Get Answers to all your Questions

header-bg qa

The expression 7^{2n}+2^{3n-3}*3^{n-1} is divisible by

Option: 1

49


Option: 2

64


Option: 3

25


Option: 4

36


Answers (1)

Principle of Mathematical Induction

Mathematical induction is one of the techniques which can be used to prove a variety of mathematical statements which are formulated in terms of n, where n is a positive integer

-

For n=1,7^2+2^0*3^0=49+1=50

It is divisible by 25

Let P(r) be true for n=r

7^{2r}+2^{3r-3}.3^{r-1}=25k\,\,\,\,......(i)

For n=r+1,

\Rightarrow 49.7^{2r}+2^{3r}.3^{r}=49.7^{2r}+8.2^{3r-3}.3.3^{r-1}

= 49.7^{2r}+24(25k - 7^{2r})  (From (i))

=25\left (7^{2r}+24k \right )

Posted by

Ramraj Saini

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions