226 . ${(1 - x)}^{- 2}$ এর সাধারণ পদ কোনটি?

A. ${(- 1)}^{r} r x^{r}$
B. $(r + 1) x^{r + 1}$
C. $(r + 1) x^{r}$
D. ${(- 1)}^{r} (r + 1) x^{r}$

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Answer: Option D

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227 . যদি $\frac{x}{y} = \frac{3}{4}$ হয়, তবে $\frac{x + y}{x - y}$ এর মান কত?

A. $2$
B. $- 7$
C. $5$
D. $7$

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Answer: Option B

Explanation:

\frac{x}{y} = \frac{3}{4} \Rightarrow \frac{x + y}{x - y} = \frac{3 + 4}{3 - 4} = \frac{7}{- 1} = - 7

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সহকারী উপজেলা/থানা শিক্ষা অফিসার (মুক্তিযোদ্ধা ও ক্ষুদ্র নৃ-গোষ্ঠী কোটা) (21-08-2015)

228 . x + y = 10, $x^{2} - y^{2} = 10$ হলে, 12xy = ?

A. 24.75
B. 297
C. 247.5
D. 247

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Answer: Option B

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B unit (অ-বাণিজ্য শাখা) শিফট-২ (২০২৩-২০২৪) || (07-03-2024) || রাজশাহী বিশ্ববিদ্যালয়

229 . $x^{2} - 4 x + 3$ এর উৎপাদক কোনটি?

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

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Answer: Option B

Explanation:

x^{2} - 4 x + 3 = x^{2} - 3 x - x + 3 = x (x - 3) - 1 (x - 3) = (x - 1) (x - 3)

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ডিপ্লোমা ইন নার্সিং সায়েন্স এন্ড মিডওয়াইফারি ভর্তি পরীক্ষা || ২০২৩-২০২৪ || নার্সিং(Nursing) ভর্তি পরীক্ষা || 2024

230 . $\frac{a}{2} = \frac{b}{3} = \frac{c}{4}$ হলে নিচের কোনটি সঠিক?

A. 4 : 3 : 2
B. 6 : 7 : 8
C. 8 : 7 : 6
D. 2 : 3 : 4

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Answer: Option D

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231 . a + b = 8 এবং ab = 15 হলে $a^{2} + b^{2}$ এর মান কত?

A. 40
B. 36
C. 36
D. 34

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Answer: Option D

Explanation:

দেওয়া আছে, a+b=8 a b = 15 a^{2} - b^{2} = {(a + b)}^{2} - 2 a b = 8^{2} - 2 \times 15 = 64 - 30 = 34

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A. {−3, −2, −1}
B. {−4,0}
C. {1,2,3}
D. কোনোটিই নয়

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Answer: Option D

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233 . (x - y) = 2 এবং xy= 24 হলে (x + y) এর মান কত?

A. 20
B. 100
C. 48
D. 10

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Answer: Option D

Explanation:

{(x + y)}^{2} = {(x - y)}^{2} + 4 x y \Rightarrow {(x + y)}^{2} = 2^{2} + 4.24 \Rightarrow {(x + y)}^{2} = 4 + 96 \Rightarrow {(x + y)}^{2} = 100 \Rightarrow x + y = 10

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ডিপ্লোমা ইন নার্সিং ভর্তি পরীক্ষা। ২০২২-২০২৩

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

235 . ${\{{(x + 3 x)}^{2} {(x - 3 y)}^{2}\}}^{2}$ 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)

236 . $a^{x} = y$ 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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237 . $8^{2 x + 3} = 2^{3 x + 6}$ 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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238 . 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

239 . $a^{3} + b^{3} = 16$ 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

240 . 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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232 . |x+2|<2 এবং x∈N হলে, x এর মান কত?

233 . (x - y) = 2 এবং xy= 24 হলে (x + y) এর মান কত?

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

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