JEE PYQ: Functions Question 15
Question 15 - 2020 (04 Sep Shift 1)
Let $[t]$ denote the greatest integer $\le t$. Then the equation in $x$, $[x]^2 + 2[x+2] - 7 = 0$ has:
(1) exactly two solutions
(2) exactly four integral solutions
(3) no integral solution
(4) infinitely many solutions
Type: MCQ
Show Answer
Answer: (4) infinitely many solutions
Solution
$[x]^2 + 2[x] - 3 = 0$
$([x] + 3)([x] - 1) = 0 \Rightarrow [x] = 1$ or $-3$
$x \in [-3, -2) \cup [1, 2)$: infinitely many solutions.
BETA
