Practice MCQ Questions and Answer on Simplification

91.

$$\sqrt {\frac{{0.25}}{{0.0009}}} \times \sqrt {\frac{{0.09}}{{0.36}}} $$     is equal to ?

• (A) $$\frac{5}{6}$$
• (B) $${\text{7}}\frac{1}{6}$$
• (C) $${\text{7}}\frac{1}{3}$$
• (D) $${\text{8}}\frac{1}{3}$$

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \sqrt {\frac{{0.25}}{{0.0009}}} \times \sqrt {\frac{{0.09}}{{0.36}}\,\,} \cr & \Rightarrow \sqrt {\frac{{25}}{9} \times 100} \times \sqrt {\frac{9}{{36}}\,\,} \cr & \Rightarrow \frac{{5 \times 10}}{3} \times \frac{3}{6} \cr & \Rightarrow \frac{{25}}{3} \cr & \Rightarrow 8\frac{1}{3} \cr} $$

92.

(71 × 29 + 27 × 15 + 8 × 4) equals = ?

• (A) 3450
• (B) 3458
• (C) 2496
• (D) None of these

Show Answer

 71 × 29 + 27 × 15 + 8 × 4 = 2059 + 405 +32 = 2496

93.

A students was asked to find the value of $$9\frac{4}{9} \div 11\frac{1}{3}{\text{ of }}\frac{1}{6} + \left( {1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}} \right) \times 2\frac{1}{6}{\text{ of }}\frac{2}{3} \div \frac{4}{3}{\text{ of }}\frac{2}{3}.$$           His answer was $$19\frac{1}{4}.$$  What is the difference between his answer and the correct answer?

• (A) $$7\frac{1}{2}$$
• (B) $$6\frac{1}{3}$$
• (C) $$7\frac{3}{4}$$
• (D) $$6\frac{2}{3}$$

Show Answer

 $$\eqalign{ & 9\frac{4}{9} \div 11\frac{1}{3}{\text{ of }}\frac{1}{6} + \left( {1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}} \right) \times 2\frac{1}{6}{\text{ of }}\frac{2}{3} \div \frac{4}{3}{\text{ of }}\frac{2}{3} \cr & = \frac{{85}}{9} \div \frac{{34}}{3}{\text{ of }}\frac{1}{6} + \left( {\frac{4}{3} \times \frac{9}{5} \div \frac{3}{5}} \right) \times \frac{{13}}{6}{\text{ of }}\frac{2}{3} \div \frac{4}{3}{\text{ of }}\frac{2}{3} \cr & = \frac{{85}}{9} \times \frac{{18}}{{34}} + \left( 4 \right) \times \frac{{13}}{9} \times \frac{9}{8} \cr & = 5 + \frac{{13}}{2} \cr & = \frac{{23}}{2} \cr & {\text{Difference of answer}} = \frac{{77}}{4} - \frac{{46}}{4} \cr & = \frac{{31}}{4} \cr & = 7\frac{3}{4} \cr} $$

94.

The value of $$\frac{8}{9}{\text{ of}}\left( {5\frac{1}{4} \div 2\frac{1}{3}{\text{ of }}4} \right) \div \left( {8 \div \frac{2}{3}{\text{ of }}\frac{4}{5}} \right){\text{of}}\left( {8 \times \frac{2}{3} \div \frac{4}{5}} \right){\text{is:}}$$

• (A) $${\text{1}}\frac{1}{8}$$
• (B) $$\frac{4}{{15}}$$
• (C) $$\frac{1}{{200}}$$
• (D) $$\frac{1}{{100}}$$

Show Answer

 $$\eqalign{ & \frac{8}{9}{\text{ of}}\left( {5\frac{1}{4} \div 2\frac{1}{3}{\text{ of }}4} \right) \div \left( {8 \div \frac{2}{3}{\text{ of }}\frac{4}{5}} \right){\text{of}}\left( {8 \times \frac{2}{3} \div \frac{4}{5}} \right) \cr & = \frac{8}{9}{\text{ of}}\left( {\frac{{21}}{4} \div \frac{7}{3} \times 4} \right) \div \left( {8 \div \frac{8}{{15}}} \right){\text{of}}\left( {8 \times \frac{2}{3} \times \frac{5}{4}} \right) \cr & = \frac{8}{9}{\text{ of}}\left( {\frac{{21}}{4} \times \frac{3}{{28}}} \right) \div \left( {8 \times \frac{{15}}{8}} \right){\text{of}}\left( {\frac{{20}}{3}} \right) \cr & = \left( {\frac{8}{9} \times \frac{9}{{16}}} \right) \div 100 \cr & = \frac{1}{{200}} \cr} $$

95.

