subject-primary-assistant-teacher-math?page=468-BD-Merit-Freelancing,-BCS,-Bank,-Primary,-Admission,-NTRCA

7006 . If $\log_{a} 2 = a a n d \log_{a} 5 = b t h e n \log_{a} 50$

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

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Answer: Option D

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বাংলাদেশ অর্থনৈতিক অঞ্চল কর্তৃপক্ষ (সহকারী ব্যবস্থাপক) 25-09-2020

A. 4.31

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Answer: Option A

Explanation:

দেওয়া আছে, \log_{5} 1024 = \frac{\log 1024}{\log 5} = \frac{\log 2^{10}}{\log \frac{10}{2}} = \frac{10 \log 2}{\log 10 - \log 2} = \frac{10 \times 0.3010}{1 - 0.3010} = \frac{3.01}{0.699} = \frac{3010}{699} = 4.31

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Microcredit Regulatory Authority (সহকারী পরিচালক) 05-03-2021

7008 . If k is an integer and $k = \frac{462}{n}$ , then which of the following could be the value of n?

A. 4
B. 5
C. 9
D. 22

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Answer: Option D

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বাংলাদেশ অর্থনৈতিক অঞ্চল কর্তৃপক্ষ (সহকারী ব্যবস্থাপক) 25-09-2020

A. 4
B. 5
C. 9
D. 22

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Answer: Option D

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বাংলাদেশ সিকিউরিটিজ অ্যান্ড এক্সচেঞ্জ কমিশন(ব্যক্তিগত কর্মকর্তা) 19-06-2021 || 2021

A. 2
B. 5
C. 10
D. 65

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Answer: Option D

Explanation:

To find the smallest possible value of k such that 1040k is the square of an integer, we need to factorize 1040 and then find the least value of k that makes the result a perfect square.

First, let's factorize 1040:

1040 = 2^4 * 5 * 13

Now, to make 1040k a perfect square, we need to make the exponents of all prime factors even. So, we need to find the least value of k that will make the exponents of 2, 5, and 13 even.

Exponent of 2: Since it's already raised to the power of 4, we don't need to change it.

Exponent of 5: We need to raise it to an even power. So, k should be multiplied by 5 to make it even.

Exponent of 13: We need to raise it to an even power. So, k should be multiplied by 13 to make it even.

Now, let's consider the exponents of 5 and 13:

Exponent of 5: It's currently 1, so we need to raise it to an even power, which means multiplying by 5 again. So, k should be at least 5.

Exponent of 13: It's currently 1, so we need to raise it to an even power, which means multiplying by 13 again. So, k should be at least 13.

To make sure both exponents are even, we need to take the least common multiple (LCM) of 5 and 13, which is 65.

So, the smallest possible value of k such that 1040k is the square of an integer is k = 65.

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বাংলাদেশ সিকিউরিটিজ অ্যান্ড এক্সচেঞ্জ কমিশন(সহকারী পরিচালক) 19-06-2021

A. 0.5
B. 1
C. 4
D. 8
E. None

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Answer: Option C

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তিতাস গ্যাস ট্রান্সমিশন এন্ড ডিষ্ট্রিবিউশন কোম্পানী লি. | সহকারী ব্যবস্থাপক (অ্যাকাউন্টস) | ২৭.০৪.২০১৮

A. I x-5 I
B. 2x + 50
C. I x-5 I
D. I 2x-3 I
E. X

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Answer: Option C

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জাতীয় নিরাপত্তা গোয়েন্দা সংস্থা (NSI) - সহকারী পরিচালক (23-05-2025)

A. 5 to 6
B. 5 to 7
C. 6 to 5
D. 7 to 5

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Answer: Option D

Explanation:

5 hrs 50 mins = 5 x 60 + 50 = 350 minutes

Salam makes = 350/5 = 70 boxes

Kalam makes = 350/7 = 50 boxes

Ratio = 70 : 50 = 7 : 5

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Global Islami Bank || Probationary Officer (10-02-2024) || 2024

7014 . If b > d and $a^{2} c - d > a^{2} e - d$ then which of the following must be true given that a,b,c,d & e are positive integers?

A. a > c
B. a > e
C. c > e
D. c < e
E. None

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Answer: Option C

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পায়রা বন্দর কর্তৃপক্ষ (বিভিন্ন পদ) 06-11-2020

A. 2
B. 1
C. abc
D. 1/abc

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Answer: Option B

Explanation:

From ax = b, we get x =b/a -------------------------- (i)
From by = c, we get y =c/b ---------------------------(ii)
From cz = a, we get z = c/a ---------------------------(iii)

Multiplying the left hand sides and right hand sides of (i), (ii) and (iii) we get
xyz = (b/a) x (c/b) x (c/a)

When we simplify, we find that xyz=1.

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7016 . If ${(\frac{a}{b})}^{x - 1} = {(\frac{b}{a})}^{x - 3}$ then x is equal to--

A. 1
B. 2
C. $\frac{1}{2}$
D. $\frac{1}{7}$

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Answer: Option B

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7017 . If $a b c$ are positive real numbers, then $\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c \times} \sqrt{c^{- 1} a}$ is equal to:

A. 8
B. 1
D. 4

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Answer: Option B

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7018 . If $\frac{a}{b} = \frac{1}{3}, = 2, \frac{c}{d} = \frac{1}{2}, \frac{d}{e}$ 3 and $\frac{e}{f} = \frac{1}{4}$ , then what is the value of $\frac{a b c}{d e f}$ ?

A. $\frac{3}{8}$
B. $\frac{27}{8}$
C. $\frac{2}{8}$
D. $\frac{27}{4}$

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Answer: Option A

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বাংলাদেশ রপ্তানি প্রক্রিয়াকরণ কর্তৃপক্ষ (সহকারী ম্যানেজার) 02-04-2021 || 2021

A. 38
B. 122
C. 182
D. 22

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Answer: Option A

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ওয়েজ আর্নার্স কল্যাণ বোর্ড || উপ সহকারী পরিচালক (22-11-2024) || 2024

7020 . If $a = \frac{2}{7}, b = \frac{1}{3}, x = \frac{1}{8},$ the value of $y = a - 3 b + 16 x$ is

A. $\frac{16}{7}$
B. $\frac{9}{7}$
C. $\frac{7}{16}$
D. $1$

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Answer: Option B

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7007 . If log 2= 0.3010 and log 3=0.4771. What is the value of log5 1024?

7009 . If k is an integer and k = 462/n, then which of the following could be the value of n?

7010 . If K is an integer, what is the smaller: possible value of k such that 1040 is the square of an integer?

7011 . If f(x)=5-2x and f(3k)=f(k+1),then f(k)= ?

7012 . If f(a) = a - 5 and f(b) = 5 - b what is the value of the expression x _________

7013 . If Elias makes a box every 5 minutes and Nadim takes minutes to make a box, what will be the ratio of the number of boxes produced by Elias to the number of boxes produced by Nadim if they work for 5 hours and 50 minutes?

7015 . If ax=b, by=c and cz=a, then the value of xyz is

7019 . If a=4, b=5, c=3, what is the value of 4ab-6ac+2bc?

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