हिंदी

Write Last Two Digits of the Number 3400. - Mathematics

Advertisements
Advertisements

प्रश्न

Write last two digits of the number 3400.

 

उत्तर

\[3^{400} = \left( 9 \right)^{200} \]
\[ = \left( 10 - 1 \right)^{200} \]
\[ =^{200} C_0 \left( 10 \right)^{200} +^{200} C_1 \left( 10 \right)^{199} \left( - 1 \right)^1 + . . . . . +^{200} C_{198} \left( 10 \right)^2 \left( - 1 \right)^{198} +^{200} C_{199} \left( 10 \right)^1 \left( - 1 \right)^{199} +^{200} C_{200} \left( - 1 \right)^{200} \]
\[ = 100\left[ \left( 10 \right)^{198} +^{200} C_1 \left( 10 \right)^{197} \left( - 1 \right)^1 + . . . . . +^{200} C_{198} \left( - 1 \right)^{198} \right] + 200 \left( 10 \right)^1 \left( - 1 \right)^{199} + \left( - 1 \right)^{200} \]
\[ = 100\left[ \left( 10 \right)^{198} -^{200} C_1 \left( 10 \right)^{197} + . . . . . +^{200} C_{198} - 2\left( 10 \right) \right] + 1\]
\[ = 100(\text{ a natural number } ) + 1\]

Hence, last two digits of the number 3400 is 01.

 
shaalaa.com
Proof of Binomial Therom by Combination
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 18: Binomial Theorem - Exercise 18.3 [पृष्ठ ४५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 18 Binomial Theorem
Exercise 18.3 | Q 14 | पृष्ठ ४५
Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×