The simplified value of $$\frac{{\sqrt {32} + \sqrt {48} }}{{\sqrt 8 + \sqrt {12} }}{\text{ is = ?}}$$

• (A) 3
• (B) 2
• (C) 6
• (D) 4

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \frac{{\sqrt {32} + \sqrt {48} }}{{\sqrt 8 + \sqrt {12} }} \cr & = \frac{{\sqrt {4 \times 4 \times 2} + \sqrt {4 \times 4 \times 3} }}{{\sqrt {2 \times 2 \times 2} + \sqrt {2 \times 2 \times 3} }} \cr & = \frac{{4\sqrt 2 + 4\sqrt 3 }}{{2\sqrt 2 + 2\sqrt 3 }} \cr & = \frac{{4\left( {\sqrt 2 + \sqrt 3 } \right)}}{{2\left( {\sqrt 2 + \sqrt 3 } \right)}} \cr & = \frac{4}{2} \cr & = 2 \cr} $$

96.

If $$\frac{4}{5}$$ of an estate be worth Rs. 16800, then the value of $$\frac{3}{7}$$ of the estate is = ?

• (A) Rs. 9000
• (B) Rs. 21000
• (C) Rs. 72000
• (D) Rs. 90000

Show Answer

 Let the value of the estate be Rs. x $$\eqalign{ & {\text{Then}}\frac{4}{5}{\text{ of }}x = 16800 \cr & \Leftrightarrow x = \left( {\frac{{16800 \times 5}}{4}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 21000 \cr & \Leftrightarrow \frac{3}{7}x = \left( {\frac{3}{7} \times 21000} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 9000 }} \cr} $$

97.

$$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$            is equal to = ?

• (A) 24
• (B) 32
• (C) 44
• (D) 100

Show Answer

 $$\eqalign{ & {\text{Given experssion ,}} \cr & \frac{{{a^3} + {b^3} + {c^3} - 3abc}}{{{a^2} + {b^2} + {c^2} - ab - bc - ca}} \cr & \left( {Let,\,38 = a,\,34 = b,\,28 = c} \right) \cr & = a + b + c \cr & = 38 + 34 + 28 \cr & = 100 \cr} $$

98.

The simplification of $$\left( {\frac{{75983 \times 75983 - 45983 \times 45983}}{{30000}}} \right)$$       yields the result = ?

• (A) 121796
• (B) 121866
• (C) 121956
• (D) 121966

Show Answer

 $$\eqalign{ & {\text{Given expression,}} \cr & \,\,\,\,\,\frac{{{{\left( {75983} \right)}^2} - {{\left( {45983} \right)}^2}}}{{75983 - 45983}} \cr & = \frac{{\left( {75983 - 45983} \right)\left( {75983 + 45983} \right)}}{{(75983 - 45983)}} \cr & = \,75983 + 45983 \cr & = 121966 \cr} $$

99.

Simplify : $$1 - \left[ {1 - \left\{ {1 - \left( {1 - \overline {1 - 1} } \right)} \right\}} \right]$$

• (A) 0
• (B) 1
• (C) 2
• (D) 3

Show Answer

 Given Expression = 1 - [ 1 - { 1 - ( 1 - 0 ) } ] = 1 - [ 1 - ( 1 - 1 ) ] = 1 - [ 1 - 0 ] = 0

100.

$$\frac{1}{{1.2.3}} + \frac{1}{{2.3.4}} + \frac{1}{{3.4.5}} + \frac{1}{{4.5.6}}$$       is equal to = ?

• (A) $$\frac{7}{{30}}$$
• (B) $$\frac{{11}}{{30}}$$
• (C) $$\frac{{13}}{{30}}$$
• (D) $$\frac{{17}}{{30}}$$

Show Answer

 $$\eqalign{ & {\text{Given expression,}} \cr & \frac{{4.5.6 + 5.6 + 2.6 + 2.3}}{{1.2.3.4.5.6}} \cr & = \frac{{120 + 30 + 12 + 6}}{{720}} \cr & = \frac{{168}}{{720}} \cr & = \frac{7}{{30}} \cr} $$