − 2² = 3 + 2
4² − 3² = 4 + 3
5² − 4² = 5 + 4
and find the value of 

100² − 99²

Observe the following pattern
2² − 1² = 2 + 1
3² − 2² = 3 + 2
4² − 3² = 4 + 3
5² − 4² = 5 + 4
and find the value of 

 111² − 109²

Observe the following pattern
2² − 1² = 2 + 1
3² − 2² = 3 + 2
4² − 3² = 4 + 3 
5² − 4² = 5 + 4
and find the value of 

99² − 96²

Which of the following triplets are pythagorean? 

 (8, 15, 17)

Which of the following triplet is pythagorean? 

 (18, 80, 82) 

Which of the following triplet  pythagorean? 

 (14, 48, 51)

Which of the following triplet  pythagorean?  

(10, 24, 26)

Which of the following triplet pythagorean? 

(16, 63, 65)

Which of the following triplet  pythagorean? 

(12, 35, 38) 

Observe the following pattern 

\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) = \frac{2 \times 3 \times 4}{3}\] 

\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) = \frac{3 \times 4 \times 5}{3}\] 

\[\left( 1 \times 2 \right) + \left( 2 \times 3 \right) + \left( 3 \times 4 \right) + \left( 4 \times 5 \right) = \frac{4 \times 5 \times 6}{3}\] 

and find the value of(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + (5 × 6)

Observe the following pattern \[1 = \frac{1}{2}\left\{ 1 \times \left( 1 + 1 \right) \right\}\]
\[ 1 + 2 = \frac{1}{2}\left\{ 2 \times \left( 2 + 1 \right) \right\}\]
\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\] 

and find the values of  following: 

1 + 2 + 3 + 4 + 5 + ... + 50

Observe the following pattern \[1 = \frac{1}{2}\left\{ 1 \times \left( 1 + 1 \right) \right\}\]
\[ 1 + 2 = \frac{1}{2}\left\{ 2 \times \left( 2 + 1 \right) \right\}\]
\[ 1 + 2 + 3 = \frac{1}{2}\left\{ 3 \times \left( 3 + 1 \right) \right\}\]
\[1 + 2 + 3 + 4 = \frac{1}{2}\left\{ 4 \times \left( 4 + 1 \right) \right\}\]and find the values of following:

31 + 32 + ... + 50

Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :  

1² + 2² + 3² + 4² + ... + 10²

Observe the following pattern \[1^2 = \frac{1}{6}\left[ 1 \times \left( 1 + 1 \right) \times \left( 2 \times 1 + 1 \right) \right]\]
\[ 1^2 + 2^2 = \frac{1}{6}\left[ 2 \times \left( 2 + 1 \right) \times \left( 2 \times 2 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 = \frac{1}{6}\left[ 3 \times \left( 3 + 1 \right) \times \left( 2 \times 3 + 1 \right) \right]\]
\[ 1^2 + 2^2 + 3^2 + 4^2 = \frac{1}{6}\left[ 4 \times \left( 4 + 1 \right) \times \left( 2 \times 4 + 1 \right) \right]\] and find the values :  

5² + 6² + 7² + 8² + 9² + 10² + 11² + 12²

Which of the following number  square of even number? 

121

Which of the following number  square of even number? 

 225