Q77 / 180 · KCET 2023 · Mathematics

Which of the following is an empty set?

  • Correct answer
    A
    $\left\{x: x^2+1=0, x \in R\right\}$
  • B
    $\left\{x: x^2-9=0, x \in R\right\}$
  • C
    $\left\{x: x^2=x+2 x \in R\right\}$
  • D
    $\left\{x: x^2-1=0, x \in R\right\}$

Solution

Here, $x^2+1=0$ $\begin{array}{ll}\Rightarrow & x^2=-1 \\ \Rightarrow & \dot{x}= \pm i\end{array}$ It $x$ is an imaginary number. Hence, $\left\{x: x\right.$ is a real number and $\left.x^2+1=0\right\}$ is an empty set

Hence, the correct answer is option: 'A'.

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