Practice MCQ Questions and Answer on Simplification

271.

Simplify : -7m -[3n -{8m -(4n - 10m)}]

• (A) 11m - 5n
• (B) 11m - 7n
• (C) 11n - 7m
• (D) 13n - 11m

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 $$\eqalign{ & {\text{ = }}\, - 7m - \left[ {3n - \left\{ {8m - \left( {4n - 10m} \right)} \right\}} \right]\,\,\, \cr & = \, - 7m - \left[ {3n - \left\{ {8m - 4n + 10m} \right\}} \right]\, \cr & = - 7m - \left[ {3n - 18m + 4n} \right] \cr & = - 7m - \left[ {7n - 18m} \right] \cr & = - 7m - 7n + 18m\,\,\, \cr & = \,11m - 7n\,\, \cr} $$

272.

$$\left[ {2\sqrt {54} - 6\sqrt {\frac{2}{3}} - \sqrt {96} } \right]$$     is equal to = ?

• (A) 0
• (B) 1
• (C) 2
• (D) $$\sqrt 6 $$

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 $$\eqalign{ & {\text{According to question,}} \cr & 2\sqrt {54} - 6\sqrt {\frac{2}{3}} - \sqrt {96} \cr & = \,6\sqrt 6 - 2\sqrt {\frac{2}{3} \times 9} - 4\sqrt 6 \cr & = 6\sqrt 6 - 2\sqrt 6 - 4\sqrt 6 \cr & = 0 \cr} $$

273.

Find the value of $$a$$ in the following equation. (Given: $$a$$ 10.)
$$\frac{{\left( {187 \div 17 \times a - 3 \times 3} \right)}}{{\left( {{8^2} - 9 \times 7 + {a^2}} \right)}} = 1$$

• (A) 2
• (B) 1
• (C) 4
• (D) 3

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 $$\eqalign{ & \frac{{\left( {187 \div 17 \times a - 3 \times 3} \right)}}{{\left( {{8^2} - 9 \times 7 + {a^2}} \right)}} = 1 \cr & 11a - 9 = 64 - 63 + {a^2} \cr & 11a - 9 = 1 + {a^2} \cr & {a^2} - 11a + 10 = 0 \cr & {a^2} - \left( {10 + 1} \right)a + 10 = 0 \cr & {a^2} - 10a - a + 10 = 0 \cr & a\left( {a - 10} \right) - 1\left( {a - 10} \right) = 0 \cr & \left( {a - 10} \right)\left( {a - 1} \right) = 0 \cr & a = 1,\,10{\text{ Answer}} \cr} $$

274.

The simplest value of $$\left( {\frac{1}{{\sqrt 9 - \sqrt 8 }} - \frac{1}{{\sqrt 8 - \sqrt 7 }} + \frac{1}{{\sqrt 7 - \sqrt 6 }} - \frac{1}{{\sqrt 6 - \sqrt 5 }}} \right)$$          is = ?

• (A) $$3 - \sqrt 5 $$
• (B) 3
• (C) $$\sqrt 5 $$
• (D) $$\sqrt 5 - 3$$

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 $$\left( {\frac{1}{{\sqrt 9 - \sqrt 8 }} - \frac{1}{{\sqrt 8 - \sqrt 7 }} + \frac{1}{{\sqrt 7 - \sqrt 6 }} - \frac{1}{{\sqrt 6 - \sqrt 5 }}} \right)$$ $$\eqalign{ & = \sqrt 9 + \sqrt 8 - \sqrt 8 - \sqrt 7 + \sqrt 7 + \sqrt 6 - \sqrt 6 - \sqrt 5 \cr & = \sqrt 9 - \sqrt 5 \cr & = 3 - \sqrt 5 \cr} $$

275.

$$\frac{{{{\left( {7.5} \right)}^3} + 1}}{{{{\left( {7.5} \right)}^2} - 6.5}}$$    is equal to = ?

