2021 · Q7
If x is a negative real number, then which of the following are not correct ? 1. There is some natural number k such that kx > 0. 2. x² + x > 0 always. 3. 2x < x < −x. 4. x² is always a rational number. Select the correct answer using the code given below:
Elementary MathematicsNumber System
- A1, 2 and 3
- B1, 2 and 4
- C1, 3 and 4
- D2, 3 and 4
Explanation
Take x < 0. Statement 1 is false: kx < 0 for every natural k, so no such k exists. Statement 2 is false: e.g. x = −1/2 gives x² + x = −1/4 < 0. Statement 3 is true: for x < 0, 2x < x and x < −x both hold. Statement 4 is false: e.g. x = −π gives x² = π², which is irrational. The statements that are not correct are 1, 2 and 4, i.e. option (b).