Clearly, 9261 is a perfect cube satisfying the given property.

Let 0.0169 x x = 1.3.

Then, 0.0169x = (1.3)² = 1.69

x = 1.69 = 100 0.0169

Answer : Option A

Explanation :

$MF#%\dfrac{{\sqrt{144}}}{11} \times \dfrac{11}{{\sqrt{225}}} \times \dfrac{15}{{\sqrt{196}}}\\\\
=\dfrac{{12}}{11} \times \dfrac{11}{{15}} \times \dfrac{15}{{14}}\\\\
=\dfrac{12}{14} \\\\= \dfrac{6}{7}\\\\ = 0.85\\\\$MF#%

Money collected = (59.29 x 100) paise = 5929 paise.

Number of members = 5929 = 77.

Answer : Option D

Explanation :

A number ending with 8 can never become a perfect square
Let's examine this in detail
1 × 1 = 1
Hence, if the unit digit of a number is 1, unit digit of its square is 1
2 × 2 = 4
Hence, if the unit digit of a number is 2, unit digit of its square is 4
3 × 3 = 9
Hence, if the unit digit of a number is 3, unit digit of its square is 9
4 × 4 = 16
Hence, if the unit digit of a number is 4, unit digit of its square is 6
5 × 5 = 25
Hence, if the unit digit of a number is 5, unit digit of its square is 5
6 × 6 = 36
Hence, if the unit digit of a number is 6, unit digit of its square is 6
7 × 7 = 49
Hence, if the unit digit of a number is 7, unit digit of its square is 9
8 × 8 = 64
Hence, if the unit digit of a number is 8, unit digit of its square is 4
9 × 9 = 81
Hence, if the unit digit of a number is 9, unit digit of its square is 1
0 × 0 = 0
Hence, if the unit digit of a number is 0, unit digit of its square is 0

Answer : Option A

Explanation :

$MF#%\sqrt{16641} = 129$MF#%

Answer : Option B

Explanation :

$MF#%\begin{align}&\left[\dfrac{\dfrac{1}{\sqrt{9}}-\dfrac{1}{\sqrt{11}}}{\dfrac{1}{\sqrt{9}}+\dfrac{1}{\sqrt{11}}}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{\sqrt{11}-\sqrt{9}}{\sqrt{11}+\sqrt{9}}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{\left(\sqrt{11}-\sqrt{9}\right)\left(\sqrt{11}-\sqrt{9}\right)}{\left(\sqrt{11}+\sqrt{9}\right)\left(\sqrt{11}-\sqrt{9}\right)}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{\left(\sqrt{11}-\sqrt{9}\right)^2}{11-9}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{11-2\sqrt{11}\sqrt{9}+9}{2}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left[\dfrac{20-2\sqrt{99}}{2}\right]+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \left(10-\sqrt{99}\right)+\left[\dfrac{10 + \sqrt{99}}{x}\right]=\dfrac{1}{2}\\\\
&\Rightarrow \dfrac{\left(10-\sqrt{99}\right) \left(10+\sqrt{99}\right)}{x}=\dfrac{1}{2}\\\\
&\Rightarrow \dfrac{\left(100-99\right)}{x}=\dfrac{1}{2}\\\\
&\Rightarrow \dfrac{1}{x}=\dfrac{1}{2}\\\\
&\Rightarrow x=2\end{align}$MF#%

x2 + y2 = (1 + √2)² + (1 - √2)²
= 2[(1)² + (√2)²]
= 2 * 3
= 6.

Answer : Option B

Explanation :

$MF#%16*9 = 16 + 9 - \sqrt{16 \times 9} \\\\= 25 - \sqrt{16 \times 9} \\\\= 25 - (\sqrt{16} \times \sqrt{9} )
\\\\= 25 - ( 4 \times 3) \\\\= 25-12 = 13$MF#%

1|1.5625( 1.25 |1 |------- 22| 56 | 44 |------- 245| 1225 | 1225 |------- | X |-------

1.5625 = 1.25.