Mahabir Singh Solutions for Chapter: Number Systems, Exercise 1: MATHEMATICAL REASONING

The greater number among $\sqrt{17}-\sqrt{12}$ and $\sqrt{11}-\sqrt{6}$ is _____

The value of $x,$ if $5^{x-3}.3^{2x-8}=225$ is ______

If $x=2-\sqrt{3},$ then the value of $x^2+\frac{1}{x^2}$ and $x^2-\frac{1}{x^2}$ respectively are ________

Which of the following statements is incorrect?

If $\frac{\sqrt{3}-1}{\sqrt{3}+1}=\left(a-b\sqrt{3}\right),$ then find values of $a$ and $b$

The number $x=1.242424\dots \dots .$ can be expressed in the form $x=\frac{p}{q}$ , where $p$ and $q$ are positive integers having no common factors. Then $p+q$equals ____________

If $x$ and $y$ are positive real numbers, then which of the following is Correct?

If $x$ $=1-\sqrt{2,}$ then find the value of ${\left(x-\frac{1}{x}\right)}^2$