CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

$$49^n + 16n - 1$$ is divisible by


A
3
loader
B
29
loader
C
19
loader
D
64
loader

Solution

The correct option is B $$64$$
Now, $$49^n + 16n-1 = (1 + 48)^n + 16n-1$$
$$= 1 + ^nC_1(48) + ^nC_2 (48)^2 +........ + ^nC_n (48)^n + 16n-1$$
$$= (48n + 16n) + ^nC_2(48)^2 + ^nC_3 (48)^3 + .. + ^nC_n (48)^n$$
$$= 64n + 8^2(^nC_2 6^2 + ^nC_3 . 6^3 . 8 + ^nC_4 . 6^4. 8^2+ + ^nC_n .6^n 8^{n-2})$$
Hence, $$49^n + 16n - 1$$ is divisible by $$64$$.

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image