Q: Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. What is the largest number ?

Average = (0 + 1 + 2 + 3 + 4) ÷ 5

= 10 ÷ 5
= 2

Ans: (a) 2

Q. Find the average of first 20 whole numbers

Options: (a) 10 (b) 9.5 (c) 11 (d) 10.5

Solⁿ

First 20 whole numbers = 0 to 19

Average formula for first n whole numbers:

Average = 0 + (n−1)2

Here n = 20

Ans: (b) 9.5

Q: Find the average of the first 51 whole numbers.

Options: (a) 24  (b) 24.5  (c) 25  (d) 26

Solⁿ

First 51 whole numbers = 0 to 50

Use the formula: Average = 0 + (n - 1)/2

Here n = 51

Average = 50/2 = 25

Ans: (c) 25

Q.(525x533 + 16)1/4 = ? 

Options: (a) 24 (b) 29 (c) 23 (d) 25

Solⁿ

Notice the pattern : (529 - 4)(529 + 4) = 529^2 - 4^2

                  529^2 – 16 + 16 = 529^2

Everything cancels → only 529^2 remains.

 (529^2)1/4 = sqrt{529}

sqrt{529} = 23

Ans: 23

Q. Find the average of first 20 whole numbers

Options: (a) 10 (b) 9.5 (c) 11 (d) 10.5

Solⁿ

First 20 whole numbers = 0 to 19

Average formula for first n whole numbers:

Average = 0 + (n−1)2

Here n = 20

Ans: (b) 9.5

Q: Find the average of the first 51 whole numbers.

Options: (a) 24  (b) 24.5  (c) 25  (d) 26

Solⁿ

First 51 whole numbers = 0 to 50

Use the formula: Average = 0 + (n - 1)/2

Here n = 51

Average = 50/2 = 25

Ans: (c) 25

Q. (525x533 + 16)1/4 = ? 

Options: (a) 24 (b) 29 (c) 23 (d) 25

Solⁿ

Notice the pattern : (529 - 4)(529 + 4)

                                    = 529^2 - 4^2

                                    = 529^2 -16 + 16

                                 = 529^2

Everything cancels → only 529^2 remains.

 (529^2)1/4 = sqrt{529}

sqrt{529} = 23

Ans: 23

Q. (281x293 + 36)1/2 = ?

(a) 287  (b) 297  (c) 283  (d) 285

Solⁿ

 (287 - 6)(287 + 6)

= (287^2 - 6^2 + 36)^1/2

= (287^2)^1/2

= 287

Ans: 287