Sum of Squares of First N Natural Numbers

Q.

The sum of the series
${45}^2-{43}^2+{44}^2-{42}^2+{43}^2-{41}^2+{42}^2-{40}^2+\cdots 15terms$ is

1. 1900

2. 2220

3. 1290

4. 1650

Q. If sum of cubes of first 'm' natural numbers is 441 then sum of first 'm' natural numbers is _____

1. 6
2. 16
3. 7
4. 21

Q. How many non square numbers lie between $2^2$ and $3^2$?

1. 3
2. 4
3. 6
4. 2

Q. $\sqrt[n]{nx}$ can also be represented as

1. $x^{\frac{1}{n}}$
2. $\frac{1}{\frac{1}{n}}$
3. $Noneofthese$
4. $\frac{1}{n}.x$

Q. The sum of the squares of the first n natural numbers is

1. $\frac{n(n+1)}{2}$
2. $\frac{n(n+1)(2n+1)}{6}$
3. $\frac{n(n+1)(n+2)}{12}$
4. $\frac{n(n+1)(2n+1)}{12}$

Q. $1^2+2^2+3^2+4^2+...+7^2=$ .

1. 120
2. 140
3. 105

Q.

If $x^2\ge 0$ which of the following may be true for x?

1. x>0

2. x<0

3. x = 0

4. None of these

Q.

Which of the following expression gives the value of "s". "s" is given as $1^2+2^2+3^2+4^2+................+7^2$

1. $s=\frac{7\times (7+1)(2\times 7+1)}{8}$

2. $s=\frac{7\times (7+1)(3\times 7+1)}{6}$

3. $s=\frac{7\times (7+2)(2\times 7+1)}{6}$

4. $s=\frac{7\times (7+1)(2\times 7+1)}{6}$

Q.

Find the sum of the squares of the first 9 natural numbers.

1. 185

2. 385

3. 285

4. 485

Q. State whether the statement is true (T) or false (F).
The difference of the squares of two consecutive numbers is their sum.

1. True
2. False