The last two digits of the number (23)14 are

Question

The last two digits of the number (23)14 are (A) 01 (B) 03 (C) 09 (D) none of these

Tardigrade Admin · Accepted Answer

(23)14=(529)7=(530-1)7 = 7 C 0(530)7- 7 C 1(530)6+ ldots- 7 C 5(530)2+ 7 C 6 530-1 = 7 C 0(530)7- 7 C 1(530)6+ ldots .+3710-1 =100 m +3709 Therefore, last two digits are 09 .

Q. The last two digits of the number $(23)^{14}$ are

01

03

09

none of these

$(23)^{14} = (529)^{7} = (530 - 1)^{7}$
$=^{7} C_{0} (530)^{7} -^{7} C_{1} (530)^{6} + \dots -^{7} C_{5} (530)^{2} +^{7} C_{6} 530 - 1$
$=^{7} C_{0} (530)^{7} -^{7} C_{1} (530)^{6} + \dots . + 3710 - 1$
$= 100 m + 3709$
Therefore, last two digits are $09$ .

Q. The last two digits of the number (23)14 are

01

03

09

none of these

(23)14=(529)7=(530−1)7 =7C0​(530)7−7C1​(530)6+…−7C5​(530)2+7C6​530−1 =7C0​(530)7−7C1​(530)6+….+3710−1 =100m+3709 Therefore, last two digits are 09.

Q. The last two digits of the number $(23)^{14}$ are

$(23)^{14} = (529)^{7} = (530 - 1)^{7}$
$=^{7} C_{0} (530)^{7} -^{7} C_{1} (530)^{6} + \dots -^{7} C_{5} (530)^{2} +^{7} C_{6} 530 - 1$
$=^{7} C_{0} (530)^{7} -^{7} C_{1} (530)^{6} + \dots . + 3710 - 1$
$= 100 m + 3709$
Therefore, last two digits are $09$ .