• (A) 2.75
• (B) $$\frac{9}{5}$$
• (C) 4.75
• (D) 8.5

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 $$\eqalign{ & {\text{According to question,}} \cr & \Rightarrow \frac{{{{\left( {7.5} \right)}^3} + 1}}{{{{\left( {7.5} \right)}^2} - 6.5}}\,\,\,\,\,\,\, \cr & \,\,\,\,\,\,\,\,\,\,\,\left[ {\therefore {a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} + {b^2} - ab} \right)} \right] \cr & \Rightarrow \frac{{\left( {7.5 + 1} \right)\left[ {{{\left( {7.5} \right)}^2} + 1 - 7.5 \times 1} \right]}}{{{{\left( {7.5} \right)}^2} - 7.5 \times 1 + {1^2}}} \cr & \Rightarrow 8.5 \cr} $$

276.

If the expression $${\text{2}}\frac{1}{2}{\text{ of }}\frac{3}{4} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \frac{3}{2}\left[ {\frac{2}{3} - \frac{1}{2}{\text{ of }}\frac{2}{3}} \right]$$        is simplified, we get -

• (A) $$\frac{1}{2}$$
• (B) $$\frac{7}{8}$$
• (C) $${\text{1}}\frac{5}{8}$$
• (D) $${\text{2}}\frac{3}{5}$$

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 $$\eqalign{ & {\text{Given expression,}} \cr & = \frac{5}{2}of\frac{3}{4} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \frac{3}{2}\left[ {\frac{2}{3} - \frac{1}{3}} \right] \cr & = \frac{5}{2}of\frac{3}{4} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \left( {\frac{3}{2} \times \frac{1}{3}} \right) \cr & = \frac{{15}}{8} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \frac{1}{2} \cr & = \frac{{15}}{8} \times \frac{1}{2} \times \frac{2}{3} + \frac{1}{2} \times 2 \cr & = \frac{5}{8} + 1 \cr & = \,1\frac{5}{8} \cr} $$

277.

The value of $$\sqrt {32} $$  - $$\sqrt {128} $$  + $$\sqrt {50} $$ correct to 3 places of decimal is $$\sqrt {32} $$  - $$\sqrt {128} $$  + $$\sqrt {50} $$  = ?

• (A) 1.732
• (B) 1.141
• (C) 1.414
• (D) 1.441

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 $$\eqalign{ & {\text{According to question,}} \cr & \sqrt {32} {\text{ }} - \sqrt {128} {\text{ + }}\sqrt {50} \cr & \Rightarrow \sqrt {16 \times 2} - \sqrt {64 \times 2} + \sqrt {25 \times 2} \cr & \Rightarrow 4\sqrt 2 - 8\sqrt 2 + 5\sqrt 2 \cr & \Rightarrow \sqrt 2 \cr & \Rightarrow 1.414 \cr} $$

278.

$$\left( {999\frac{{999}}{{1000}} \times 7} \right)$$   is equal to = ?

• (A) $${\text{6633}}\frac{7}{{1000}}$$
• (B) $${\text{6993}}\frac{7}{{1000}}$$
• (C) $${\text{6999}}\frac{993}{{1000}}$$
• (D) $$7000\frac{7}{{1000}}$$

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 $$\eqalign{ & {\text{Given expression ,}} \cr & \left( {1000 - \frac{1}{{1000}}} \right) \times 7 \cr & = \left( {7000 - \frac{7}{{1000}}} \right) \cr & = 6999\frac{{993}}{{1000}} \cr} $$

279.

Simplify : $$\sqrt {3 + \frac{{33}}{{64}}} \div $$   $$\sqrt {9 + \frac{1}{7}} \times $$   $$2\sqrt {3\frac{1}{9}} $$   = ?

• (A) $$\frac{{45}}{{256}}$$
• (B) $$1\frac{{17}}{{28}}$$
• (C) $$4\frac{3}{8}$$
• (D) $$2\frac{3}{{16}}$$

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 $$\eqalign{ & {\text{According to question,}} \cr & \sqrt {3 + \frac{{33}}{{64}}} \div \sqrt {9 + \frac{1}{7}} \times 2\sqrt {3\frac{1}{9}} \cr & = \sqrt {\frac{{225}}{{64}}} \div \sqrt {\frac{{64}}{7}} \times 2\sqrt {\frac{{28}}{9}} \cr & = \sqrt {\frac{{225}}{{64}} \times \frac{7}{{64}} \times \frac{{28}}{9}} \times 2 \cr & = \frac{{5 \times 7}}{{8 \times 4}} \times 2 \cr & = \frac{{35}}{{16}} \cr & = 2\frac{3}{{16}} \cr} $$