Simplification

\text{1. } 100 + 50 \times 2 = \,\, ?

 

A. 300

B. 200

C. 250

D. 100

Ans: B

Explanation:

\text{According to BODMAS rule here we first apply multiplication.}

 

\text{Given} = 100 +50 \times 2

 

= 100 + 100

 

= 200

 

 

\text{2. } 5004 \div 139 - 6 = \,\, ?

 

A. 24

B. 30

C. 36

D. 42

Ans: B

Explanation:

\text{According to BODMAS rule here we first apply division.}

 

\text{Given} = 5004 \div 139 - 6

 

= 36 - 6

 

= 30

 

 

\text{3. The value of } 1001 \div \text{11 of 13 is}

 

A. 7

B. 91

C. 143

D. 169

Ans: A

Explanation:

\text{According to BODMAS rule here we first apply of.}

 

\text{Given} = 1001 \div \text{11 of 13}

 

= 1001 \div 143

 

= 7

 

 

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

 

A. 0

B. -6

C. -8

D. 4

Ans: B

Explanation:

\text{Given} = 2-\left [ 2-\left \{ 2-2\left ( 2+2 \right ) \right \} \right ]

 

=2-\left [ 2-\left \{ 2-2\left ( 4 \right ) \right \} \right ]

 

=2-\left [ 2-\left \{ 2-8 \right \} \right ]

 

= 2-\left [ 2-\left \{ -6 \right \} \right ]

 

= 2 - \left [ 8 \right ]

 

= -6

 

 

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

 

 

A. 7.75

B. 6.65

C. 8.95

D. 9.20

Ans: A

Explanation:

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

 

 

= \frac{4 + 72 - 6 - 8}{738 - 730}

 

 

= \frac{76 - 14}{8}

 

= \frac{62}{8} = 7.75

 

 

 

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

 

 

\text{A. 1}

 

\text{B. 0}

 

\text{C. } \frac{3}{2}

 

\text{D. } \frac{4}{13}

 

 

Ans: D

Explanation:

\text{Given} = \frac{\left ( 6 + 6 + 6 + 6 \right ) \div 6}{4+4+4+4 \div 4}

 

 

= \frac{\left ( 24 \right ) \div 6}{4 + 4 + 4 + 1}

 

 

= \frac{4}{13}

 

 

 

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

 

 

\text{A. 1}

 

\text{B. 0}

 

\text{C. } 2\frac{2}{3}

 

\text{D. } 1\frac{1}{4}

 

 

Ans: A

Explanation:

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

 

 

= \frac{1}{\frac{7}{3}} + \frac{1}{\frac{7}{4}}

 

 

= \frac{3}{7} + \frac{4}{7}

 

 

= \frac{7}{7}

 

 

= 1

 

 

\text{8. } \,\, \frac{0.01 \times 0.01 \times 0.01 + 0.02 \times 0.02 \times 0.02}{0.01 \times 0.01 - 0.01 \times 0.02 + 0.02 \times 0.02} = \, ?

 

 

A. 0.002

B. 0.009

C. 0.03

D. 0.12

Ans: C

Explanation:

\text{Given } = \frac{0.01 \times 0.01 \times 0.01 + 0.02 \times 0.02 \times 0.02}{0.01 \times 0.01 - 0.01 \times 0.02 + 0.02 \times 0.02}

 

 

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

 

 

= 0.01 + 0.02

 

= 0.03

 

 

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

 

A. 128

B. 1600

C. 786

D. 884

Ans: D

Explanation:

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

 

= 784 + \left ( 10 \right )^2

 

= 784 + 100

 

= 884

 

 

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

 

 

\text{A. }\frac{1}{5}

 

\text{B. } \frac{1}{6}

 

\text{C.} \, \frac{1}{8}

 

\text{D. } \frac{1}{7}

 

 

Ans : D

Explanation :

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

 

 

= \frac{3}{4}\left ( \frac{4}{3} \right )\left ( \frac{5}{3} \right )\left ( \frac{3}{5} \right )\left ( \frac{13}{7} \right )\left ( \frac{1}{13} \right )

 

 

= \frac{1}{7}