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CTET Paper II (Mathematics and Science) 27 Dec 2021 Solved Paper

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Question : 31 of 150

Marks: +1, -0

The value of

(\frac{5}{2})^{-3}\times (\frac{-3}{4})^{4}\div (\frac{3}{5})^{3}\times (\frac{4}{5})^{2}

is

0.04
0.6
0.06
0.08

Solution:

Concept:

Use exponent rules:

a^{-m} = \frac{1}{a^m}

, and division is multiplication by the reciprocal.

Explanation:

Rewrite each term separately.

(\frac{5}{2})^{-3} = (\frac{2}{5})^3 = \frac{8}{125}

.

(\frac{-3}{4})^{4} = \frac{81}{256}

(even power makes it positive).

(\frac{3}{5})^{3} = \frac{27}{125}

, so

\div (\frac{3}{5})^{3}

means

\times \frac{125}{27}

.

(\frac{4}{5})^{2} = \frac{16}{25}

.

Now multiply all:

\frac{8}{125} \times \frac{81}{256} \times \frac{125}{27} \times \frac{16}{25}

.

Cancel

\frac{125}{125} = 1

;

\frac{8}{256} = \frac{1}{32}

;

\frac{81}{27} = 3

.

Remaining:

\frac{1 \times 3 \times 16}{32 \times 25} = \frac{48}{800} = \frac{3}{50}

.

Convert to decimal:

\frac{3}{50} = 0.06

.

Answer:

Option C (0.06)

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