8371 . $\frac{x}{a} + a = \frac{x}{b} + b$ 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

8372 . $x^{2} - x - 6 = 0$ 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

8373 . $\log 2 (\frac{1}{32}$ এর মান_

A. $\frac{1}{25}$
B. -5
C. $\frac{1}{5}$
D. $\frac{- 1}{5}$

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Answer: Option B

Explanation:

\log_{2} (\frac{1}{32}) = \log_{2} (\frac{1}{2^{5}}) = {\log_{2}}^{2^{- 5}} = - 5 {\log_{2}}^{2} = - 5

8374 . যদি $(64) \frac{2}{3} + (625) \frac{1}{2} = 3 k$ হয় তবে kএর মান___

A. $9 \frac{2}{3}$
B. $11 \frac{1}{3}$
C. $12 \frac{2}{5}$
D. $13 \frac{2}{3}$

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Answer: Option D

Explanation:

(64) \frac{2}{3} + (625) \frac{1}{2} = 3 k \Rightarrow (4^{3}) \frac{2}{3} + \{{(25)}^{2}\} \frac{1}{2} = 3 k \Rightarrow 4^{2} + 25 = 3 k \Rightarrow 16 + 25 = 3 k \Rightarrow 41 = 3 k \Rightarrow k = \frac{41}{3} = 13 \frac{2}{3}

8375 . সরল করুনঃ $3 \log \frac{36}{25} + \log {(\frac{2}{9})}^{3} - 2 \log \frac{16}{125}$

A. $\log^{2}$
B. $\log^{3}$
C. $\log^{5}$
D. $\log^{7}$

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Answer: Option A

Explanation:

8376 . ${(1000)}^{\frac{y}{3}} = 10$ হলে y এর মান কত?

A. 2
B. 1
C. 3
D. 1.5

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Answer: Option B

Explanation:

(1000)y/3=10 (103)y/3=10 10y=101 Y=1

সংস্থাপন মন্ত্রণালয়ের প্রশাসনিক কর্মকর্তা-১৩.০১.২০০৭

8377 . $\log_{2} \sqrt{6} + \log_{2} \sqrt{\frac{2}{3}} =$ কত ?

A. 2
B. 1
C. 3

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Answer: Option B

Explanation:

{\log_{3}}^{\sqrt{6}} + {\log_{2}}^{\sqrt{\frac{2}{3}}} = {\log_{2}}^{6^{\frac{1}{2}}} + {\log_{2}}^{{\frac{2}{3}}^{\frac{1}{2}}} = \frac{1}{2} ({\log_{2}}^{6} + {\log_{2}}^{\frac{2}{3}}) = \frac{1}{2} {\log_{2}}^{(6 \times \frac{2}{3})} = \frac{1}{2} {\log_{2}}^{4} = \frac{1}{2} \log_{2} {(2)}^{2} = \frac{1}{2} \times 2 {\log_{2}}^{2} = {\log_{2}}^{2} = 1

8378 . ${(1000)}^{\frac{x}{3}} = 10$ হলে x এর মান কত?

A. 1
B. 2
C. 3
D. 10

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Answer: Option A

Explanation:

8379 . ${\log_{3}}^{81}$ এর মান কত?

A. 4
B. 9
C. 3
D. 27

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Answer: Option A

Explanation:

{\log_{3}}^{81} = \log_{3} {(3)}^{4} = 4 {\log_{3}}^{3} = 4 \times 1 = 4

4 হলে, নীচের কোনটি সঠিক?

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

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Answer: Option D

Explanation:

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

8381 . $\log_{a} 1$ এর মান কত?

A. 1
B. a
C. $\log_{a} 1$

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Answer: Option D

Explanation:

8382 . $a^{m} \times a^{n} \times a^{p} =$ কত?

A. $a^{m n p}$
B. $a^{m + n + p}$
C. $a^{- m n p}$
D. $a^{- m + n + p}$

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Answer: Option B

Explanation:

যখন বাজ বা ভিত্তি একই তখন গুন থাকলে পাওয়ার বা ঘাত যোগ হয়। ∴ a^{m} \times a^{n} \times a^{p} = a^{m + n + p}

8383 . $\log_{2} 64 + \log_{2} 8$ এর মান কত?

A. 9
B. 7
C. 28
D. 72

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Answer: Option A

Explanation:

{\log_{2}}^{64} + {\log_{2}}^{8} = {\log_{2}}^{2^{6}} + {\log_{2}}^{2^{3}} = 6 \times 1 + 3 \times 1 = 6 + 3 = 9

8384 . $\log_{4} 2$ এর মান কত?

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

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Answer: Option C

Explanation:

{\log_{4}}^{2} = x \Rightarrow 4^{x} = 2 \Rightarrow 2^{2 x} = 2 \Rightarrow 2 x = 1 \Rightarrow x = \frac{1}{2}

8385 . $\log_{x} = 144 = 4$ হলে , x এর মান কত?

A. $2 \sqrt{3}$
B. 3
C. 4
D. 12

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Answer: Option A

Explanation:

8380 . a/2 = b/3 = c/4 হলে, নীচের কোনটি সঠিক?

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