Question Detail

if a = 0.1039, then the value of
\begin{aligned} \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}

12.039
1.2039
11.039
1.1039

Answer: Option D

Explanation:

Tip: Please check the question carefully before answering. As 3a is not under the root we can convert it into a formula , lets evaluate now :

\begin{aligned}
= \sqrt{4a^2 - 4a + 1} + 3a \end{aligned}

\begin{aligned}
= \sqrt{(1)^2 + (2a)^2 - 2x1x2a} + 3a \end{aligned}

\begin{aligned}
= \sqrt{(1-2a)^2} + 3a \end{aligned}

\begin{aligned}
= (1-2a) + 3a \end{aligned}

\begin{aligned}
= (1-2a) + 3a \end{aligned}

\begin{aligned}
= 1 + a = 1 + 0.1039 = 1.1039 \end{aligned}

1. Evaluate \begin{aligned}
\sqrt{1471369}
\end{aligned}

1213
1223
1233
1243

Answer: Option A

2. \begin{aligned} \sqrt{0.00059049} \end{aligned}

24.3
2.43
0.243
0.0243

Answer: Option D

3. \begin{aligned}
\sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9}}}}
\end{aligned}

Answer: Option D

Explanation:

\begin{aligned}
= \sqrt{41 - \sqrt{21 + \sqrt{19 - 3}}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{21 + \sqrt{16}}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{21 + 4}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{25}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - \sqrt{25}}
\end{aligned}

\begin{aligned}
= \sqrt{41 - 5}
\end{aligned}

\begin{aligned}
= \sqrt{36} = 6
\end{aligned}

4. \begin{aligned} \sqrt{\frac{0.081 * 0.484 }{0.0064 * 6.25}} \end{aligned}

0.66
0.77
0.88
0.99

Answer: Option D

5. The least perfect square, which is divisible by each of 21, 36 and 66 is

213414
213424
213434
213444

Answer: Option D

Explanation:

L.C.M. of 21, 36, 66 = 2772

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444