Question 14 Marks
Mr. Roy, a Mathematics teacher explained some key points of unit 1 of class IX to his students. Some are given here.
• There are infinite rational numbers between any two rational numbers.
• Rationalisation of a denominator means to change the irrational denominator to rational form.
• A number is irrational if its decimal form is non-terminating and non-recurring. On the basis of these key points, choose the correct option in the following questions:
(i) What is the reciprocal of $2+\sqrt{3}$ ?
(a) $\sqrt{3}+2$ $\quad$(b) $\frac{1}{\sqrt{3}-2}$$\quad$ (c) $2-\sqrt{3}$ $\quad$(d) $\frac{1}{2}+\frac{1}{\sqrt{3}}$
(ii) Which of the following is irrational?
(a) $\frac{\sqrt{4}}{\sqrt{9}}$$\quad$ (b) $\frac{\sqrt{12}}{\sqrt{3}}$ $\quad$(c) $\sqrt{7}$ $\quad$(d) $\sqrt{81}$
(iii) Which of the following is irrational?
(a) 0.14 $\quad$(b) $0.14 \overline{16}$ $\quad$(c) $0.1 \overline{416}$ $\quad$(d) 0.401400140001......
(iv) Which of the following is value of $(\sqrt{11}+\sqrt{7})(\sqrt{11}-\sqrt{7})$ ?
(a) $\sqrt{11}$$\quad$ (b) 4 $\quad$(c) -4 $\quad$(d) $\sqrt{7}$
• There are infinite rational numbers between any two rational numbers.
• Rationalisation of a denominator means to change the irrational denominator to rational form.
• A number is irrational if its decimal form is non-terminating and non-recurring. On the basis of these key points, choose the correct option in the following questions:
(i) What is the reciprocal of $2+\sqrt{3}$ ?
(a) $\sqrt{3}+2$ $\quad$(b) $\frac{1}{\sqrt{3}-2}$$\quad$ (c) $2-\sqrt{3}$ $\quad$(d) $\frac{1}{2}+\frac{1}{\sqrt{3}}$
(ii) Which of the following is irrational?
(a) $\frac{\sqrt{4}}{\sqrt{9}}$$\quad$ (b) $\frac{\sqrt{12}}{\sqrt{3}}$ $\quad$(c) $\sqrt{7}$ $\quad$(d) $\sqrt{81}$
(iii) Which of the following is irrational?
(a) 0.14 $\quad$(b) $0.14 \overline{16}$ $\quad$(c) $0.1 \overline{416}$ $\quad$(d) 0.401400140001......
(iv) Which of the following is value of $(\sqrt{11}+\sqrt{7})(\sqrt{11}-\sqrt{7})$ ?
(a) $\sqrt{11}$$\quad$ (b) 4 $\quad$(c) -4 $\quad$(d) $\sqrt{7}$
Answer
View full question & answer→(i) c (ii) c (iii) d (iv) b