Lakshya Education MCQs

Question:

If a = 0.1039 , then the velue of  \( \sqrt{4a^{2}-4a+1}+3a. is :\)

Options:
A.0.1039
B.0.2078
C.1.1039
D.2.1039
Answer: Option C

\( \sqrt{4a^{2}-4a+1}+3a = \sqrt{(a^{2})+(2a)^{2}-2\times1\times2a}+3a\)

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

   = (1 - 2a) + 3a

   = (1 + a)

   = (1 + 0.1039)

   = 1.1039

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More Questions on This Topic :

Question 1.

If     \(3\sqrt{5}+\sqrt{125} = 17.88\) , then what will be the value of \(\sqrt{80}+6\sqrt{5}?\)

Options:
  1.    13.41
  2.    20.46
  3.    21.66
  4.    22.35
Answer: Option D

\(3\sqrt{5}+\sqrt{125} = 17.88\)

\(\Rightarrow 3\sqrt{5}+\sqrt{25\times5} = 17.88\)

\(\Rightarrow 3\sqrt{5}+5\sqrt{5} = 17.88\)

\(\Rightarrow8\sqrt{5} = 17.88\)

\(\Rightarrow \sqrt{5}=2.235\)

\(\therefore \sqrt{80}+6\sqrt{5} =\sqrt{16\times5}+6\sqrt{5}\)

\(= 4\sqrt{5}+6\sqrt{5}\)

\(= 10\sqrt{5} = (10\times2.235)=22.35\)

Question 2.

\(\sqrt{1.5625} =?\)

Options:
  1.    1.05
  2.    1.25
  3.    1.45
  4.    1.55
Answer: Option B
1|1.5625( 1.25
    |1
    |-------
  22| 56
    | 44
    |-------
 245| 1225
    | 1225
    |-------
    |    X
    |-------    

Therefore \(\sqrt{1.5625} = 1.25\)

Question 3.

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

Options:
  1.    213444
  2.    214344
  3.    214434
  4.    231444
Answer: Option A

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 = 22 x 32 x 72 x 112 = 213444

Question 4.

If x = \(\frac{\sqrt{3}+1}{\sqrt{3}-1} and y = \frac{\sqrt{3}-1}{\sqrt{3}+1} , then the value of (x^{2}+y^{2}) is:\)

Options:
  1.    10
  2.    13
  3.    14
  4.    15
Answer: Option C

\(x =\frac{(\sqrt{3}+1)}{(\sqrt{3}-1)}\times\frac{(\sqrt{3}+1)}{(\sqrt{3}+1)} = \frac{(\sqrt{3}+1)}{(3-1)}^{2} = \frac{3+1+2\sqrt{3}}{2} = 2+\sqrt{3}.\)

\(y =\frac{(\sqrt{3}-1)}{(\sqrt{3}+1)}\times\frac{(\sqrt{3}-1)}{(\sqrt{3}-1)} = \frac{(\sqrt{3}-1)}{(3-1)}^{2} = \frac{3+1-2\sqrt{3}}{2} = 2-\sqrt{3}\)

\(\therefore a^{b}+a^{b} = (2+\sqrt{3})^{2}+(2-\sqrt{3})^{2}\)

= 2(4 + 3)

   = 14

Question 5.

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

Options:
  1.    57
  2.    67
  3.    77
  4.    87
Answer: Option C

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

\(\therefore Number of members = \sqrt{5929} = 77.\)

Question 6.

The square root of \( (7+3\sqrt{5)}(7-3\sqrt{5)} is \)

Options:
  1.    5
  2.    2
  3.    4
  4.    35
Answer: Option B

\( \sqrt{(7+3\sqrt{5)}(7-3\sqrt{5)}}=\sqrt{(7)^{2}-(3\sqrt{5})^{2}} = \sqrt{49-45} = \sqrt{4} = 2\)