সপ্তম শ্রেণি - সাধারণ গণিত - ষষ্ঠ অধ্যায় - বীজগণিতীয় ভগ্নাংশ (অনুশীলনী-৬.২)
বীজগণিতীয় ভগ্নাংশের যোগ-বিয়োগ
সঠিক উত্তরটি বাছাই কর (১-৯):
১. |
2 3a |
ও |
2 5ab |
এর সমহরবিশিষ্ট ভগ্নাংশ নিচের কোনটি? |
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(ক) |
10b 15ab |
, |
9 15ab |
(খ) |
6 15ab |
, |
b 15ab |
(গ) |
2 15ab |
, |
3 15ab |
(ঘ) |
10a 15a2b |
, |
9a 15a2b |
উত্তরঃ |
ক |
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২. |
x yz |
ও |
y zx |
এর সাধারন হরবিশিষ্ট ভগ্নাংশ নিচের কোনটি? |
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(ক) |
zx2 xyz2 |
, |
y2z syz2 |
(খ) |
x2 xyz2 |
, |
y2 xyz2 |
(গ) |
x xyz |
, |
y xyz |
(ঘ) |
x2 xyz |
, |
y2 xyz |
উত্তরঃ |
ঘ |
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৩. |
a a+b |
+ |
b a+b |
এর মান কত? |
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(ক) |
2 a+b |
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(খ) |
1 a+b |
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(গ) |
1 |
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(ঘ) |
ab a+b |
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উত্তরঃ |
গ |
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৪. |
x 2 |
+ |
1 |
এর সমাধান নিচের কোনটি? |
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(ক) |
1 |
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(খ) |
4 |
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(গ) |
6 |
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(ঘ) |
8 |
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উত্তরঃ |
খ |
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৫. |
a b |
এর সমতুল ভগ্নাংশ নিচের কোনটি? |
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(ক) |
a2 bc |
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(খ) |
ac b |
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(গ) |
a3 b2 |
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(ঘ) |
ac bc |
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উত্তরঃ |
ঘ |
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৬. |
4a2b-9b3 4a2b+6ab2 |
এর লঘিষ্ঠ রুপ নিচের কোনটি? |
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(ক) |
2a+3b 2ab |
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(খ) |
2a-3b 2ab |
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(গ) |
2a-3b 2a |
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(ঘ) |
2a+3b 2a |
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উত্তরঃ |
গ |
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৭. |
a x |
+ |
b x |
- |
c x |
এর মান কত? |
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(ক) |
a+b+c x |
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(খ) |
a+b-c x |
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(গ) |
a+b-c |
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(ঘ) |
a-b+c x |
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উত্তরঃ |
খ |
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নিচের তথ্যের আলোকে ৮ ও ৯ নং প্রশ্নের উত্তর দাওঃ |
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x2+4x+4 x2-4 |
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৮. |
হরের উৎপাদকে বিশ্লেষিত রূপ কোনটি? |
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(ক) |
(x+2)(x-2) |
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(খ) |
(2+x)(2-x) |
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(গ) |
(x-2)(x-2) |
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(ঘ) |
(x+1)(x-4) |
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উত্তরঃ |
ক |
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৯. |
ভগ্নাংশটির লঘিষ্ঠ আকার কোনটি? |
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(ক) |
x+2 x-2 |
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(খ) |
x-2 x+2 |
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(গ) |
x+2 x2+2 |
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(ঘ) |
x-2 x2-4 |
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উত্তরঃ ক |
যোগফল নির্ণয় কর (১০-১৫):
১০. |
3a 5 |
+ |
2b 5 |
সমাধানঃ |
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3a 5 |
+ |
2b 5 |
= |
3a+2b 5 |
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১১. |
1 5x |
+ |
2 5x |
সমাধানঃ |
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1 5x |
+ |
2 5x |
= |
1+2 5x |
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= |
3 5x |
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১২. |
x 2a |
+ |
y 3b |
সমাধানঃ |
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x 2a |
+ |
y 3b |
= |
x✕3b+y✕2a 6ab |
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= |
3bx+2ay 6ab |
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১৩. |
2a x+1 |
+ |
2a x-2 |
সমাধানঃ |
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2a x+1 |
+ |
2a x-2 |
= |
2a(x-2)+2a(x+1) (x+1)(x-2) |
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= |
2ax-4a+2ax+2a (x+1)(x-2) |
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= |
4ax-2a (x+1)(x-2) |
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= |
2a(2x-1) (x+1)(x-2) |
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১৪. |
a a+2 |
+ |
2 a-2 |
সমাধানঃ |
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a a+2 |
+ |
2 a-2 |
= |
a(a-2)+2(a+2) (a+2)(a-2) |
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= |
a2-2a+2a+4 a2-4 |
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= |
a2+4 a2-4 |
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১৫. |
3 x2-4x-5 |
+ |
4 x+1 |
সমাধানঃ |
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3 x2-4x-5 |
