Simplification math practice set for competitive exams in bengali Set 1
Q1. \(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots+\frac{1}{9\times10} = ?\)
A. 0.1
B. 1.1
C. 0.9
D. 0.09
Q2. মান নির্ণয় করো: \(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)
A. \(\frac{5}{36}\)
B. \(\frac{1}{36}\)
C. \(\frac{5}{72}\)
D. \(\frac{1}{72}\)
Q3. \(\frac{1}{5 \times 6} + \frac{1}{6 \times 7} + \frac{1}{7 \times 8} + \cdots\) - 20তম পদ পর্যন্ত সমষ্টি নির্ণয় কর।
A. 0.016
B. 1.6
C. 0.16
D. 16
Q4. মান নির্ণয় করো: \(\frac{1}{1\;\cdot\;3}+\frac{1}{3\;\cdot\;5}+\frac{1}{5\;\cdot\;7}+\cdots+\frac{1}{101\;\cdot\;103}=\;?\)
A. \(\frac{1}{72}\)
B. \(\frac{51}{73}\)
C. \(\frac{103}{51}\)
D. \(\frac{51}{103}\)
Q5. মান নির্ণয় করো: \(\frac{1}{1\;\cdot\;4}+\frac{1}{4\;\cdot\;7}+\frac{1}{7\;\cdot\;10}+\frac{1}{10\;\cdot\;13}+\frac{1}{13\;\cdot\;16}=\;?\)
A. \(\frac{1}{3}\)
B. \(\frac{5}{16}\)
C. \(\frac{3}{8}\)
D. \(\frac{41}{7280}\)
Q6. মান নির্ণয় করো: \(\frac{1}{1\;\cdot\;5}+\frac{1}{5\;\cdot\;9}+\frac{1}{9\;\cdot\;13}+\cdots+\frac{1}{97\;\cdot\;101}\)
A. \(\frac{5}{101}\)
B. \(\frac{25}{101}\)
C. \(\frac{1}{3}\)
D. \(\frac{1}{101}\)
Q7. মান নির্ণয় করো: \(\frac{3}{1^{2}\times2^{2}}+\frac{5}{2^{2}\times3^{2}}+\frac{7}{3^{2}\times4^{2}}+\cdots\)
A. 1
B. 4
C. 7
D. 9
Q8. \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\cdots\left(1+\frac{1}{100}\right)=?\)
A. 101
B. 50.5
C. 50
D. 51.5
Q9. \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\cdots\left(1-\frac{1}{100}\right)=?\)
A. 0.01
B. 0.001
C. 1
D. 0.1
Q10. \(\left(1-\frac{3}{7}\right)\left(1-\frac{3}{10}\right)\left(1-\frac{3}{13}\right)\left(1-\frac{3}{16}\right)\cdots\left(1-\frac{3}{49}\right)=?\)
A. \(\frac{2}{49}\)
B. \(\frac{3}{7}\)
C. \(\frac{4}{49}\)
D. \(\frac{3}{49}\)
Q11. \(\left(1+\frac{3}{4}\right)\left(1+\frac{3}{7}\right)\left(1+\frac{3}{10}\right)\cdots\left(1+\frac{3}{61}\right)=?\)
A. 16
B. 8
C. \(\frac{1}{16}\)
D. 12
Q12. \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\cdots\left(1-\frac{1}{99}\right)\left(1-\frac{1}{100}\right)=?\)
A. \(\frac{2}{99}\)
B. \(\frac{1}{25}\)
C. \(\frac{1}{50}\)
D. \(\frac{1}{100}\)
Q13. \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\ldots+\frac{1}{15.16}=?\)
A. \(\frac{15}{16}\)
B. \(\frac{15}{13}\)
C. \(\frac{15}{11}\)
D. \(\frac{15}{7}\)
Q14. \(\frac{1}{7 \times 8} + \frac{1}{8 \times 9} + \frac{1}{9 \times 10} + \ldots\) 10-তম পদ পর্যন্ত সমষ্টি নির্ণয় করো।
A. \(\frac{11}{119}\)
B. \(\frac{10}{119}\)
C. \(\frac{13}{119}\)
D. \(\frac{15}{119}\)
Q15. \(\frac{1}{1 \times 3} + \frac{1}{3 \times 5} + \frac{1}{5 \times 7} + \ldots + \frac{1}{39 \times 41} = ?\)
