Tag: limits and continuity of a function

Questions Related to limits and continuity of a function

If $|z-1|+ |z+3| \le 8$, then the range of values of $|z-4|$ is

  1. $(0, 7)$

  2. $(1,8)$

  3. $[1,9]$

  4. $[2,5]$


Correct Option: C

If all the roots of $z^3 +az^2 +bz+c=0$ are of unit modulus, then

  1. $|a| \le 3$

  2. $|b| > 3$

  3. $|c| < 3$

  4. $None\ of\ these$


Correct Option: A

The solution set of the equation $(x+1)^2+[x-1]^2=(x-1)^2+[x+1]^2$ where $[x]$ and $(x)$ are the greatest integer and nearest integer to $x$, isĀ 

  1. $ x\in R$

  2. $x\in N$

  3. $x\in I$

  4. $x\in Q$


Correct Option: C