Practice MCQ Questions and Answer on Simplification

181.

If $$\frac{547.527}{0.0082}\text{ = }x\text{,}$$   then the value of $$\frac{547527}{82}$$   is = ?

• (A) 10x
• (B) 100x
• (C) $$\frac{x}{100}$$
• (D) $$\frac{x}{10}$$

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \,\,\,\,\,\,\frac{{547.527}}{{0.0082}}{\text{ = }}x{\text{ }} \cr & \Rightarrow \frac{{547527}}{{82}} \times 10 = x \cr & \Rightarrow \frac{{547527}}{{82}} = \frac{x}{{10}} \cr} $$

182.

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

Show Answer

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

183.

The greatest 4 digit number which is a perfect square, is = ?

• (A) 9999
• (B) 9909
• (C) 9801
• (D) 9081

Show Answer

 $$\eqalign{ & {\text{Greatest 4 digit number}} \cr & {\text{ = 9999 }} \cr & \,\,\,\,\,\,\,\,{\text{9| }}\,{\text{9999 | 99}} \cr & \,\,\,\,\,\,\,\,\,\,\,|\,\,\,81 \cr & \overline {189\,\,|\,\,\,1899} \cr & \,\,\,\,\,\,\,\,\,\,\,|\,\,\,1701 \cr & \,\,\,\,\,\,\,\,\,\,\,\overline {|\,\,\,\,\,198} \cr} $$ Greatest four digit number is a perfect square = 999 - 198 = 9801

184.

2.8 + (5.2 ÷ 1.3 × 2) - 6 × 3 ÷ 8 + 2 the value of:

• (A) 6.45
• (B) 4.55
• (C) 8.44
• (D) 10.55

Show Answer

 2.8 + (5.2 ÷ 1.3 × 2) - 6 × 3 ÷ 8 + 2 = 2.8 + (4 × 2) - $$\frac{{6 \times 3}}{8}$$ + 2 = 2.8 + 8 - 2.25 + 2 = 10.55

185.

Find the value of * in the following. $$\text{1}\frac{2}{3}÷\frac{2}{7}\times \frac{\ast }{7}=1\frac{1}{4}\times \frac{2}{3}÷\frac{1}{6}$$

• (A) 0.006
• (B) $$\frac{1}{6}$$
• (C) 0.6
• (D) 6

Show Answer

 $$\eqalign{ & {\text{Let,}} \cr & \frac{5}{3} \div \frac{2}{7} \times \frac{x}{7} = \frac{5}{4} \times \frac{2}{3} \div \frac{1}{6} \cr & {\text{Then,}} \cr & \frac{5}{3} \times \frac{7}{2} \times \frac{x}{7} = \frac{5}{4} \times \frac{2}{3} \times 6 \cr & \Leftrightarrow \frac{5}{6}x = 5 \cr & \Leftrightarrow x = \left( {\frac{{5 \times 6}}{5}} \right) \cr & \Leftrightarrow x = 6 \cr} $$

186.

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

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

Show Answer

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

187.

$$\text{If }\frac{3a+4b}{3c+4d}\text{ = }\frac{3a-4b}{3c-4d}\text{ then}$$

• (A) ab = cd
• (B) ad = bc
• (C) ac = bd
• (D) a = b =c ≠ d

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \frac{{3a + 4b}}{{3a - 4b}}{\text{ = }}\frac{{3c + 4d}}{{3c - 4d}} \cr & \Rightarrow \frac{{3a}}{{4b}} = \frac{{3c}}{{4d}} \cr & \Rightarrow ad = bc \cr} $$

188.

A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

• (A) 45
• (B) 60
• (C) 75
• (D) 90

Show Answer

 Let number of notes of each denomination be x. Then x + 5x + 10x = 480 ⇒ 16x = 480 ∴ x = 30. Hence, total number of notes = 3x = 90.

189.

If $$\sqrt[3]{3^n}\text{ = 27,}$$   then the value of n is = ?

• (A) 9
• (B) 6
• (C) 1
• (D) 3

Show Answer

 According to question, $$\eqalign{ & \root 3 \of {{3^n}} {\text{ = 27}} \cr & \Rightarrow {\left( {{3^n}} \right)^{\frac{1}{3}}} = {\left( 3 \right)^3} \cr & \Rightarrow {3^{\frac{n}{3}}} = {3^3} \cr & \Rightarrow \frac{n}{3} = 3 \cr & \Rightarrow n = 9 \cr} $$

190.

The value of $$\frac{2}{3}÷\frac{3}{10}\text{ of }\frac{4}{9}-\frac{4}{5}\times 1\frac{1}{9}÷\frac{8}{15}+\frac{3}{4}÷\frac{1}{2}\text{ is:}$$

• (A) $$\frac{17}{9}$$
• (B) $$\frac{29}{6}$$
• (C) $$\frac{14}{3}$$
• (D) $$\frac{49}{12}$$

Show Answer

 $$\eqalign{ & \frac{2}{3} \div \frac{3}{{10}}{\text{ of }}\frac{4}{9} - \frac{4}{5} \times 1\frac{1}{9} \div \frac{8}{{15}} + \frac{3}{4} \div \frac{1}{2} \cr & = \frac{2}{3} \div \frac{2}{{15}} - \frac{4}{5} \times \frac{{10}}{9} \times \frac{{15}}{8} + \frac{3}{4} \times 2 \cr & = \frac{2}{3} \times \frac{{15}}{2} - \frac{5}{3} + \frac{3}{2} \cr & = 5 - \frac{5}{3} + \frac{3}{2} \cr & = \frac{{29}}{6} \cr} $$