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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2016 · Mathematics · Basics of Mathematics

If A=\ x ∈ ℝ: x^2+6 x-7 0\ , then which of the following is/are...

If A={x∈R:x2+6x−7<0}A=\left\{x \in \mathbb{R}: x^2+6 x-7 < 0\right\} and B={x∈R:x2+9x+14>0}B=\left\{x \in \mathbb{R}: x^2+9 x+14 > 0\right\}, then which of the following is/are correct? 1. A∩B={X∈R:−2<x<1}2.A \cap B=\{X \in \mathbb{R}:-2 < x < 1\} 2.A \backslash B=\{x \in R\mathbb{R}:-7 < x < -2\}Selectthecorrectanswerusingthecodegivenbelow:Select the correct answer using the code given below:

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

We have : x2+6x−7<0x2+9x+14>0⇒(x−1)(x+7)<0⇒(x+2)(x+7)>0⇒x∈(−7,1)⇒x∈(−∞,−7)∪(−2,∞)\begin{array}{lll} x^2+6 x-7 < 0 & & & x^2+9 x+14 > 0 \\ \Rightarrow(x-1)(x+7) < 0 & & & \Rightarrow(x+2)(x+7) > 0 \\ \Rightarrow x \in(-7,1) & & & \Rightarrow \mathrm{x} \in(-\infty,-7) \cup(-2, \infty) \end{array}\therefore A \cap B=\{x \in \mathbb{R}:-2 < x < 1\} \rightarrowItistrue.It is true.A \backslash B=A-B=\{x \in \mathbb{R}:-7 < x < -2\} \rightarrow$ It is also true.
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