सरलीकरण BODMAS #5 Part

सरलीकरण BODMAS (भाग – 5) में SSc लेवल Type – IV के 15 सवालों को हल किया गया है जो कि सरलीकरण से सम्बंधित है

सरलीकरण BODMAS

सरलीकरण BODMAS (Type – IV) के 15 सवाल हल सहित :-

Q1. b – [b – (a + b) – {b – (b – a – b)} + 2a] सरल कीजिए ?

= b – [b – (a + b) – {b – b + a + b} + 2a]
= b – [b – a – b – a – b + 2a]
= b – b
= 0

Q2. यदि \frac{256}{0.256} = \frac{25.6}{x} है तो x का मान क्या होगा ?

\frac{256000}{256} = \frac{256}{10x}
10x = \frac{256×256}{256000}
10x = 0.256
x = 0.0256

Q3. \frac{7|2 - 6|- 4|5| ÷ 5}{-7(2) - 2×2 ÷ 2 + 2}

= \frac{7|- 4|- 4(1)}{-14 - 2×(1) + 2}
= \frac{28 - 4}{-14 - 2 + 2}
= \frac{28 - 4}{-14 - 2 + 2}
= \frac{24}{-14}
= \frac{12}{-7}

Q4. \frac{675×675×675 + 325×325×325}{67.5×67.5 + 32.5×32.5 - 67.5×32.5}

माना a = 67.5 और b = 32.5

= 1000(a3 + b3) / (a2 + b2 – ab)
= 1000(a + b)(a2 + b2 – ab) / (a2 + b2 – ab)
= 1000(a + b)

= 1000000

Q5. 9 \frac{3}{4} ÷ [2 \frac{1}{6} + {4 \frac{1}{3} – (2 \frac{1}{2} + \frac{3}{4} )}]

= \frac{39}{4} ÷ [ \frac{13}{6} + { \frac{13}{3} – ( \frac{5}{2} + \frac{3}{4} )}]
= \frac{39}{4} ÷ \frac{26+52-30-9}{12}
= \frac{39}{4} ÷ \frac{39}{12}
= \frac{39}{4} × \frac{12}{39}
= 3

Q6. 4 \frac{4}{5} ÷ \frac{3}{7} का 7 + \frac{4}{5} × \frac{3}{10} \frac{1}{5}

= \frac{24}{5} ÷ \frac{3}{7} × 7 + \frac{4}{5} × \frac{3}{10} \frac{1}{5} {By using BODMAS rule}
= \frac{24}{5} ÷ 3 + \frac{12}{50} \frac{1}{5}
= \frac{24}{5} × \frac{1}{3} + \frac{12}{50} \frac{1}{5}
= \frac{8}{5} + \frac{1}{25}
= \frac{41}{25}

Q7. \frac{6.75×6.75×6.75 - 4.25×4.25×4.25}{67.5×67.5 + 42.5×42.5+67.5×42.5}

माना a = 6.75 और b = 4.25

= (a3 – b3) / 100(a2 + b2 + ab)
= (a – b)(a2 + b2 + ab) / 100(a2 + b2 + ab) {∵ using formula of (a3 – b3)}

= (a – b) / 100

= 0.025

Q8. 5 \frac{1}{5} – [3 \frac{1}{2} – { \frac{5}{6} – ( \frac{3}{5} + \frac{1}{10} \frac{4}{15} )}]

= \frac{26}{5} – [ \frac{7}{2} – { \frac{5}{6} – ( \frac{3}{5} + \frac{1}{10} \frac{4}{15} )}]
= \frac{26}{5} – [ \frac{7}{2} – { \frac{5}{6} – ( \frac{7}{10} \frac{4}{15} )}]
= \frac{26}{5} – [ \frac{7}{2} – { \frac{5}{6} – ( \frac{13}{30} )}]
= \frac{26}{5} – [ \frac{7}{2} \frac{12}{30} ]
= \frac{26}{5} - \frac{93}{30}
= \frac{63}{30}

Q9. [3 \frac{2}{3} - { \frac{15}{4} (5 \frac{4}{5} ÷ 14 \frac{1}{2} )}]

= [ \frac{11}{3} – { \frac{15}{4} ( \frac{29}{5} ÷ \frac{29}{2} )}]
= [ \frac{11}{3} – { \frac{15}{4} ( \frac{29}{5} × \frac{2}{29} )}]
= [ \frac{11}{3} – { \frac{3}{2} }]
= \frac{13}{6}

Q10. 5 ÷ 5 का 5 × 2 + 2 ÷ 2 का 2 × 5 – (5 – 2) ÷ 6 × 2 का मान है

= 5 ÷ 5 × 5 × 2 + 2 ÷ 2 × 2 × 5 – (5 – 2) ÷ 6 × 2 {∵ BODMAS rule}
= 5 ÷ 25 × 2 + 2 ÷ 4 × 5 – (5 – 2) ÷ 6 × 2
= \frac{1}{5} × 2 + \frac{1}{2} × 5 – (3) ÷ 6 × 2
= \frac{1}{5} × 2 + \frac{1}{2} × 5 – \frac{1}{2} × 2
= \frac{2}{5} + \frac{5}{2} \frac{2}{2}
= \frac{29}{10} \frac{2}{2}
= \frac{19}{10}

Q11. 2 \frac{7}{8} ÷ (3 \frac{5}{6} ÷ \frac{2}{7} का 2 \frac{1}{3} ) × [(2 \frac{6}{7} का 4 \frac{1}{5} ÷ \frac{2}{3} ) × \frac{5}{9} ] का मान है ?

