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316 . $x^{2} - y^{2}, x^{3} - y^{3}, x^{4} + x^{2} y^{2} + y^{4}$ রাশিগুলোর গ. সা.গু কত?

A. x+y
B. x -y
D. 1

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Answer: Option D

Explanation:

{১ম রাশি= x}^{2} {-y}^{2} = (x + y) (x - y) {২য় রাশি= x}^{3} {-y}^{3} = (x - y) (x^{2} + x y + y^{2}) {৩য় রাশি= x}^{4} {+x}^{2} y^{2} {+y}^{4} = {(x^{2})}^{2} {+2x}^{2} y^{2} + {(y^{2})}^{2} {-x}^{2} y^{2} = {(x^{2} + y^{2})}^{2} - {(xy)}^{2} = (x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y) 1 ব্যাতীত কোনো সধারন উৎপাদক নেই। অতএব গ.সা.গু=1

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317 . $x^{2} - 3 x, x^{2} - 9$ এবং $x^{2} - 4 x + 3$ বীজগাণিতীক রাশির গ. সা.গু কত হবে?

A. x-4
B. x + 3
C. x -3
D. x -1

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Answer: Option C

Explanation:

a² - 3a = a ( a - 3) a² - 9 = a² - 3² = (a+3) (a-3) a² - 4a + 3 = a² - 3a - a + 3 = a (a-3) - 1 (a-3) = (a-3) (a-1) নির্ণেয় গ.সা.গু = (a-3)

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১৬ তম বেসরকারি প্রভাষক নিবন্ধন পরীক্ষা (30-08-2019)

318 . If a+b =8 and ab =15, what is the value of $a^{2} + b^{2} ?$

A. 94
B. 79
C. 34
D. 30

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Answer: Option C

Explanation:

আমরা জানি, {(a + b)}^{2} = a^{2} + 2 a b + b^{2} \Rightarrow {(8)}^{2} = a^{2} + b^{2} + 2 a b \Rightarrow 64 = a^{2} + b^{2} + (2 \times 15) \Rightarrow a^{2} + b^{2} + (2 \times 15) = 64 \Rightarrow a^{2} + b^{2} = 64 - 30 = 34

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319 . If x +y = 1/a and x-y =a then the value of $x^{2} - y^{2}$ is:

A. 4
C. 1
D. $a^{2}$

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Answer: Option C

Explanation:

দেওয়া আছে, x + y = \frac{1}{a} এবং x-y=a {এখন, x}^{2} {-y}^{2} = (x + y) (x - y) = \frac{1}{a} ×a=1

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320 . If $x + y = 7$ and $x^{2} + y^{2} = 25,$ then which one of the following equals the value of $x^{3} + y^{3} ?$

A. 7
B. 25
C. 65
D. 91

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Answer: Option D

Explanation:

দেওয়া আছে, x + y = 7 x^{2} + y^{2} = 25 \Rightarrow {(x + y)}^{2} - 2 x y = 25 \Rightarrow 7^{2} - 25 = 2 x y \Rightarrow 2 x y = 49 - 25 \Rightarrow x y = \frac{24}{2} = 12 x^{3} + y^{3} = {(x + y)}^{3} - 3 x y (x + y) = 7^{3} - 3 \times 12 \times 7 = 343 - 252 = 91

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321 . a2-3a,a3-9a এবং $a^{3} - 4 a^{2} + 3 a$ এর গ.সা.গু=?

A. a(a-3)
B. a-3
C. a
D. a(a+3)

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Answer: Option B

Explanation:

a² - 3a = a ( a - 3) a² - 9 = a² - 3² = (a+3) (a-3) a² - 4a + 3 = a² - 3a - a + 3 = a (a-3) - 1 (a-3) = (a-3) (a-1) নির্ণেয় গ.সা.গু = (a-3)

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322 . $9 a^{3} b^{2} c^{2}, 9 a^{3} b^{2} c^{2} 12 a^{2} b c, 15 a b^{3} c^{3}$ এর গ.সা.গু কোনটি?

A. 9abc
B. $9 a^{3} b^{3} c^{3}$
C. $3 a^{3} b^{3} c^{3}$
D. 3abc

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Answer: Option D

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পোস্টাল অপারেটর ২৩.০৮.২০১৯

323 . a+b, $a^{2} - b^{2}$ এবং $a^{3} + b^{3}$ এর গ. সা.গু কত?

A. $a^{2} - b^{2}$
B. $a - b$
C. ${(a + b)}^{2}$
D. $a + b$

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Answer: Option D

Explanation:

১ম রাশি= a + b ২য় রাশি= a^{2} - b^{2} = (a + b) (a - b) {৩য় রাশি=a}^{3 +} {+b}^{3} = (a + b) (a^{2} - a b + b^{2}) ∴ নির্ণেয় গ.সা.গু= (a + b)

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324 . If $x^{2} + 4 x + 13 = 1 + x^{2}$ then find out the value of $x^{2}$

A. 9
C. 4
D. 7

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Answer: Option A

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325 . $x^{2} - 3 x + 2$ এবং $x^{2} - 5 x + 6$ এর ল.সা.গু=কত?

A. (x-1)(x-2)(x-3)
B. (x-1)(x-2)(x+3)
C. (x-1)(x+2)(x-3)
D. (x-2)

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Answer: Option A

Explanation:

x²-3x+2 =x²-x-2x+2 =x(x-1)-2(x-1) =(x-1)(x-2) And, x²-5x+6 =x²-3x-2x+6 =(x-3)(x-2) So, HCM=(x-1)(x-2)(x-3) (ans)

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জনপ্রশাসন মন্ত্রণালয় ।। ব্যক্তিগত কর্মকর্তা (27-06-2016)

326 . $a (a + b), a b {(a + b)}^{2}$ এর গ.সা.গু কত ?

A. a(a+b)
B. ab(a+b)
C. a+b
D. $a {(a + b)}^{2}$

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Answer: Option A

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327 . $x - 2, x^{2} - 4$ এবং x+2 এর গ.সা.গু নিচের কোনটি?

B. 1
C. x-2
D. x+2

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Answer: Option B

Explanation:

x - 2 x + 4 x^{2} - 4 = (x + 2) (x - 2) H C M = 1 (a n s)

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328 . $x^{2} + 5 x, x^{2} - 25, x^{2} + 7 x + 10$

A. x-5
B. x+5
C. x(x+5)
D. x(x-5)

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Answer: Option B

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329 . $x^{2} - y^{2}, x^{2} + x y + y^{2}, x^{3} - y^{3}$ রাশিত্রয়ের ল.সা.গু-

A. $(x^{2} - y^{2}) (x^{2} + x y + y^{2})$
B. $x^{3} - y^{3}$
C. $x - y$
D. $x + y$

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Answer: Option A

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330 . If $(x^{2} - 4 x + 9) = 6,$ which of the following must be false?

A. x=1
B. x=3
C. x>3
D. x>0

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Answer: Option C

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