Lakshya Education MCQs

Question: The least number that must be subtracted from 63522 to make the result a perfect square is = ?
Options:
 A. 18 B. 20 C. 24 D. 30

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Question 1. The simplification of $$\frac{5}{{3 + \frac{3}{{1 - \frac{2}{3}}}}}\, = ?$$
1.    5
2.    $$\frac{5}{3}$$
3.    $$\frac{5}{{12}}$$
4.    $$\frac{3}{4}$$
Question 2. Simplify : $$\left[ {\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) \times \left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) - \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right) \times \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)} \right] \div \left[ {\left( {1 + \frac{1}{{10 + \frac{1}{{10}}}}} \right) + \left( {1 - \frac{1}{{10 + \frac{1}{{10}}}}} \right)} \right] = ?$$
1.    $$\frac{{100}}{{101}}$$
2.    $$\frac{{90}}{{101}}$$
3.    $$\frac{{20}}{{101}}$$
4.    $$\frac{{101}}{{100}}$$
Question 3. If the expression $${\text{2}}\frac{1}{2}{\text{ of }}\frac{3}{4} \times \frac{1}{2} \div \frac{3}{2} + \frac{1}{2} \div \frac{3}{2}\left[ {\frac{2}{3} - \frac{1}{2}{\text{ of }}\frac{2}{3}} \right]$$        is simplified, we get -
1.    $$\frac{1}{2}$$
2.    $$\frac{7}{8}$$
3.    $${\text{1}}\frac{5}{8}$$
4.    $${\text{2}}\frac{3}{5}$$
Question 4. \eqalign{ & {\text{If}} \cr & {\text{I = }}\frac{3}{4} \div \frac{5}{6}{\text{,}} \cr & {\text{II = 3}} \div \left[ {\left( {4 \div 5} \right) \div 6} \right]{\text{,}} \cr & {\text{III = }}\left[ {{\text{3}} \div \left( {4 \div 5} \right)} \right] \div {\text{6,}} \cr & {\text{IV = 3}} \div {\text{4}} \div \left( {5 \div 6} \right), \cr & {\text{Then - }} \cr}
1.    I and II are equal
2.    I and III are equal
3.    I and IV are equal
4.    All are equal
Question 5. The difference of $${\text{1}}\frac{3}{{16}}$$  and its reciprocal is equal to = ?
1.    $$1\frac{1}{8}$$
2.    $$\frac{4}{3}$$
3.    $$\frac{{15}}{{16}}$$
4.    None of these