- Express \(49\) as the sum of \(7 \) odd numbers.
- Express \(121\) as the sum of \(11\) odd numbers.
- Express \(49\) as the sum of \(7 \) odd numbers.
- Express \(121\) as the sum of \(11\) odd numbers.
Solution and Explanation
We know that the sum of first \(n\) odd natural numbers is \(n^2\).
(i) \(49 = (7)^2\)
Therefore, \(49\) is the sum of first \(7\) odd natural numbers.
\(49 = 1 + 3 + 5 + 7 + 9 + 11 + 13\)
(ii) \(121 = (11)^2\)
Therefore, \(121\) is the sum of first \(11\) odd natural numbers.
\(121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21\)
Top Questions on Some More Interesting Patterns
- The following numbers are obviously not perfect squares. Give reason.
- 1057
- 23453
- 7928
- 222222
- 64000
- 89722
- 222000
- 505050
- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- Without adding find the sum
- \(1 + 3 + 5 + 7 + 9\)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 \)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\)
- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- How many numbers lie between squares of the following numbers?
- \(12\) and \(13\)
- \(25\) and \(26\)
- \(99\) and \(100\)
- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- Using the given pattern, find the missing numbers.
\(1^ 2 + 2^2 + 2^2 = 3^2\)
\(2^ 2 + 3^2 + 6^2 = 7^2 \)
\(3^ 2 + 4^2 + 12^2 = 13^2 \)
\(4 ^2 + 5^2 + ....^2 = 21^2 \)
\(5^ 2 +....^2 + 30^2 = 31^2\)
\(6^ 2 + 7^2 + ....^2 = ....^2\)- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
- Observe the following pattern and supply the missing number.
\(11^2 = 121\)
\(101^2 = 10201\)
\(10101^2 = 102030201\)
\(1010101^2 = …\)
\(...^2= 10203040504030201\)- CBSE Class VIII
- Mathematics
- Some More Interesting Patterns
Questions Asked in CBSE Class VIII exam
Underline the verbs and arrange them in two columns, Past and Earlier past.
(a) My friends set out to see the caves in the next town, but I stayed at home, because I had seen them already.
(b) When they arrived at the station, their train had left. They came back home, but by that time I had gone out to see a movie!
(c) So they sat outside and ate the lunch I had packed for them.
(d) By the time I returned, they had fallen asleep!
Past Earlier Past - CBSE Class VIII
- The Best Christmas Present in the world
- Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2q
- CBSE Class VIII
- Addition and Subtraction of Algebraic Expressions
Fill in the blanks using the correct form of the verbs in brackets.
My little sister is very naughty. When she ____ (come) back from school yesterday, she had _____(tear) her dress. We _____(ask) her how it had _____(happen). She ______(say) she _____ _____ (have, quarrel) with a boy. She _____ _____ (have, beat) him in a race and he _____ ____ (have, try) to push her. She _____ ____ (have, tell) the teacher and so he _____ _____ (have, chase) her, and she _____ _____ (have, fall) down and _____ _____ (have, tear) her dress.
- CBSE Class VIII
- The Best Christmas Present in the world
- Match the organisms in Column A with their action in Column B.
A
B
(i) Bacteria (a) Fixing nitrogen (ii) Rhizobium (b) Setting of curd (iii) Lactobacillus (c) Baking of bread (iv) Yeast (d) Causing malaria (v) A protozoan (e) Causing cholera (vi) A virus (f) Causing AIDS (g) Producing antibodies - CBSE Class VIII
- Microorganisms
Say whether the following are true or false.
1. Ignesious lost his wife, two children, his father-in-law, and his brother-in-law in the tsunami.
2. Sanjeev made it to safety after the tsunami.
3. Meghna was saved by a relief helicopter.
4. Almas’s father realised that a tsunami was going to hit the island.
5. Her mother and aunts were washed away with the tree that they were holding on to.
- CBSE Class VIII
- The Tsunami