The given limit $ = \mathop {\lim }\limits_{x \to 0} {x^4} \times \mathop {\lim }\limits_{x \to 0} \cos \frac{1}{x}$
$ = 0 \times $ a finite number
(cosine function is a bounded function lying between -1 to 1)
= 0
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096 $ $\therefore 2^n = 4096 =2^{12} $ $\Rightarrow n = 12 $ Greatest coefficient = ${}^{12}{C_6} = 924$