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1186 . x+y=8, xy==15 হলে ${(x - y)}^{4} = ?$

A. 4
B. 8
C. 9
D. 16

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Answer: Option D

Explanation:

আমরা জানি, {(x - y)}^{2} = {(x + y)}^{2} - 4 x y = 8^{2} - 4 \times 15 = 64 - 60 = 4 ∴ x - y = 2 ∴ (x + y) + (x - y) = 8 + 2 \Rightarrow 2 x = 10 ∴ x = 5 ∴ y = 8 - 5 = 3 ∴ {(x - y)}^{4} = {(5 - 3)}^{4} = 2^{4} = 16

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1187 . $x + \frac{1}{x} = 3$ হলে $x^{3} + \frac{1}{x^{3}}$ এর মান কত?

A. 16
B. 18
C. 22
D. 1

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Answer: Option B

Explanation:

দেওয়া আছে, x + \frac{1}{x} = 3 এখন, x^{3} + \frac{1}{x^{3}} = {(x + \frac{1}{x})}^{3} - 3 . x . \frac{1}{x} (x + \frac{1}{x}) = 3^{3} - 3.3 = 27 - 9 = 18

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অর্থ মন্ত্রণালয়ের অফিস সহকারী-০৬.০৫.২০১১

1188 . $\frac{x}{y} + \frac{y}{x} = 6$ হলে $\frac{x^{2}}{y^{2}} + \frac{y^{2}}{x^{2}}$ এর মান কত?

A. 30
B. 32
C. 34
D. 36

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Answer: Option C

Explanation:

{(x/y) + (y + x)}² = 6²

= > (x²/y²) + 2.(x/y).(y/x) + (y²/x²) = 6²

= > (x²/y²) + (y²/x²) = 36 - 2 = 34

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1189 . $x^{2} - 4 x + 1 = 0$ হলে $x \div (x^{2} - 3 x + 1)$ এর মান কত?

B. 1
C. 2
D. 4

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Answer: Option B

Explanation:

x² - 4x + 1 = 0

বা, x² + 1 = 4x

x/( x² - 3x + 1)

বা, x / 4x - 3x

∴x/x = 1

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বাংলাদেশ পাবলিক সার্ভিস কমিশন (BPSC) || জুনিয়র ইন্সট্রাক্টর (18-03-2023) ||

1190 . $\frac{a^{3} - b^{3}}{a + b}$ কে $\frac{a^{4} + b^{4} + a^{2} b^{2}}{a^{3} + b^{3}}$ দ্বারা ভাগ করলে ভাগফল কত হবে?

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

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Answer: Option A

Explanation:

\frac{a^{3} - b^{3}}{a + b} \div \frac{a^{4} + b^{4} + a^{2} b^{2}}{a^{3} + b^{3}} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \div \frac{{(a^{2})}^{2} + 2 . a^{2} . b^{2} + {(b^{2})}^{2} - {(a b)}^{2}}{(a + b) (a^{2} - a b + b^{2})} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \times \frac{(a + b) (a^{2} - a b + b^{2})}{{(a^{2} + b^{2})}^{2} - {(a b)}^{2}} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \times \frac{(a + b) (a^{2} - a b + b^{2})}{(a^{2} + b^{2} + a b) (a^{2} + b^{2} - a b)} = (a - b)

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1191 . $4 x^{2} - 2$ হতে কত বিয়োগ করলে রাশিটি পূর্ণবর্গ হবে?

A. $- \frac{1}{4 x^{2}}$
B. $- \frac{1}{2 x^{2}}$
C. $\frac{1}{4 x^{2}}$
D. $\frac{1}{2 x^{2}}$

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Answer: Option A

Explanation:

4 x^{2} - 2 = {(2 x)}^{2} - 2.2 x . \frac{1}{2 x} + {(\frac{1}{2 x})}^{2} - {(\frac{1}{2 x})}^{2} = {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} {সুতরাং, 4x}^{2} -2 হতে - \frac{1}{4 x^{2}} বিয়োগ করলে রাশিটি পূর্ণবর্গ হবে। {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} - (- \frac{1}{4 x^{2}}) = {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} + \frac{1}{4 x^{2}} = {(2 x - \frac{1}{2 x})}^{2}

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1192 . $a^{4} - 51 a^{2} + 1 = 0$ হলে $a - \frac{1}{a}$ এর মান কত?