A. \(\frac{20}{41}\)
B. \(\frac{21}{41}\)
C. \(\frac{23}{41}\)
D. \(\frac{15}{41}\)
Q16. \(\frac{1}{10 \times 13} + \frac{1}{13 \times 16} + \frac{1}{16 \times 19} + \ldots + \frac{1}{37 \times 40} = ?\)
A. \(\frac{1}{10}\)
B. \(\frac{1}{20}\)
C. \(\frac{1}{30}\)
D. \(\frac{1}{40}\)
Q17. \(\frac{1}{1 \times 5} + \frac{1}{5 \times 9} + \frac{1}{9 \times 13} + \ldots + \frac{1}{77 \times 81} = ?\)
A. \(\frac{20}{81}\)
B. \(\frac{21}{81}\)
C. \(\frac{23}{81}\)
D. \(\frac{25}{81}\)
Q18. \(\frac{1}{1 \times 6} + \frac{1}{6 \times 11} + \frac{1}{11 \times 16} + \ldots + \frac{1}{101 \times 106} = ?\)
A. \(\frac{20}{106}\)
B. \(\frac{21}{106}\)
C. \(\frac{23}{106}\)
D. \(\frac{25}{106}\)
Q19. \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)\ldots\left(1+\frac{1}{50}\right) = ?\)
A. \(25.5\)
B. \(50.5\)
C. \(75.5\)
D. \(100.5\)
Q20. \(\left(1-\frac{3}{5}\right)\left(1-\frac{3}{8}\right)\left(1-\frac{3}{11}\right)\ldots\left(1-\frac{3}{32}\right) = ?\)
A. \(\frac{7}{16}\)
B. \(\frac{5}{16}\)
C. \(\frac{3}{16}\)
D. \(\frac{1}{16}\)
Q21. \(\left(1+\frac{2}{5}\right)\left(1+\frac{2}{7}\right)\left(1+\frac{2}{9}\right)\ldots\left(1+\frac{2}{23}\right) = ?\)
A. \(15\)
B. \(10\)
C. \(5\)
D. \(4\)
Q22. \(\left(1+\frac{3}{5}\right)\left(1+\frac{3}{8}\right)\left(1+\frac{3}{11}\right)\ldots\left(1+\frac{3}{47}\right) = ?\)
A. \(10\)
B. \(15\)
C. \(5\)
D. \(25\)
Q23. \(\left(1+\frac{4}{3}\right)\left(1+\frac{4}{7}\right)\left(1+\frac{4}{11}\right)\ldots\left(1+\frac{4}{95}\right) = ?\)
A. \(31\)
B. \(33\)
C. \(32\)
D. \(37\)
Q24. \(\left(2-\frac{1}{4}\right)\left(2-\frac{1}{7}\right)\left(2-\frac{1}{13}\right)\left(2-\frac{1}{25}\right)\left(2-\frac{1}{49}\right) = ?\)
A. \(\frac{97}{4}\)
B. \(\frac{91}{4}\)
C. \(\frac{93}{4}\)
D. \(\frac{99}{4}\)
Q25. \(\frac{1}{20} + \frac{1}{30} + \frac{1}{42} + \frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110} + \frac{1}{132} = ?\)
A. \(\frac{1}{8}\)
B. \(\frac{1}{7}\)
C. \(\frac{1}{6}\)
D. \(\frac{1}{10}\)
Q26. \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\ldots\left(1-\frac{1}{25}\right) = ?\)
A. \(\frac{2}{25}\)
B. \(\frac{1}{25}\)
C. \(1\frac{19}{25}\)
D. \(\frac{1}{325}\)
Q27. \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\ldots\left(1-\frac{1}{n}\right) = ?\)
A. \(\frac{1}{n-1}\)
B. \(\frac{n}{n-1}\)
C. \(\frac{1}{n}\)
D. None of these.
Q28. \(\frac{1}{56} + \frac{1}{72} + \frac{1}{90} + \frac{1}{110} + \frac{1}{132} = ?\) - এর সরলতম মান নির্ণয় করো।
A. \(\frac{1}{84}\)
B. \(\frac{1}{28}\)
C. \(\frac{5}{84}\)
D. \(\frac{1}{12}\)
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