226 . (x + 3) (x - 3) = 16 হলে, x এর মান কত?

A. 16
B. 9
C. 5
D. 4

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Answer: Option C

Explanation:

দেওয়া আছে, (x + 3) (x - 3) = 16 \Rightarrow x^{2} - 3^{2} = 16 \Rightarrow x^{2} = 16 + 9 \Rightarrow x^{2} = 25 ∴ x = 5

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ডিপ্লোমা ইন নার্সিং ভর্তি পরীক্ষা। ২০২২-২০২৩

227 . ${\{{(x + 3 x)}^{2} {(x - 3 y)}^{2}\}}^{2}$ কে সরল করলে কয়টি পদ পাওয়া যাবে?

A. 4
B. 8
C. 5
D. 3

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Answer: Option C

Explanation:

\{{(x + 3 x)}^{2} {(x - 3 y)}^{2}\} = {[{\{(x + 3 x) (x - 3 y)\}}^{2}]}^{2} = {[{\{{(x)}^{2} - {(3 y)}^{2}\}}^{2}]}^{2} = {[{\{x^{2} - 9 y^{2}\}}^{2}]}^{2} = {\{x^{4} - 18 x^{2} y^{2} + 81 y^{4}\}}^{2} = (x^{4} - 18 x^{2} y^{2} + 81 y^{4}) (x^{4} - 18 x^{2} y^{2} + 81 y^{4}) = x^{8} - 18 x^{2} y^{2} + 81 x^{4} y^{4} - 18 x^{6} y^{2} + 324 x^{4} y^{4} - 1458 x^{2} y^{6} + 81 x^{4} y^{4} - 1458 x^{2} y^{6} + 651 y^{8} = x^{8} - 36 x^{6} y^{2} + 486 x^{4} y^{4} - 2916 x^{2} y^{6} + 66561 y^{8} ∴ {\{{(x + 3 x)}^{2} {(x - 3 y)}^{2}\}}^{2} এর ৫ টি পদ।

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

228 . $a^{x} = y$ হলে নিচের কোন সম্পর্কটি সঠিক?

A. $y = \log x^{a}$
B. $x = \log a^{y}$
C. $a = \log x^{y}$
D. $x = \log y^{a}$

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Answer: Option B

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229 . $8^{2 x + 3} = 2^{3 x + 6}$ হলে x এর মান-

A. -3
B. -1
D. 4

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Answer: Option B

Explanation:

8^{2 x + 3} = 2^{3 x + 6} \Rightarrow {(2^{3})}^{2 x + 3} = 2^{3 x + 6} \Rightarrow 6 x + 9 = 3 x + 6 \Rightarrow 6 x - 3 x = 6 - 9 \Rightarrow 3 x = - 3 \Rightarrow x = - 1 a n s

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230 . x+y=6,xy=8,then, ${(x - y)}^{3} = ?$

A. 3
B. 8
C. 9
D. 12

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Answer: Option B

Explanation:

আমরা জানি, {(x - y)}^{2} = {(x + y)}^{2} =4xy \Rightarrow 6^{2} - 4 \times 8 = 36 - 32 = 4 \Rightarrow x - y = 2 \Rightarrow {(x - y)}^{3} = 2^{3} = 8 a n s

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যুব ও ক্রীড়া মন্ত্রণালয়ের যুব উন্নয়ন অধিদপ্তর | ক্যাশিয়ার | ০৪.০৫.২০১৮

231 . $a^{3} + b^{3} = 16$ এবং $a \pm b = 4$ হলে $a b = ?$

A. 1
B. 2
C. 3
D. 4

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Answer: Option D

Explanation:

a^{3} + b^{3} = 16 \Rightarrow {(a + b)}^{3} - 3 a b (a + b) = 16 \Rightarrow 4^{3} - 3 a b . 4 = 16 \Rightarrow 64 - 12 a b = 16 \Rightarrow - 12 a b = - 48 \Rightarrow a b = \frac{- 48}{- 12} ∴ a b = 4 a n s

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বিভিন্ন মন্ত্রণালয়/বিভাগ/অধিদপ্তর | প্রশাসনিক কর্মকর্তা (মুক্তিযোদ্ধা) | ০৮.০৩.২০১৮

232 . x+y+z=0 হলে $\frac{1}{x} \frac{1}{3} (x^{3} + y^{3} + z^{3})$ এর মান কত?

