PYQ Vault
EbooksTutor

Values for which a limit with greatest integer terms exists

This type of question, asked 2 times: 27 Jun 2022, 24 Jan 2023. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    27 Jun 2022

    65
    Let aa be an integer such that lim⁡x→718−[1−x][x−3a]\lim_{x\rightarrow 7} \frac{18 - \lbrack 1 -x\rbrack}{\lbrack x- 3a\rbrack} exists, where [t]\lbrack t\rbrack is greatest integer ≤t\leq t. Then a is equal to:

    Tap an option to check your answer.

  2. Question 2

    24 Jan 2023

    167
    The set of all values of a for which lim⁡x→a([x−5]−[2x+2])=0\lim_{x \rightarrow a} (\lbrack x - 5\rbrack - \lbrack 2x + 2\rbrack) = 0, where [α]\lbrack\alpha\rbrack denotes the greatest integer less than or equal to α\alpha is equal to

    Tap an option to check your answer.