RD Sharma (2020, 2021) - GeniusJnr

Classify the following numbers as rational or irrational:

(i) (ii) (iii)

(iv) (v) 2π

Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Show that the following numbers are irrational.
(i) $\frac{1}{\sqrt{2}}$
(ii) $7\sqrt{5}$
(iii) $6+\sqrt{2}$
(iv) $3-\sqrt{5}$

Complete the following sentences:
(i) Every point on the number line corresponds to a .... number which many be either ... or ...
(ii) The decimal form of an irrational number is neither ... nor ...
(iii) The decimal representation of a rational number is either ... or ...
(iv) Every real number is either ... number or ... number.

How many milligrams make on kilogram?

Multiply:
(i) $\frac{7}{11} \mathrm{by} \frac{5}{4}$
(ii) $\frac{5}{7} \mathrm{by} \frac{-3}{4}$
(iii) $\frac{-2}{9} \mathrm{by} \frac{5}{11}$
(iv) $\frac{-3}{17} \mathrm{by} \frac{-5}{-4}$
(v) $\frac{9}{-7} \mathrm{by} \frac{36}{-11}$
(vi) $\frac{-11}{13} \mathrm{by} \frac{-21}{7}$
(vii) $-\frac{3}{5} \mathrm{by} -\frac{4}{7}$
(viii) $-\frac{15}{11} \mathrm{by} 7$

If A and B are two sets such that $A\subset B$, then find:
(i) $A\cap B$
(ii) $A\cup B$

Find:

(i) (ii) (iii)

If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩Y).

Round off each of the following numbers to nearest tens:

(i) 84
(ii) 98
(iii) 984
(iv) 808
(v) 998
(vi) 12,096
(vii) 10,908
(viii) 28,925

Verify the property: x × y = y × x by taking:
(i) $x=-\frac{1}{3}, y=\frac{2}{7}$
(ii) $x=\frac{-3}{5}, y=\frac{-11}{13}$
(iii) $x=2, y=\frac{7}{-8}$
(iv) $x=0, y=\frac{-15}{8}$

Find the smallest set A such that $A\cup \left\{1, 2\right\}=\left\{1, 2, 3, 5, 9\right\}$.