Question
If $17^200$ is divided by 18, the remainder is—
Answer: Option D
Answer: (d)$(17)^200$ = $(18 –1)^200$ We know that $ (x + a)^n$ =$x^n + nx^(n–1).a + {n(n - 1)}/{1 × 2}x^{n - 2}a^2 +{n(n - 1)(n - 2)}/{1 × 2 × 3}x^{n - 3}a^3+…+a^n$We see that all the terms on the R.H.S. except $a^n$ has x as one of its factor and hence are divisible by x. So,$(x +a)^n$ is divisible by x or not will be decided by $a^n$ . Let x = 18, a = – 1 and n = 200 ∴ $(18 –1)^200$ is divisible by 18 or not will depend on $(–1)^200$ as all other terms in its expansion will be divisible by 18 because each of them will have 18 as one of their factors. $(–1)^200$ = 1 (Since 200 is even) 1 is not divisible by 18 and is also less than 18. ∴1 is the remainder
Was this answer helpful ?
Answer: (d)$(17)^200$ = $(18 –1)^200$ We know that $ (x + a)^n$ =$x^n + nx^(n–1).a + {n(n - 1)}/{1 × 2}x^{n - 2}a^2 +{n(n - 1)(n - 2)}/{1 × 2 × 3}x^{n - 3}a^3+…+a^n$We see that all the terms on the R.H.S. except $a^n$ has x as one of its factor and hence are divisible by x. So,$(x +a)^n$ is divisible by x or not will be decided by $a^n$ . Let x = 18, a = – 1 and n = 200 ∴ $(18 –1)^200$ is divisible by 18 or not will depend on $(–1)^200$ as all other terms in its expansion will be divisible by 18 because each of them will have 18 as one of their factors. $(–1)^200$ = 1 (Since 200 is even) 1 is not divisible by 18 and is also less than 18. ∴1 is the remainder
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution