# Simplification

$\text{1.&space;}&space;100&space;+&space;50&space;\times&space;2&space;=&space;\,\,&space;?$

A. 300

B. 200

C. 250

D. 100

Ans: B

Explanation:

$\text{According&space;to&space;BODMAS&space;rule&space;here&space;we&space;first&space;apply&space;multiplication.}$

$\text{Given}&space;=&space;100&space;+50&space;\times&space;2$

$=&space;100&space;+&space;100$

$=&space;200$

$\text{2.&space;}&space;5004&space;\div&space;139&space;-&space;6&space;=&space;\,\,&space;?$

A. 24

B. 30

C. 36

D. 42

Ans: B

Explanation:

$\text{According&space;to&space;BODMAS&space;rule&space;here&space;we&space;first&space;apply&space;division.}$

$\text{Given}&space;=&space;5004&space;\div&space;139&space;-&space;6$

$=&space;36&space;-&space;6$

$=&space;30$

$\text{3.&space;The&space;value&space;of&space;}&space;1001&space;\div&space;\text{11&space;of&space;13&space;is}$

A. 7

B. 91

C. 143

D. 169

Ans: A

Explanation:

$\text{According&space;to&space;BODMAS&space;rule&space;here&space;we&space;first&space;apply&space;of.}$

$\text{Given}&space;=&space;1001&space;\div&space;\text{11&space;of&space;13}$

$=&space;1001&space;\div&space;143$

$=&space;7$

$\text{4.&space;}&space;2-\left&space;[&space;2-\left&space;\{&space;2&space;-2&space;\left&space;(&space;2&space;+&space;2&space;\right&space;)&space;\right&space;\}&space;\right&space;]&space;=&space;\,&space;?$

A. 0

B. -6

C. -8

D. 4

Ans: B

Explanation:

$\text{Given}&space;=&space;2-\left&space;[&space;2-\left&space;\{&space;2-2\left&space;(&space;2+2&space;\right&space;)&space;\right&space;\}&space;\right&space;]$

$=2-\left&space;[&space;2-\left&space;\{&space;2-2\left&space;(&space;4&space;\right&space;)&space;\right&space;\}&space;\right&space;]$

$=2-\left&space;[&space;2-\left&space;\{&space;2-8&space;\right&space;\}&space;\right&space;]$

$=&space;2-\left&space;[&space;2-\left&space;\{&space;-6&space;\right&space;\}&space;\right&space;]$

$=&space;2&space;-&space;\left&space;[&space;8&space;\right&space;]$

$=&space;-6$

$\text{5.&space;}&space;\frac{4+4&space;\times&space;18&space;-&space;6&space;-8}{123&space;\times&space;6&space;-&space;146&space;\times&space;5}&space;=&space;\,&space;?$

A. 7.75

B. 6.65

C. 8.95

D. 9.20

Ans: A

Explanation:

$\text{Given}&space;=&space;\frac{4&space;+4&space;\times&space;18&space;-&space;6&space;-&space;8}{123&space;\times&space;6&space;-&space;146&space;\times&space;5}$

$=&space;\frac{4&space;+&space;72&space;-&space;6&space;-&space;8}{738&space;-&space;730}$

$=&space;\frac{76&space;-&space;14}{8}$

$=&space;\frac{62}{8}&space;=&space;7.75$

$\text{6.&space;The&space;value&space;of}&space;\,\,&space;\frac{\left&space;(&space;6&space;+&space;6&space;+&space;6&space;+&space;6&space;\right&space;)&space;\div&space;6}{4&space;+&space;4&space;+&space;4&space;+&space;4&space;\div&space;4}&space;\,&space;\,&space;\text{is&space;equal&space;to}$

$\text{A.&space;1}$

$\text{B.&space;0}$

$\text{C.&space;}&space;\frac{3}{2}$

$\text{D.&space;}&space;\frac{4}{13}$

Ans: D

Explanation:

$\text{Given}&space;=&space;\frac{\left&space;(&space;6&space;+&space;6&space;+&space;6&space;+&space;6&space;\right&space;)&space;\div&space;6}{4+4+4+4&space;\div&space;4}$

$=&space;\frac{\left&space;(&space;24&space;\right&space;)&space;\div&space;6}{4&space;+&space;4&space;+&space;4&space;+&space;1}$

$=&space;\frac{4}{13}$

$\text{7.&space;Simplify}&space;\,\,&space;\frac{1}{\left&space;(&space;2\frac{1}{3}&space;\right&space;)}&space;+&space;\frac{1}{\left&space;(&space;1\frac{3}{4}&space;\right&space;)}$

$\text{A.&space;1}$

$\text{B.&space;0}$

$\text{C.&space;}&space;2\frac{2}{3}$

$\text{D.&space;}&space;1\frac{1}{4}$

Ans: A

Explanation:

$\text{Given}&space;=&space;\frac{1}{\left&space;(&space;2\frac{1}{3}&space;\right&space;)}&space;+&space;\frac{1}{\left&space;(&space;1\frac{3}{4}&space;\right&space;)}$

$=&space;\frac{1}{\frac{7}{3}}&space;+&space;\frac{1}{\frac{7}{4}}$

$=&space;\frac{3}{7}&space;+&space;\frac{4}{7}$

$=&space;\frac{7}{7}$

$=&space;1$

$\text{8.&space;}&space;\,\,&space;\frac{0.01&space;\times&space;0.01&space;\times&space;0.01&space;+&space;0.02&space;\times&space;0.02&space;\times&space;0.02}{0.01&space;\times&space;0.01&space;-&space;0.01&space;\times&space;0.02&space;+&space;0.02&space;\times&space;0.02}&space;=&space;\,&space;?$

A. 0.002

B. 0.009

C. 0.03

D. 0.12

Ans: C

Explanation:

$\text{Given&space;}&space;=&space;\frac{0.01&space;\times&space;0.01&space;\times&space;0.01&space;+&space;0.02&space;\times&space;0.02&space;\times&space;0.02}{0.01&space;\times&space;0.01&space;-&space;0.01&space;\times&space;0.02&space;+&space;0.02&space;\times&space;0.02}$

$=&space;\frac{\left&space;(&space;0.01&space;\right&space;)^3&space;+&space;\left&space;(&space;0.02&space;\right&space;)^3}{\left&space;(&space;0.01&space;\right&space;)^2&space;-&space;0.01&space;\times&space;0.02&space;+&space;\left&space;(&space;0.02&space;\right&space;)^2}&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\frac{a^3&space;+&space;b^3}{b^2&space;-ab&space;+&space;b^2}&space;=&space;a&space;+&space;b&space;\right&space;]$

$=&space;0.01&space;+&space;0.02$

$=&space;0.03$

$\text{9.&space;}&space;784&space;+&space;\left&space;(&space;7&space;+&space;3&space;\right&space;)^2&space;=&space;\,&space;?$

A. 128

B. 1600

C. 786

D. 884

Ans: D

Explanation:

$\text{Given}&space;=&space;784&space;+&space;\left&space;(&space;7&space;+&space;3&space;\right&space;)^2$

$=&space;784&space;+&space;\left&space;(&space;10&space;\right&space;)^2$

$=&space;784&space;+&space;100$

$=&space;884$

$\text{10.&space;}&space;\frac{3}{4}\left&space;(&space;1&space;+&space;\frac{1}{3}\right&space;)&space;\left&space;(&space;1&space;+&space;\frac{2}{3}&space;\right&space;)\left&space;(&space;1&space;-&space;\frac{2}{5}&space;\right&space;)&space;\left&space;(&space;1&space;+&space;\frac{6}{7}&space;\right&space;)&space;\left&space;(&space;1&space;-&space;\frac{12}{13}&space;\right&space;)&space;=&space;\,\,&space;?$

$\text{A.&space;}\frac{1}{5}$

$\text{B.&space;}&space;\frac{1}{6}$

$\text{C.}&space;\,&space;\frac{1}{8}$

$\text{D.&space;}&space;\frac{1}{7}$

Ans : D

Explanation :

$\text{Given}&space;=&space;\frac{3}{4}\left&space;(&space;1&space;+&space;\frac{1}{3}\right&space;)&space;\left&space;(&space;1&space;+&space;\frac{2}{3}&space;\right&space;)\left&space;(&space;1&space;-&space;\frac{2}{5}&space;\right&space;)&space;\left&space;(&space;1&space;+&space;\frac{6}{7}&space;\right&space;)&space;\left&space;(&space;1&space;-&space;\frac{12}{13}&space;\right&space;)$

$=&space;\frac{3}{4}\left&space;(&space;\frac{4}{3}&space;\right&space;)\left&space;(&space;\frac{5}{3}&space;\right&space;)\left&space;(&space;\frac{3}{5}&space;\right&space;)\left&space;(&space;\frac{13}{7}&space;\right&space;)\left&space;(&space;\frac{1}{13}&space;\right&space;)$

$=&space;\frac{1}{7}$