RD Sharma XI (2020, 2021)_Volume 1 - GeniusJnr

Write the expression for each of the following statements using brackets:
(i) Four multiplied by the sum of 13 and 7.
(ii) Eight multiplied by the difference of four from nine.
(iii) Divide the difference of twenty eight and seven by 3.
(iv) The sum of 3 and 7 in multiplied by the difference of twelve and eight.

Estimate the following by rounding off each factor to nearest hundreds:

(i) 730 + 998
(ii) 796 − 314
(iii) 875 − 384

If A and B are two sets such that $n \left(A\cup B\right)=50, n \left(A\right)=28 \mathrm{and} n \left(B\right)=32$, find $n \left(A\cap B\right)$.

Find a rational number between −3 and 1.

For any two sets A and B, prove that : $A\text{'}-B\text{'}=B-A$

Divide:
(i) $1 \mathrm{by} \frac{1}{2}$

(ii) $5 \mathrm{by} \frac{-5}{7}$

(iii) $\frac{-3}{4} \mathrm{by} \frac{9}{-16}$

(iv) $\frac{-7}{8} \mathrm{by} \frac{-21}{16}$

(v) $\frac{7}{-4} \mathrm{by} \frac{63}{64}$

(vi) $0 \mathrm{by} \frac{-7}{5}$

(vii) $\frac{-3}{4} \mathrm{by} -6$

(viii) $\frac{2}{3} \mathrm{by} \frac{-7}{12}$

(ix) $-4 \mathrm{by} \frac{-3}{5}$

(x) $\frac{-3}{13} \mathrm{by} \frac{-4}{65}$

Estimate the following by rounding off each factor to nearest thousands:

(i) 12,904 + 2,888
(ii) 28,292 − 21,496

Simplify each of the following:
(i) 124 − (12 − 2) × 9
(ii) (13 + 7) × (9 − 4) − 18
(iii) 210 − (14 − 4) × (18 + 2) − 10

If P and Q are two sets such that P has 40 elements, $P\cup Q$ has 60 elements and $P\cap Q$ has 10 elements, how many elements does Q have?

 Find any five rational numbers less than 2.

For any two sets A and B, prove the following:
(i) $A\cap \left(A\text{'}\cup B\right)=A\cap B$
(ii) $A-\left(A-B\right)=A\cap B$
(iii) $A\cap \left(A\cup B\right)\text{'}=\varphi$
(iv) $A-B=A \Delta \left(A\cap B\right)$.

Find the value and express as a rational number in standard form:
(i) $\frac{2}{5}÷\frac{26}{15}$

(ii) $\frac{10}{3}÷\frac{-35}{12}$

(iii) $-6÷\left(\frac{-8}{17}\right)$

(iv) $\frac{-40}{99}÷(-20)$

(v) $\frac{-22}{27}÷\frac{-110}{18}$

(vi) $\frac{-36}{125}÷\frac{-3}{75}$