বীজগণিতীয় অনুপাত ও সমানুপাত, গণিত

বীজগণিতীয় অনুপাত ও সমানুপাত

Question: 5 : 3 = 15 : 9 হলে এদের যোজন ফল নিচের কোনটি?
A
`5/8 = 9/(24)`

B
`8/3 = (24)/(15)`

C
`8/3 = (24)/9`

D
`5/8 = (24)/(15)`

Note: `5/8 = (15)/9, (5 + 3)/3 = (15 + 9)/9`[যোজন] `8/3 = (24)/9`
1. Report
Question: a : b = c : d হলে নিচের কোনটি ব্যাস্তকরণ নির্দেশ কর?
A
`a/b = c/d`

B
`b/a = d/c`

C
`b/a = c/d`

D
`a/b = d/c`

Note: Not available
1. Report
Question: `a/b = c/d = e/f = 2/3` `(a + c + e)/(b + d + f)`
A
`4/9`

B
`2/3`

C
2

D
3

Note: `(a + c + e)/(b + d + f) = (2 + 2 + 2)/(3 + 3 + 3) = 6/9 = 2/3`
1. Report
Question: `(1.5)/5 = 3/(10) = 9/(10) = (27)/(90)`হলে, প্রত্যেকটি অনুপাতের মান নিচের কোনটি?
A
`(45)/(135)`

B
`(135)/(40)`

C
`(81)/(270)`

D
`(135)/(40.5)`

Note: প্রত্যেকটি অনুপাত `= (1.5 + 3 + 9 + 27)/(5 + 10 + 30 + 90) = (40.5)/(1.35)` `= (40.5 xx 2)/(1.35 xx 2) = (81)/(270)`
1. Report
Question: 11 : 5 = 44 : 20 এর যোজন বিয়োজন ফল নিচের কোনটি?
A
`(16)/6 = (24)/(64)`

B
`8/3 = (32)/(12)`

C
`(64)/6 = (16)/(24)`

D
`8/3 = (12)/(32)`

Note: `(11)/5 = (44)/(20) ; (11 + 5)/(11 - 5)` ` = (44 + 20)/(44 - 20)` [যোজন বিয়োজন করে]; `(16)/6 = (64)/(24);` বা, `8/3 = (32)/(12)`
1. Report
Question: `a/b = 2` হলে `(a^2 + b^2)/(a^2 - b^2)`= কত?
A
1

B
`5/3`

C
3

D
8

Note: `a/b = 2` বা,`a^2/b^2 = 4` বা, `(a^2 + b^2)/(a^2 - b^2)` =` (4 + 1)/(4 - 1) = 5/3`
1. Report
Question: `(2x + 3y)/(3x + 5y) = (18)/(29)` হলে x : y = কত?
A
4 : 5

B
3 : 4

C
2 : 3

D
4 : 3

Note: `(2x + 3y)/(3x + 5y) = (18)/(29)` 58x + 87y = 54x + 90y বা, 58x - 54x = 90y - 87y বা, 4x = 3y বা, `x/y = 3/4` :. x : y = 3 : 4
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Question: 13, 51, 17, 39 চারটি সংখ্যার ক্ষেত্রে--- i. 51 : 17 = 39 : 13 ii. `(39)/(17) = (26)/(13)` iii. `(68)/(34) = (52)/(26)` নিচের কোনটি সঠিক?
A
i ও ii

B
i ও iii

C
ii ও iii

D
i, i ও iii

Note: Not available
1. Report
Question: a = 2, b = 11; c = 22 d = 121 i. `(a + b)/(a - b) = (c + d)/(c - d)` ii. `a/(a - b) = c/(c - d)` iii. `(a + b)/b = (c - d)/d` নিচের কোনটি সঠিক?
A
i ও ii

B
i ও iii

C
ii ও iii

D
i, i ও iii

Note: সঠিক নয়; `(a + b)/b = (2 + 11)/(11) ` `= (13)/(11); (c - d)/d = (22 - 121)/(121) = (-99)/(12)`
1. Report
Question: `a/b = c/d` হলে-- i. 1 - a/b = 1 - c/d` ii. `(a - 1)/b = (c - 1)/d` iii. a + b : c + d = b : d নিচের কোনটি সঠিক?
A
i ও ii

B
i ও iii

C
ii ও iii

D
i, ii ও iii

Note: `(a + b)/b = (c + d)/d` বা, `(a + b)/(c + d) = b/d` :. a + b : c + d = b : d
1. Report

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Question: 5 : 3 = 15 : 9 হলে এদের যোজন ফল নিচের কোনটি?

Question: a : b = c : d হলে নিচের কোনটি ব্যাস্তকরণ নির্দেশ কর?

Question: `a/b = c/d = e/f = 2/3` `(a + c + e)/(b + d + f)`

Question: `(1.5)/5 = 3/(10) = 9/(10) = (27)/(90)`হলে, প্রত্যেকটি অনুপাতের মান নিচের কোনটি?

Question: 11 : 5 = 44 : 20 এর যোজন বিয়োজন ফল নিচের কোনটি?

Question: `a/b = 2` হলে `(a^2 + b^2)/(a^2 - b^2)`= কত?

Question: `(2x + 3y)/(3x + 5y) = (18)/(29)` হলে x : y = কত?

Question: 13, 51, 17, 39 চারটি সংখ্যার ক্ষেত্রে--- i. 51 : 17 = 39 : 13 ii. `(39)/(17) = (26)/(13)` iii. `(68)/(34) = (52)/(26)` নিচের কোনটি সঠিক?

Question: a = 2, b = 11; c = 22 d = 121 i. `(a + b)/(a - b) = (c + d)/(c - d)` ii. `a/(a - b) = c/(c - d)` iii. `(a + b)/b = (c - d)/d` নিচের কোনটি সঠিক?

Question: `a/b = c/d` হলে-- i. 1 - a/b = 1 - c/d` ii. `(a - 1)/b = (c - 1)/d` iii. a + b : c + d = b : d নিচের কোনটি সঠিক?