Class 7 Math BD-সপ্তম শ্রেণি সাধারণ গণিতঃ অনুশীলনী-৬.২ বীজগণিতীয় ভগ্নাংশের যোগ-বিয়োগ
বীজগণিতীয় ভগ্নাংশের যোগ-বিয়োগ
সঠিক উত্তরটি বাছাই কর (১-৯):
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১. |
2 3a
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ও |
2 5ab
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এর সমহরবিশিষ্ট ভগ্নাংশ নিচের কোনটি?
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(ক) |
10b 15ab
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, |
9 15ab
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(খ) |
6 15ab
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, |
b 15ab
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(গ) |
2 15ab
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, |
3 15ab
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(ঘ) |
10a 15a2b
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, |
9a 15a2b
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উত্তরঃ |
ক |
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২. |
x yz
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ও |
y zx
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এর সাধারন হরবিশিষ্ট ভগ্নাংশ নিচের কোনটি?
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(ক) |
zx2 xyz2
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, |
y2z syz2
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(খ) |
x2 xyz2
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, |
y2 xyz2
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(গ) |
x xyz
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, |
y xyz
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(ঘ) |
x2 xyz
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, |
y2 xyz
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উত্তরঃ |
ঘ |
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৩. |
a a+b
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+ |
b a+b
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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
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+ |
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
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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
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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
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+ |
b x
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- |
c x
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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):
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১০. |
3a 5
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+ |
2b 5
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সমাধানঃ |
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3a 5
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+ |
2b 5
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= |
3a+2b 5
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১১. |
1 5x
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+ |
2 5x
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সমাধানঃ |
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1 5x
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+ |
2 5x
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= |
1+2 5x
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= |
3 5x
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১২. |
x 2a
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+ |
y 3b
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সমাধানঃ |
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x 2a
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+ |
y 3b
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= |
x✕3b+y✕2a 6ab
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= |
3bx+2ay 6ab
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১৩. |
2a x+1
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+ |
2a x-2
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সমাধানঃ |
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2a x+1
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+ |
2a x-2
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= |
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
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+ |
2 a-2
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সমাধানঃ |
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a a+2
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+ |
2 a-2
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= |
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
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+ |
4 x+1
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সমাধানঃ |
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3 x2-4x-5
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+ |
4 x+1
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= |
3 x2-5x+x-5
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+ |
4 x+1
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= |
3 x(x-5)+1(x-5)
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+ |
4 x+1
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= |
3 (x-5)(x+1)
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+ |
4 x+1
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= |
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):
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১৬. |
2a 7
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- |
4b 7
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সমাধানঃ |
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2a 7
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- |
4b 7
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= |
2a-4b 7
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= |
2(a-2b) 7
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১৭. |
2x 5a
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- |
4y 5a
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সমাধানঃ |
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2x 5a
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- |
4y 5a
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= |
2x-4y 5a
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= |
2(x-2y) 5a
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১৮. |
a 8x
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- |
b 4y
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সমাধানঃ |
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a 8x
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- |
b 4y
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= |
a✕y-b✕2x 8xy
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= |
ay-2bx 8xy
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১৯. |
3 x+3
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- |
2 x+2
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সমাধানঃ |
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3 x+3
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- |
2 x+2
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= |
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
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- |
q+r qr
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সমাধানঃ |
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p+q pq
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- |
q+r qr
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= |
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
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- |
x xy+2y2
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সমাধানঃ |
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2x x2-4y2
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- |
x xy+2y2
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= |
2x x2-(2y)2
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- |
x y(x+2y)
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= |
2x (x+2y)(x-2y)
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- |
x y(x+2y)
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= |
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):
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২২. |
5 a2-6a+5
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+ |
1 a-1
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সমাধানঃ |
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5 a2-6a+5
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+ |
1 a-1
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= |
5 a2-5a-a+5
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+ |
1 a-1
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= |
5 a(a-5)-1(a-5)
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+ |
1 a-1
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= |
5 (a-1)(a-5)
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+ |
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
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- |
1 x2-4
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সমাধানঃ |
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1 x+2
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- |
1 x2-4
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= |
1 x+2
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- |
1 x2-22
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= |
1 x+2
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- |
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
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+ |
a 6
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- |
3a 8
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সমাধানঃ |
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a 3
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+ |
a 6
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- |
3a 8
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= |
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
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2a 3b
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সমাধানঃ |
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a b
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- |
3a 2b
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2a 3b
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= |
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
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- |
y zx
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+ |
z xy
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সমাধানঃ |
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x yz
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- |
y zx
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+ |
z xy
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= |
x✕x-y✕y+z✕z xyz
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= |
x2-y2+z2 xyz
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২৭. |
x-y xy
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+ |
y-z yx
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+ |
z-x zx
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সমাধানঃ |
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x-y xy
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+ |
y-z yx
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+ |
z-x zx
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= |
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 |
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