Product of Two Consecutive Even or Odd Natural Numbers

Q.

Express $49$ as a sum of seven odd numbers.

Q. Evaluate: (i) $88\times 92$, (ii) $78\times 82$.

Q.

Evaluate: $\left(i\right)69\times 71$, (ii) $94\times 106$.

Q.

The sum of first 5 consecutive odd numbers is:

1. 16

2. 36

3. 18

4. 25

Q.

The sum of two consecutive triangular numbers gives a __ number.

Q. Which of the following numbers can be written in the form $2^n$, where $n$ is a natural number?

1. 8
2. 256
3. 120
4. 24
5. 84
6. 32
7. 40
8. 20
9. 512
10. 64

Q. Express each of the following odd numbers as the sum of three odd prime numbers:
(i) 31
(ii) 35
(iii) 49
(iv) 63

Q.

Question 6(ii)
Simplify:
(ii) $7^2\times 2^2$

Q. Find the value of ${49}^2$

Q. Question 3(iv)
Find the products:
$x\times x^2\times x^3\times x^4$

Q. If a number is not a perfect number, then it has to be a sum of succesive odd numbers starting from 1.

1. True
2. False

Q. Evaluate: $176\times 176-124\times 124$

1. 15400

2. 15600

3. 16500

4. 12280

Q.

In a number pattern 66, 127, 218, t​​​​​​​​​​​​ , the value of t will be

A.472

B.514

C.555

D.670

Q.

Question 170

Long back in ancient times, a farmer saved the life of a king's daughter. The king decided to reward the farmer with whatever he wished. The farmer, who was a chess champion, made an unusal request
"I would like you to place 1 rupee on the first square of my chessboard . 2 rupees on the second square, 4 on the third square, 8 on the fourth square and so on, until you have covered all 64 squares. Each square should have twice as many rupees as the previous square ' The king thought this to be too less and asked the farmer to think of some better reward, but the farmer didn't agree.

How much money has the farmer earned?

[Hint The following table may help you. What is the first square on which the king will place at least 10 lakh?]

Q. How many numbers lie between the squares of the numbers $99$ and $100$?
[2 marks]

1. $200$
2. $199$
3. $201$
4. $198$

Q.

find the following product 43x45?

1. 1935

2. 1835

3. 2115

4. 2025

Q. $(n-1)(n+1)=n^2-1$ pattern is useful for which of the following?

1. Only for even numbers
2. Only for odd numbers
3. Both even and odd numbers
4. Neither even nor odd numbers

Q. What is the value of $(166{)}^2$?

Q.

What is the sum of any two even number?

Q. If the product of four consecutive natural numbers increased by a natural number $\rho$ is a perfect square, then the value of $\rho$ is:

1. 4
2. 2
3. 8
4. 1

Q. Respected Teacher,
i have searched for a good answer for ex.2.4 question 7, 8, and 10 which a re pretty hard i could not find it i got the answers but it was not still clear for me.thank you.

Q.

1 + 3 + 5 + 7 =

1. 3²

2. 7²

3. 5²

4. 4²

Q.

Which of the following functions are identical to f(x)?

$f\left(x\right)=\{\begin{array}{cc}x,& 1\le x<2\\ x^2,& 2\le x<3\end{array}$

(1 $\le$ x < 3 )

1. 

2. 

3. 

4. 

Q. Find the value of x:
x - 10 = 7

Q.

5² =

1. 1 + 3 + 5 + 7 + 9 + 11

2. 1 + 3 + 5 + 7

3. 1 + 3 + 5

4. 1 + 3 + 5 + 7 + 9

Q. If the product of four consecutive natural numbers increased by a natural number p is a perfect square, then the value of p is

1. 1
2. 8
3. 4
4. 2

Q.

find the following product 43x45?

1. 1835

2. 1935

3. 2115

4. 2025

Q. ${11}^2-1$ is a product of two consecutive even numbers. Find those two even numbers.

1. 12 and 22
2. 12 and 13
3. 10 and 12
4. 12 and 14

Q. What is square number?

Q. Which of the following numbers can be written in the form $2^n$, where $n$ is a natural number?

1. 32
2. 84
3. 20
4. 256
5. 24
6. 64
7. 40
8. 8
9. 120
10. 512