Continued Fraction questions in bengali with answers Set 1
Q1. \(\frac{1}{3+\frac{1}{2-\frac{1}{\frac{7}{9}}}}+\frac{17}{22}\) = ?
A. \(1\)
B. \(\frac{12}{23}\)
C. \(\frac{22}{5}\)
D. \(\frac{5}{22}\)
Q2. \(\frac{2\frac{1}{3}-1\frac{2}{11}}{3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}}\) = ?
A. \(\frac{35}{109}\)
B. \(\frac{109}{38}\)
C. \(1\)
D. \(\frac{116}{109}\)
Q3. \(1-\frac{a}{1-\frac{1}{1+\frac{a}{1-a}}}\) = ?
A. \(a\)
B. \((1-a)\)
C. \(1\)
D. \(0\)
Q4. \(\frac{9}{3\times\frac{1}{3\times\frac{1}{3\times\frac{1}{1-\frac{1}{3}}}}}\) = ?
A. 2
B. 3
C. 4
D. 1
Q5. \(\frac{16}{8\div\frac{1}{4\div\frac{1}{3\div\frac{1}{1-\frac{1}{3}}}}}\) = ?
A. \(¼\)
B. \(½\)
C. \(⅓\)
D. \(⅕\)
Q6. \(x=1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}\) হলে, \(2x+\frac{3}{4}\) = ?
A. 3
B. 4
C. 5
D. 6
Q7. \(\frac{2+2\times2}{2\times2+2}\times\frac{\frac{1}{2}\div\frac{1}{2}\text{ এর }\frac{1}{2}}{\frac{1}{2}\text{ এর }\frac{1}{2}\div\frac{1}{2}}\) = ?
A. 1
B. 3
C. 2
D. 4
Q8. সরল করো: \(\frac{\frac{1}{2}\div\frac{3}{4}\div\frac{2}{3}}{2\div4}\div\frac{5}{8}\text{ এর }\frac{4}{5}\) = ?
A. 4
B. 3
C. 2
D. 5
Q9. \(\frac{2}{3}\times\frac{3}{\frac{5}{6}\div\frac{2}{3}\text{ এর }1\frac{1}{4}}\) = ?
A. 2
B. 1
C. \(½\)
D. \(\frac{2}{3}\)
Q10. মান নির্ণয় করো: \(\frac{2}{1+\frac{1}{1-\frac{1}{2}}}\times\frac{3}{\frac{5}{6}\text{ এর }\frac{3}{2}\div1\frac{1}{4}}\)
A. 1
B. 2
C. 3
D. 4
Q11. \(\frac{\frac{1}{3}\div\frac{1}{3}\times\frac{1}{3}}{\frac{1}{3}\div\frac{1}{3}\text{ এর }\frac{1}{3}}-\frac{1}{9}\) = ?
A. 0
B. 1
C. \(⅓\)
D. \(⅑\)
Q12. \(\frac{3\frac{1}{4}-\frac{4}{5}\text{ এর }\frac{5}{6}}{4\frac{1}{3}\div\frac{1}{5}-(\frac{3}{10}+21\frac{1}{5})}-(1\frac{2}{3}\text{ এর }1\frac{1}{2})\) = ?
A. 9
B. 11½
C. 13
D. 15½
Q13. সরল করো: \(1+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}\)
A. \(\frac{5}{8}\)
B. \(\frac{8}{5}\)
C. \(1\frac{5}{8}\)
D. \(1\frac{8}{5}\)
Q14. সরল করো: \(\frac{1}{1-\frac{1}{1-\frac{1}{1-\frac{1}{1-\frac{1}{2}}}}}\)
A. \(½\)
B. \(3\)
C. \(2\)
D. \(⅓\)
Q15. সরল করো: \(\frac{6}{2\times\frac{1}{2\times\frac{1}{2\times\frac{1}{1-\frac{2}{3}}}}}\)
A. 2
B. 5
C. 1
D. 3
Q16. সরল করো: \(\frac{4}{2\div\frac{1}{4\div\frac{2}{8\div\frac{1}{1-\frac{7}{8}}}}}\)
A. 1
B. \(½\)
C. 3
D. \(⅓\)
Q17. \(2=x+\frac{1}{1+\frac{1}{3+\frac{1}{4}}}\) হলে, \(x=\)?
A. \(\frac{18}{17}\)
B. \(\frac{21}{17}\)
C. \(\frac{13}{17}\)
D. \(\frac{12}{17}\)
Q18. মান নির্ণয় করো: \(1+\frac{4}{2+\frac{3}{5-\frac{1}{2}}}-\frac{1}{2}(10\div2)\)
A. 1
B. 0
C. \(-\frac{1}{2}\)
D. \(-\frac{15}{2}\)
Q19. \(\frac{2}{3}\div\frac{4}{9}\times7\frac{1}{2}+999\frac{494}{495}\times99\)
A. \(99999\)
B. \(10000\)
C. \(99000\)
D. \(11111\)
Q20. \(\frac{2\frac{3}{4}}{1\frac{5}{6}}\div\frac{7}{8}\times\left(\frac{1}{3}+\frac{1}{4}\right)+\frac{5}{7}\div\frac{3}{4}\text{ এর }\frac{3}{7}\)
A. \(\frac{56}{77}\)
B. \(\frac{49}{50}\)
C. \(\frac{2}{3}\)
D. \(3\frac{2}{9}\)
Q21. যদি \(\frac{1}{a+\frac{1}{b+\frac{1}{c+\frac{1}{d+\frac{1}{e}}}}}\) = \(\frac{421}{972}\) হয়, তাহলে \(a \times b \times c \times d \times e\) এর মান কতো?
A. 720
B. 480
C. 360
D. 600
Q22. যদি \(x=\frac{1}{2+\frac{3}{4+\frac{5}{6+\frac{7}{8+\frac{9}{10}}}}}\) হয়, তাহলে কোনটি সঠিক?
A. \(0<x<0.5\)
B. \(x=0.5\)
C. \(0.5<x<1.0\)
D. \(x>1.0\)
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