+ |
4 x+1 |
= |
3 x2-5x+x-5 |
+ |
4 x+1 |
= |
3 x(x-5)+1(x-5) |
+ |
4 x+1 |
= |
3 (x-5)(x+1) |
+ |
4 x+1 |
= |
3✕1+4(x-5) (x-5)(x+1) |
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= |
3+4x-20 (x-5)(x+1) |
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= |
4x-17 (x-5)(x+1) |
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বিয়োগফল নির্ণয় কর (১৬-২১):
১৬. |
2a 7 |
- |
4b 7 |
সমাধানঃ |
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2a 7 |
- |
4b 7 |
= |
2a-4b 7 |
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= |
2(a-2b) 7 |
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১৭. |
2x 5a |
- |
4y 5a |
সমাধানঃ |
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2x 5a |
- |
4y 5a |
= |
2x-4y 5a |
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= |
2(x-2y) 5a |
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১৮. |
a 8x |
- |
b 4y |
সমাধানঃ |
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a 8x |
- |
b 4y |
= |
a✕y-b✕2x 8xy |
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= |
ay-2bx 8xy |
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১৯. |
3 x+3 |
- |
2 x+2 |
সমাধানঃ |
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3 x+3 |
- |
2 x+2 |
= |
3(x+2)-2(x+3) (x+2)(x+3) |
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= |
3x+6-2x-6 (x+2)(x+3) |
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= |
x (x+2)(x+3) |
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২০. |
p+q pq |
- |
q+r qr |
সমাধানঃ |
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p+q pq |
- |
q+r qr |
= |
r(p+q)-pp(q+r) pqr |
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= |
pr+qr-pq-pr pqr |
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= |
qr-pq pqr |
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= |
q(r-p) pqr |
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২১. |
2x x2-4y2 |
- |
x xy+2y2 |
সমাধানঃ |
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2x x2-4y2 |
- |
x xy+2y2 |
= |
2x x2-(2y)2 |
- |
x y(x+2y) |
= |
2x (x+2y)(x-2y) |
- |
x y(x+2y) |
= |
2x✕y-x(x-2y) y(x+2y)(x-2y) |
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= |
2xy-x2+2xy y(x+2y)(x-2y) |
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= |
4xy-x2 y(x+2y)(x-2y) |
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= |
x(4y-x) y(x2-4y2) |
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সরল করঃ (২২-২৭):
২২. |
5 a2-6a+5 |
+ |
1 a-1 |
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সমাধানঃ |
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5 a2-6a+5 |
+ |
1 a-1 |
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= |
5 a2-5a-a+5 |
+ |
1 a-1 |
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= |
5 a(a-5)-1(a-5) |
+ |
1 a-1 |
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= |
5 (a-1)(a-5) |
+ |
1 a-1 |
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= |
5✕1+1(a-5) (a-1)(a-5) |
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= |
5+a-5 (a-1)(a-5) |
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= |
a (a-1)(a-5) |
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= |
a a2-6a+5 |
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২৩. |
1 x+2 |
- |
1 x2-4 |
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সমাধানঃ |
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1 x+2 |
- |
1 x2-4 |
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= |
1 x+2 |
- |
1 x2-22 |
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= |
1 x+2 |
- |
1 (x-2)(x+2) |
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= |
1(x-2)-1✕1 (x+2)(x-2) |
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= |
x-2-1 x2-4 |
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= |
x-3 x2-4 |
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২৪. |
a 3 |
+ |
a 6 |
- |
3a 8 |
সমাধানঃ |
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a 3 |
+ |
a 6 |
- |
3a 8 |
= |
8✕a+4✕a-3✕3a 24 |
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= |
8a+4a-9a 24 |
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= |
12a-9a 24 |
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= |
3a 24 |
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= |
a 8 |
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২৫. |
a b |
-
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3a 2b |
+ |
2a 3b |
সমাধানঃ |
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a b |
-
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3a 2b |
+ |
2a 3b |
= |
a✕6-3a✕3+2a✕2 6b |
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= |
6a-9a+4a 6b |
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= |
10a-9a 6b |
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= |
a 6b |
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২৬. |
x yz |
- |
y zx |
+ |
z xy |
সমাধানঃ |
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x yz |
- |
y zx |
+ |
z xy |
= |
x✕x-y✕y+z✕z xyz |
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= |
x2-y2+z2 xyz |
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২৭. |
x-y xy |
+ |
y-z yx |
+ |
z-x zx |
সমাধানঃ |
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x-y xy |
+ |
y-z yx |
+ |
z-x zx |
= |
z(x-y)+x(y-z)+y(z-x) xyz |
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= |
xz-yz+xy-xz+yz-xy xyz |
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= |
0 xyz |
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= |
0 |
সূত্র-SCHOOLMATHBD