JEE Mains · Maths · STD 11 - 5. linear inequalities
Let \(A=\{ x \in R :[ x +3]+[ x +4] \leq 3\}\), \(B=\left\{x \in R : 3^x\left(\sum_{x=1}^{\infty} \frac{3}{10^x}\right)^{x-3} < 3^{-3 x}\right\}\), where \([t]\)denotes greatest integer function. Then,
- A \(A \cap B=\phi\)
- B \(A = B\)
- C \(B \subset C , A \neq B\)
- D \(A \subset B , A \neq B\)
Answer & Solution
Correct Answer
(B) \(A = B\)
Step-by-step Solution
Detailed explanation
\({[x]+3+[x]+4 \leq 3}\) \(2[x] \leq-4\) \({[x] \leq-2 \Rightarrow x \in(-\infty,-1) .}\) \(3^x\left(\frac{3 \cdot \frac{1}{10}}{1-\frac{1}{10}}\right)^{x-3} < 3^{-3 x}\) \(27 < 3^{-3 x}\) \(-3 x > +3\) \(x < -1 \quad \ldots \ldots \ldots \ldots \ldots . .(B)\) \(A=B\)
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