SOLUTION

1.       (place value of 6 ) -  (face value of 6)

                     = (6000 – 6) = 5994.

2.       (local value of 7) – (face value of 7)

                       = (70000 – 7) = 69993.

3.       Required difference = (700000 – 70) = 699930.

4.       Unit digit in the given product = unit digit in (4x 8 x 7 x 3) = 2

5.       Unit digit in 7¹⁰⁵ = unit digit in [(7⁴)²⁶ x 7]

                                    But, unit digit in (7⁴)²⁶ = 1

                                    Unit digit in 7¹⁰⁵ = (1 x 7) = 7

6.       Unit digit in 3⁴ = 1 unit digit in (3⁴)¹⁶ = 1

                          Unit digit in 3⁶⁵ = unit digit in [(3⁴)¹⁶ x 3] = (1x3) = 3

                          Unit digit in 6⁶⁹ = 6

                          Unit digit in 7⁴ = 1 unit digit in (7⁴)¹⁷ is 1.

                          Unit digit in 7⁷¹ =unit digit in [(7⁴)¹⁷ x 7³] = (1x3) =3

                          Required digit = unit digit in (3 x 6 x 3) = 4.

7.       Unit digit n 7⁹⁵ = unit digit in [(7⁴)²³ x7³] = (1x3)=3

                          Unit digit in 3⁵⁸= unit digit in [(3⁴)¹⁴ x 3²] = (1 x 9)=9

                           Unit digit in (7⁹⁵ - 3⁵⁸) = (13 – 9) = 4.

8.       Unit digit in (4137)⁷⁵⁴ = unit digit in  {4137)⁴}¹⁸⁸ x (4137)²   =(1x9) =9

9.        Unit digit in(6374)¹⁷⁹³ = unit digit in (4)¹⁷⁹³

                       =unit digit in [(4²)896x 4]

                        = unit digit in( 6 x  4 ) = 4.

                                       Unit digit in (625)³¹⁷ = unit digit in (5)³¹⁷ = 5.

                                      Unit digit in (341)⁴⁹¹ = unit digit (1)⁴⁹¹ == 1

                                        Required digit = unit digit in (4 x 5 x 1) =0.

10.   Let 7589 –X = 3434.

                            Then, X = 7589 – 3434

               = 4155                              7589

                                                                      -3434

                                                                       4155