A. $\pm 9$
B. $\pm 7$
C. $\pm 5$
D. $\pm 3$

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Answer: Option B

Explanation:

দেওয়া আছে, a^{4} - 51 a^{2} + 1 = 0 \Rightarrow a^{4} + 1 = 51 a^{2} \Rightarrow \frac{a^{4} + 1}{a^{2}} = \frac{51 a^{2}}{a^{2}} \Rightarrow \frac{a^{4}}{a^{2}} + \frac{1}{a^{2}} = 51 \Rightarrow a^{2} + \frac{1}{a^{2}} = 51 এখন, {(a - \frac{1}{a})}^{2} = {(a + \frac{1}{a})}^{2} - 4 . a . \frac{1}{a} = a^{2} + 2 . a . \frac{1}{a} + \frac{1}{a^{2}} - 4 = a^{2} + \frac{1}{a^{2}} - 2 = 51 - 2 = 49 ∴ a - \frac{1}{a} = \sqrt{49} = \pm 7

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1193 . $x^{2} + y^{2} + x^{2} = 5, x + y + z = 3$ হলে yz + zx -xy এর মান কত?

A. -5
B. -4
C. -3
D. -2

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Answer: Option D

Explanation:

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1194 . m-n=x এবং mn = $6 x^{2}$ হলে $m^{3} - n^{3}$ = কত?

A. $19 x^{2}$
B. $19 x^{3}$
C. $18 x^{2}$
D. $18 x^{3}$

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Answer: Option B

Explanation:

m^{3} - n^{3 = {(m - n)}^{3} + 3 m n (m - n) = x^{3} + 3.6 x^{2} . x = x^{3} + 18 x^{3} = 19 x^{3}}

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

1195 . $x^{4} - x - 1 = 0$ হলে, $x - \frac{1}{x^{2}} =$ কত ?

B. 1
C. 2
D. 4

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Answer: Option B

Explanation:

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1196 . b এর মান কত হলে $16 a^{2} - a b + 49$ রাশিটি পূর্ণবর্গ হবে ?

A. 48
B. 56
C. 49
D. 32

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Answer: Option B

Explanation:

16a^2 -ab + 49 =(4a)^2 - ab +(7)^2 =(4a)^2 - 2.4a.7 + (7)^2 =(4a)^2 - 56a + (7)^2 [ দেখা যাচ্ছে b এর জায়গায় 56 বসালে রাশিটি পূর্ণবর্গ হবে ] তাই b =56

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বাংলাদেশ পরিসংখ্যান ব্যুরো | পরিসংখ্যান সহকারী- 05-11-2021

1197 . $2 x^{2} + x - 15$ এর উৎপাদক কোনটি?

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

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Answer: Option A

Explanation:

2 x^{2} + x - 15 = 2 x^{2} + 6 x - 5 x - 15 = 2 x (x + 3) - 5 (x + 3) = (2 x - 5) (x + 3)

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বাংলাদেশ পল্লী বিদ্যুতায়ন বোর্ড || মিটার রিডার কাম মেসেঞ্জার (04-05-2024)

1198 . $x^{2} - y^{2} + 2 y - 1$ এর একটি উৎপাদক $x + y - 1$ হলে, অপর উৎপাদক কত?

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

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Answer: Option B

Explanation:

x^{2} - y^{2} + 2 y - 1 = x^{2} - (y^{2} - 2 y + 1) = x^{2} - {(y - 1)}^{2} = (x + y - 1) (x - y - 1)

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জাতীয় নিরাপত্তা গোয়েন্দা সংস্থা-ফিল্ড অফিসার-০৮.১০.২০২১ || 2021

1199 . $3 x^{3} + x - 10$ এর একটি উৎপাদক $x + 2$ হলে অপরটি কত?

A. $2 x - 5$
B. $2 x + 5$
C. $3 x - 5$
D. $3 x + 5$

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Answer: Option C

Explanation:

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1200 . $2 a^{2} + 7 a b - 15 b^{2}$ এর উৎপাদক বিশ্লেষন কত হয়?

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

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Answer: Option A

Explanation:

2a²+7ab-15b²

=2a²+10ab-3ab-15b²

=2a(a+5b)-3b(a+5b)

=(2a-3b)(a+5b).

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