subject-bank-job-math-5?page=18-BD-Merit-Freelancing,-BCS,-Bank,-Primary,-Admission,-NTRCA

256 . $x^{2} + y^{2} = x y$ হলে, ${(x + y)}^{4}$ এর মান কত?

A. $x^{2} y^{2}$
B. xy
C. ${(x^{2} + y^{2})}^{2}$
D. $9 x^{2} y^{2}$

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Answer: Option D

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পররাষ্ট্র মন্ত্রণালয় ব্যক্তিগত কর্মকর্তা ২৭.০৯.২০১৯

257 . $2 x + \frac{2}{y} = 4$ হলে x এর মান কত?

A. 2
B. 1
C. $\frac{1}{2}$
D. $\frac{1}{0}$

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Answer: Option B

Explanation:

There is wrong on this question.write question will be 2X + (2/X) = 4.As here only given one equation thats why unknown parameter must be 1.Then what will be the value of X = ? if we put X = 1,then LHS = 4 & RHS = 4 Ans:1

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বাংলাদেশ পাবলিক সার্ভিস কমিশন -২০১৯ পদের নাম : বিভিন্ন মিন্ত্রণালয়ের প্রশাসনিক কর্মকর্তা ( ১৬-০৯-২০১৯)

258 . $a^{2} - 6 a + 1 = 0$ হলে $a + \frac{1}{a} = ?$

A. $\sqrt{3}$
B. $3 \sqrt{3}$
C. 6
D. 9

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Answer: Option C

Explanation:

দেওয়া আছে, a^{2} -6a+1=0 \Rightarrow a^{2} + 1 = 6 a \Rightarrow \frac{a^{2} + 1}{a} = \frac{6 a}{a} \Rightarrow \frac{a^{2}}{a} + \frac{1}{a} = 6 \Rightarrow a + \frac{1}{a} = 6

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259 . $x^{y} = y^{x}, x = 2 y (x \neq 0, y \neq 0)$ হলে,(x,y) = কত?

A. (8,4)
B. ( 6,3)
C. (2,1)
D. (4,2)

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Answer: Option D

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260 . ${(x^{2})}^{3}$ কে $x^{3}$ দ্বারা গুণ করলে কত হবে?

A. $x^{9}$
B. $x^{18}$
C. $x^{27}$
D. $x^{24}$

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Answer: Option A

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261 . $a^{5} . a . a^{- 6}$ = কত?

A. a
B. $a^{2}$
D. 1

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Answer: Option D

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262 . $x^{2} - x - 6 = 0$ সমীকরণের মূলদ্বয় হবে-

A. 3,2
B. 3,-2
C. -3,2
D. -3,-2

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Answer: Option B

Explanation:

x^{2} - x - 6 = 0 \Rightarrow x^{2} - 3 x + 2 x - 6 = 0 \Rightarrow x (x - 3) + 2 (x - 3) = 0 \Rightarrow (x - 3) (x + 2) = 0 x - 3 = 0 ∴ x = 3 x + 2 = 0 ∴ x = - 2 ∴ x = 3, - 2

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263 . $\frac{x}{a} + a = \frac{x}{b} + b$ হলে ,x এর মান কত ?

A. ab
B. a
C. b
D. a/b

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Answer: Option A

Explanation:

\frac{x}{a} + a = \frac{x}{b} + b \Rightarrow \frac{x}{a} - \frac{x}{b} = b - a \Rightarrow \frac{b x - a x}{a b} = b - a \Rightarrow \frac{x (b - a)}{a b} = b - a \Rightarrow x = \frac{a b (b - a)}{(b - a)} ∴ x = a b

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264 . $2^{x} + 2^{1 - x} = 3$ হলে, x = কত?

A. (1,2)
B. (0,2)
C. (1,3)
D. (0,1)

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Answer: Option D

Explanation:

2^{x} + 2^{1 - x} = 3 \Rightarrow 2^{x} + \frac{2^{1}}{2^{x}} = 3 \Rightarrow a + \frac{2}{a} = 3 [2^{x} = a] \Rightarrow a^{2} + 2 = 3 a \Rightarrow a^{2} - 3 a + 2 = 0 \Rightarrow a^{2} - 2 a - a + 2 = 0 \Rightarrow a (a - 2) - 1 (a - 2) = 0 \Rightarrow (a - 1) (a - 2) = 0 এখন, a-2=0                             আবার, a-1=0 a = 2 a = 1 \Rightarrow 2^{x} = 2^{1} \Rightarrow 2^{x} = 2^{0} \Rightarrow x = 1 \Rightarrow x = 0 ∴ x = 1, 0

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রেলপথ মন্ত্রণালয় ।। কম্পিউটার অপারেটর (12-06-2021)

