estion-images/batch-001/794524db9d77.webp" data-orsrc="https://uploads-pracbee-ramanuj.s3.ap-south-1.amazonaws.com/pyq-question-images/batch-001/794524db9d77.webp" loading="lazy" style="max-width:100%;height:auto;display:block;margin:0 auto;max-height:40vh;vertical-align:baseline" alt="JEE Main 2024 (Online) 30th January Evening Shift Mathematics - Functions Question 49 English Explanation">

$$(-\infty,-2) \cup\left[\frac{-1}{3}, \infty\right)$$ ..... (1)

$$(-2,3]$$ ..... (2)

$$\left[\frac{-1}{3}, 3\right]$$ ..... (3) $$\quad (1) \cap(2) \cap(3)$$

$$\begin{aligned} & \left(\frac{3}{4}, 3\right] \\ & \alpha=\frac{3}{4} \beta=3 \\ & 5 \beta-4 \alpha=15-3=12 \end{aligned}$$

19:T404,

$$\begin{aligned} & \frac{2 x+3}{4 x^2+x-3}>0 \text { और } -1 \leq \frac{2 x-1}{x+2} \leq 1 \\ & \frac{2 x+3}{(4 x-3)(x+1)}>0 \quad \frac{3 x+1}{x+2} \geq 0 \& \frac{x-3}{x+2} \leq 0 \end{aligned}$$

JEE Main 2024 (Online) 30th January Evening Shift Mathematics - Functions Question 49 Hindi Explanation

$$(-\infty,-2) \cup\left[\frac{-1}{3}, \infty\right)$$ ..... (1)

$$(-2,3]$$ ..... (2)

$$\left[\frac{-1}{3}, 3\right]$$ ..... (3) $$\quad (1) \cap(2) \cap(3)$$

$$\begin{aligned} & \left(\frac{3}{4}, 3\right] \\ & \alpha=\frac{3}{4} \beta=3 \\ & 5 \beta-4 \alpha=15-3=12 \end{aligned}$$

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