A. 3xyz
B. -3xyz
C. -xyz
D. xyz

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Answer: Option D

Explanation:

দেওয়া আছে, x + y + z = 0 . . . . . . . (i) ∴ (\frac{1}{3}) (x^{3} + y^{3} + z^{3}) = \frac{1}{3} (x^{3} + y^{3} + z^{3} - 3 x y z) + x y z = \frac{1}{3} \{(x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x)\} + x y z = \frac{1}{3} \{0 (x^{2} + y^{2} + z^{2} - x y - y z - z x)\} + x y z = 0 + x y z = x y z a n s

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233 . a+b=8 ab=15 হলে a2-b2 সমান কত?

A. 34
B. 39
C. 36
D. 49

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Answer: Option A

Explanation:

দেওয়া আছে, (a + b) =8, ab=15 a^{2} - b^{2} = {(a + b)}^{2} - 2 a b = 8^{2} - 2.15 = 64 - 30 = 34 a n s

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234 . $x^{2} + y^{2} + b = 8, x y = 7$ হলে, ${(x + y)}^{2}$ এর মান কত?

A. ১৪
B. ১৬
C. ২২
D. ৩০

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Answer: Option C

Explanation:

দেওয়া আছে, x^{2} + y^{2} = 8 এবং xy = 7 এখন, x^{2} + y^{2} = 8 {(x + y)}^{2} - 2 xy = 8 (x + y) - 2 \times 7 = 8 {(x + y)}^{2} = 22

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প্রতিরক্ষা মন্ত্রণালয়ের মিলিটারি ইঞ্জিনিয়ার সার্ভিসেস | স্টোরম্যান | ১৮.০৫.২০১৮

235 . a+b+c=5 ab + bc +ca =12 হলে $a^{2} + b^{2} + c^{2} = ক ত ?$

A. 1
B. 2
C. 4
D. 3

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Answer: Option A

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236 . $f (x) = x^{3} + a x^{3} + 2 x^{3} = 0$ হলে, a এর মান কত?

A. 3
B. 1
D. -3

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Answer: Option D

Explanation:

f (x) = x^{3} + a x^{3} + 2 x^{3} = 0 \Rightarrow x^{3} (1 + a + 2) = 0 \Rightarrow a + 3 = 0 ∴ a = - 3

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পররাষ্ট্র মন্ত্রণালয় প্রশাসনিক কর্মকর্তা ২৫.১০.২০১৯

237 . $4 x^{2} + 7 x^{2} + 3 x^{2} = ?$

A. $14 x^{4}$
B. $14 x^{6}$
C. $14 x^{2}$
D. $12 x^{2}$

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Answer: Option C

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238 . x,y বাস্তব রাশি এবং $f (x, y) = x^{2} y^{2}$ , যদি $h (x) = (x^{2} - 5)$ হয় , তবে f(2, h(3)) এর মান কত?

A. 64
B. 16
C. 96
D. 32

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Answer: Option A

Explanation:

f (x, y) = x^{2} y^{2} এখানে, h (x) {=x}^{2} -5 \Rightarrow h (3) = 3^{2} - 5 \Rightarrow h (3) = 4 f (2, 4) = 2^{2} \times 4^{2} = 64

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239 . $16 x^{2} - 8 x + 9 = 0$ সমীকরণটির মূলদ্বয়ের যোগফল কত?

A. $\frac{3}{4}$
B. $\frac{1}{2}$
C. 144
D. $\frac{9}{16}$

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Answer: Option B

Explanation:

a x^{2} + b x + c = 0 সমীকরণের মূলের যোগফল= \frac{- b}{a} {16x}^{2} -8x+9=0 সমীকরণের মূলের যোগফল= \frac{- 8}{16} = \frac{1}{2}

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গণপূর্ত অধিদপ্তর | উপ-সহকারী প্রকৌশলী ও ড্রাফটম্যান/ সিভিল | ২৫.০১.২০১৮

240 . a এর মান কত হলে $9 - 12 x + a x^{2}$ রাশিটি একটি পূর্ণবর্গ হবে?

A. 8
B. 6
C. 1
D. 4

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Answer: Option D

Explanation:

9 - 12 x + a x^{2} = 32 - 2.3.2 x + a x^{2} রাশিমালা হতে স্পষ্ট a x^{2} = {(2 x)}^{2} হলে রাশিটি পূর্ণ বর্গ হবে। \Rightarrow a x^{2} = 4 x^{2} ∴ a = 4

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226 . (x + 3) (x - 3) = 16 হলে, x এর মান কত?

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