265 . $5 (1 - x) + 3 (2 - x) = - 29$ সমীকরণের সমীকরণ হবে-

A. 4
B. 8
C. 5
D. 10

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Answer: Option C

Explanation:

5 (1 - x) + 3 (2 - x) = - 29 \Rightarrow 5 - 5 x + 6 - 3 x = - 29 \Rightarrow - 8 x = - 40 \Rightarrow x = 5

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বিভিন্ন মন্ত্রণালয়/বিভাগ/অধিদপ্তর | ব্যক্তিগত কর্মকর্তা (সাধারণ) | ১২.০৩.২০১৮

266 . $3 x^{2} - x - 10$ এর উৎপাদক কত?

A. (x+2)(3x-5)
B. (x+2)(3x-5)
C. (x-2)(3x-5)
D. (x-2)(3x+5)

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Answer: Option A

Explanation:

3 x^{2} + x - 10 = 3 x^{2} + 6 x - 5 x - 10 = 3 x (x + 2) - 5 (x + 2) = (3 x - 5) (x + 2)

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শিক্ষা মন্ত্রণালয়ের অধীন কারিগরি শিক্ষা অধিদপ্তর | জুনিয়র ইনস্ট্রাক্টর | ০২.১১.২০১৮

267 . $x^{2} - y^{2} + 2 x + 1$ এর উৎপাদক কত?

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

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Answer: Option D

Explanation:

x^{2} - y^{2} + 2 x + 1 = x^{2} + 2 . x . 1 + 1^{2} - y^{2} = {(x + 1)}^{2} - y^{2} = (x + 1 + y) (x + 1 - y) = (x + y + 1) (x - y + 1) ∴ x^{2} - y^{2} + 2 x + 1 এর একটি উৎপাদক হচ্ছে (x + y + 1) এবং অপরটি হচ্ছে (x - y + 1)

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স্বরাষ্ট্র মন্ত্রণালয়ের অধীন আনসার ও ভিডিপি অধিদপ্তরের সার্কেল অ্যাডজুট্যান্ট-২১.০৫.২০১০

268 . $2 a^{2} + 6 a - 80$ এর একটি উৎপাদক কোনটি?

A. $2 (a - 8)$
B. $(a + 5)$
C. $(a + 4)$
D. $(a + 8)$

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Answer: Option D

Explanation:

2 a^{2} + 6 a - 80 = 2 (a^{2} + 3 a - 40) = 2 (a^{2} + 8 a - 5 a - 40) = 2 \{a (a + 8) - 5 (a + 8)\} = 2 (a + 8) (a - 5) ∴ নির্ণেয় উৎপাদক হলো (a + 8)

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সড়ক ও জনপথ অধিদপ্তরের উপসহকারী প্রকৌশলী-৩১.১২.২০১০

269 . $x^{3} + 6 x^{2} y + 11 x y^{2} + 6 y^{3}$ এর উৎপাদকে বিশ্লেষণ কোনটি?

A. (x+y)(x+3y)(x+5y)
B. (x+y)(x+2y)(x+3y)
C. (x+y)(x+4y)(x+3y)
D. (x-y)(x+y)(x+2y)

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Answer: Option B

Explanation:

x^{3} + 6 x^{2} y + 11 x y^{2} + 6 y^{3} = x^{3} + x^{2} y + 5 x^{2} y + 5 x y^{2} + 6 x y^{2} + 6 y^{3} = x^{2} (x + y) + 5 x y (x + y) + 6 y^{2} (x + y) = (x^{2} + 5 x y + + 6 y^{2}) (x + y) = (x^{2} + 3 x y + 2 x y + 6 y^{2}) (x + y) = \{x (x + 3 y) + 2 y (x + 3 y)\} (x + y) = (x + 3 y) (x + 2 y) (x + y) = (x + y) (x + 2 y) (x + 3 y)

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১৮ তম শিক্ষক নিবন্ধন পরীক্ষা (স্কুল পর্যায়) (15-03-2024)

270 . $x^{2} - 7 x + 6$ এর উৎপাদকে বিশ্লেষিত রুপ নিচের কোনটি?

A. (x -2) (x-3)
B. (x-1) (x+8)
C. (x-1) (x-6)
D. (x+1) (x+6)

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Answer: Option C

Explanation:

x^{2} - 7 x + 6 = x^{2} - 6 x - x + 6 = x (x - 6) - 1 (x - 6) = (x - 1) (x - 6)

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কারিগরি শিক্ষা অধিদপ্তর (হিসাব সহকারী/অফিস সহকারী কাম কম্পিউটার অপারেটর) 20-08-2021 || 2021

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