Standard Derivative

Q. Let $a$ be an integer such that $\underset{x\to 7}{lim}\frac{18-[1-x]}{[x-3a]}$ exists, where $\left[t\right]$ is greatest integer $\le t$. Then $a$ is equal to :

1. $6$
2. $-6$
3. $-2$
4. $2$

Q. Match the given limits to their numerical value.

1. 3
2. 12
3. 4
4. \N

Q.

$\underset{x\to 0}{lim}\frac{logcosx}{x}=$

Q. Evaluate the given limit: $\underset{x\to 0}{lim}\frac{\cos 2x-1}{\cos x-1}$