Simplification MCQ Question with Details Answer
Q1. 2.002 + 7.9 {(2.8 – 6.3 (3.6 – 1.5) + 15.6)}
(a) 2.002
(b) 4.2845
(c) 4.0843
(d) 42.845
Answer: (d) 42.845 Solution: 2.002 + 7.9 {(2.8 – 6.3 (3.6 – 1.5) + 15.6)} = 2.002 + 7.9 (2.8 – 6.3 × 2.1 + 15.6) = 2.002 + 7.9 (2.8 – 13.23 + 15.6) = 2.002 + 7.9 × 15.17 = 2.002 + 40.843 = 42.845 |
Q2. The value of 3\div \left[ \left( 8-5 \right) \div \left\{ \left( 4-2 \right) +\left( 2+\frac{8}{13} \right) \right\} \right]
(a) \frac{15}{17}
(b) \frac{13}{17}
(c) \frac{15}{19}
(d) \frac{13}{19}
Answer: (b) Solution: 3\div \left[ \left( 8-5 \right) \div \left\{ \left( 4-2 \right) \div \left( 2+\frac{8}{13} \right) \right\} \right] =3\div \left[ 3\div \left\{ 2\div \frac{34}{13} \right\} \right] =3\div \left[ 3\div \frac{13}{17} \right] =3\div \frac{3\times 17}{13} =3\times \frac{13}{3\times 17}=\frac{13}{17} |
Q3. 9-1\frac{2}{9}\mathrm{of} 3\frac{3}{11}\div 5\frac{1}{7}\,\,\mathrm{of} \frac{7}{9}\,\,=?
(a) \frac{5}{4}
(b) 8
(c) 8\frac{32}{81}
(d) 9
Answer: (b) 8 Solution: 9-1\frac{2}{9}\mathrm{of} 3\frac{3}{11}\div 5\frac{1}{7}\,\,\mathrm{of} \frac{7}{9}\,\, =\,\,9-\frac{11}{9}\,\,\mathrm{of} \frac{36}{11}\,\,\times \frac{1}{\frac{36}{7}\times \frac{7}{9}} =9-4 \times \frac{1}{4}\,\,=8 |
Q4. 777.07 + 77.77 + 0.77 + 7.07 + 7 + 77 = ?
(a) 946.78
(b) 946.68
(c) 964.68
(d) 946.86
Answer: (c) 964.68 Solution: |
Q5. Find the value of 999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}
(a) 5997
(b) 5979
(c) 5994
(d) 6997
Answer: (a) Solution: 999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7} =\,\,999+\frac{1}{7}\,\,+999+\frac{2}{7}+999+\frac{3}{7}+999+\frac{4}{7}+999+\frac{5}{7}+999+\frac{6}{7} 6\times 999 +\,\,\frac{1+2+3+4+5+6}{7}\,\, =\,\,5994 +\,\,3 =5997 |
Q6. Find the value of \frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}
(a) \frac{10}{11}
(b) \frac{9}{11}
(c) \frac{5}{11}
(d) \frac{7}{11}
Answer: (c) Solution: \frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99} =\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11} =\frac{1}{2}\left( 1-\frac{1}{11} \right) \,\,=\frac{5}{11}
Triks: \frac{1}{\mathrm{n}\left( \mathrm{n}+2 \right)}+\frac{1}{\left( \mathrm{n}+2 \right) \left( \mathrm{n}+4 \right)}+…. +\frac{1}{\left\{ \mathrm{n}\left( \mathrm{m}-2 \right) \right\} \left( \mathrm{n}+\mathrm{m} \right)} =\,\,\frac{1}{2}\left( \frac{1}{\mathrm{n}}-\frac{1}{\mathrm{n}+\mathrm{m}} \right) |
Q7. Find the value of 0.\bar{3}+0.\bar{6}+0.\bar{7}+0.\bar{8}
(a) 2\frac{3}{10}
(b) 2\frac{2}{3}
(c) 20.\overline{35}
(d) 5\frac{3}{10}
Answer: (b) Solution: 0.\bar{3}+0.\bar{6}+0.\bar{7}+0.\bar{8} =\frac{3}{9}+\frac{6}{9}+\frac{7}{9}+\frac{8}{9}=\frac{3+6+7+8}{9}=\frac{24}{9}=2\frac{2}{3} |
Q8. 1/4th of number of boys and 3/8th of number of girls participated in annual sports of the school. What fractional part of total number of students participated?
(a) 32
(b) 20
(c) 36
(d) Data inadequate
(e) None of the above
Answer: (d) Solution: total number of students participated = \frac{\mathrm{B}}{4}+\frac{3\mathrm{G}}{8} Required percentage = \frac{\frac{\mathrm{B}}{4}+\frac{3\mathrm{G}}{8}}{\left( \mathrm{B}+\mathrm{G} \right)}\times 100 % Since, B and G are unknown ; Clearly given Data is inadequate. |
Q9. Simplify : 1+\frac{1}{1+\frac{2}{2+\frac{3}{1+\frac{4}{5}}}}
(a) 1\frac{11}{17}
(b) 1\frac{5}{7}
(c) 1\frac{6}{17}
(d) 1\frac{21}{17}
Answer: (a) 1\frac{11}{17} Solution: 1st ⇒ 1+\frac{4}{5}=\frac{9}{5} 2nd ⇒ 2+\frac{3\times 5}{9}=\frac{11}{3} 3rd ⇒ 1+\frac{2\times 3}{11}=\frac{17}{11} 4th ⇒1+\frac{11}{17}=1\frac{11}{17} |
Q10. . If x = 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}} then, the value of 2\mathrm{x}+\frac{7}{4} is
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (c) 5 Solution: 1st ⇒ 1+\frac{1}{2}=\frac{3}{2} 2nd ⇒ 1+\frac{2}{3}=\frac{5}{3} 3rd ⇒ 1+\frac{3}{5}=\frac{8}{5} 4th ⇒ 1+\frac{5}{8}=\frac{13}{8} ∴ 2\mathrm{x}+\frac{7}{4}=2\times \frac{13}{8}+\frac{7}{4}=5 |