= \frac{23}{8} ÷ ( \frac{23}{6} ÷ \frac{2}{7} × \frac{7}{3} ) × [( \frac{20}{7} × \frac{21}{5} ÷ \frac{2}{3} ) × \frac{5}{9} ]
= \frac{23}{8} ÷ ( \frac{23}{6} ÷ \frac{2}{3} ) × [(12 ÷ \frac{2}{3} ) × \frac{5}{9} ]
= \frac{23}{8} ÷ ( \frac{23}{6} × \frac{3}{2} ) × [(12 × \frac{3}{2} ) × \frac{5}{9} ]
= \frac{23}{8} × ( \frac{4}{23} ) × [(18) × \frac{5}{9} ]
= \frac{1}{2} × 10

= 5

Q12. ( \frac{2}{3} ÷ \frac{3}{2} का \frac{2}{3} ) का \frac{9}{15} ÷ ( \frac{5}{4} ÷ \frac{5}{2} × \frac{4}{5} का \frac{2}{5} ) का ( \frac{3}{4} × \frac{3}{4} ÷ \frac{4}{3} का \frac{3}{4} ) का मान है :

= ( \frac{2}{3} ÷ \frac{3}{2} × \frac{2}{3} ) का \frac{9}{15} ÷ ( \frac{5}{4} ÷ \frac{5}{2} × \frac{4}{5} × \frac{2}{5} ) का ( \frac{3}{4} × \frac{3}{4} ÷ \frac{4}{3} × \frac{3}{4} )
= ( \frac{2}{3} ÷ 1) का \frac{9}{15} ÷ ( \frac{5}{4} ÷ \frac{5}{2} × \frac{8}{25} ) का ( \frac{3}{4} × \frac{3}{4} ÷ 1)
= ( \frac{2}{3} ) × \frac{9}{15} ÷ ( \frac{5}{4} ÷ \frac{5}{2} × \frac{8}{25} ) × ( \frac{3}{4} × \frac{3}{4} )
= ( \frac{2}{5} ) ÷ ( \frac{5}{4} × \frac{2}{5} × \frac{8}{25} ) × \frac{9}{16}
= ( \frac{2}{5} ) ÷ ( \frac{4}{25} ) × \frac{9}{16} )
= \frac{5}{2} × \frac{9}{16} )

= \frac{45}{32} )

Q13. 16 ÷ 4 का 4 × [3 ÷ {4 × 3 ÷ (3 + 3)} का 4] ÷ (2 ÷ 8 का 4) का मान है :

= 16 ÷ 4 × 4 × [3 ÷ {4 × 3 ÷ (3 + 3)} × 4] ÷ (2 ÷ 8 का 4)
= 16 ÷ 16 × [3 ÷ {2} × 4] ÷ (2 ÷ 8 × 4)
= 16 ÷ 16 × [3 ÷ 8] ÷ (1 ÷ 16)
= 1 × [3 ÷ 8] × 16
= 6

Q14. \frac{8}{9} का (5 \frac{1}{4} ÷ 2 \frac{1}{3} का 4) ÷ (8 ÷ \frac{2}{3} का \frac{4}{5} ) का (8 × \frac{2}{3} ÷ \frac{4}{5} ) का मान है :

= \frac{8}{9} का (5 \frac{1}{4} ÷ 2 \frac{1}{3} × 4) ÷ (8 ÷ \frac{2}{3} × \frac{4}{5} ) का (8 × \frac{2}{3} ÷ \frac{4}{5} )
= \frac{8}{9} का (5 \frac{1}{4} ÷ \frac{28}{3} ) ÷ (8 ÷ \frac{8}{15} ) का ( \frac{16}{3} ÷ \frac{4}{5} )
= \frac{8}{9} का ( \frac{21}{4} × \frac{3}{28} ) ÷ (8 × \frac{15}{8} ) का ( \frac{16}{3} × \frac{5}{4} )
= \frac{8}{9} का ( \frac{63}{112} ) ÷ (15) का ( \frac{80}{12} )
= \frac{8}{9} × ( \frac{63}{112} ) ÷ (15) × ( \frac{80}{12}))
= ( \frac{1}{2} ) ÷ 100
= \frac{1}{200}

Q15. 7 \frac{1}{2} × (3 \frac{1}{5} ÷ 4 \frac{1}{2} का 5 \frac{1}{3} ) + [11 - ( \frac{5}{8} + 3 - 1 \frac{1}{4} )] ÷ 5 \frac{3}{4} - 5 ÷ 5 × 5 का 5 ÷ 25 का मान है :

= \frac{15}{2} × ( \frac{16}{5} ÷ \frac{9}{2} × \frac{16}{3} ) + [11 - ( \frac{5}{8} + 3 - \frac{5}{4} )] ÷ \frac{23}{4} - 5 ÷ 5 × 5 × 5 ÷ 25
= \frac{15}{2} × ( \frac{16}{5} ÷ 24) + [11 - ( \frac{5}{8} + 3 - \frac{5}{4} )] ÷ \frac{23}{4} - 5 ÷ 5 × 25 ÷ 25
= \frac{15}{2} × ( \frac{2}{15} ) + [11 - ( \frac{5}{8} + 3 - \frac{5}{4} )] ÷ \frac{23}{4} - 1 × 1
= 1 + [11 - ( \frac{29}{8} - \frac{5}{4} )] ÷ \frac{23}{4} - 1
= 1 + [11 - ( \frac{19}{8} )] ÷ \frac{23}{4} - 1
= [( \frac{69}{8} )] ÷ \frac{23}{4}
= [( \frac{69}{8} )] × \frac{4}{23}
= \frac{3}{2}

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