6166 . If x> 0, $(\frac{x}{50} + \frac{x}{25}) i s w h a t p e r c e n t o f x ?$

A. 6%
B. 25%
C. 33.33%
D. 60%

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Answer: Option A

Explanation:

6167 . If x/y =1/3, then value of $(x^{2} + y^{2}) / (x^{2} - y^{2})$ is-

A. -10/9
B. 5/4
C. -5/4
D. -5/3

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Answer: Option C

Explanation:

\frac{x}{y} = \frac{1}{3} \frac{x^{2}}{y^{2}} = \frac{1}{9} \frac{x^{2} + y^{2}}{x^{2} - y^{2}} = \frac{1 + 9}{1 - 9} = \frac{10}{- 8} = - \frac{5}{4}

6168 . If x% of a is the same as y% of b. Then z% of b =?

A. $\frac{y z}{x} % o f a$
B. $\frac{x y}{z} % o f a$
C. $\frac{x z}{y} % o f a$
D. All of these

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Answer: Option C

Explanation:

6169 . If x is not a negative number, what is the maximum possible value of $2^{2} - 3^{x} ?$

A. 3
B. 2
C. 1
D. 5

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Answer: Option A

Explanation:

To find the maximum possible value of 2^2−3^x, we need to determine the value of x that minimizes 3^x.

Since x is not a negative number, 3^x is a positive number for all real values of x.

To minimize 3^x, we want x to be as small as possible. Therefore, the maximum possible value of 2^2−3^x occurs when x=0:

2^2−3^0=4−1=3

So, the maximum possible value of 2^2−3^x is 3.

6170 . If x is negative , which of the following must also be negative?

A. ${(- X^{3})}^{2}$
B. $(- 1) x$
C. $1 - x$
D. $x^{3} - x^{2}$

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Answer: Option D

Explanation:

I f x i s n e g a t i v e t h e n x^{3} i s a l s o n e g a t i v e a n d x^{2} i s p o s i t i v e . T h e r e f o r e, x^{3} - x^{2} w i l l b e n e g a t i v e .

6171 . If x = 1, then $- (x^{4} + x^{3} + x^{2} + x) =$

A. -10
B. -4
D. 4

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Answer: Option B

Explanation:

6172 . If x = -3, then the value of $- 3 x^{2}$ is--

A. -27
B. -18
C. 27
D. 18

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Answer: Option A

Explanation:

6173 . If x +y = 1/a and x-y =a then the value of $x^{2} - y^{2}$ is:

A. 4
C. 1
D. $a^{2}$

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Answer: Option C

Explanation:

দেওয়া আছে, x + y = \frac{1}{a} এবং x-y=a {এখন, x}^{2} {-y}^{2} = (x + y) (x - y) = \frac{1}{a} ×a=1

6174 . If one factor of $2 a^{4} - 5 a^{3} + 6 a^{2} - 5 a + 2$ is $(a - 1),$ what is the other factor?

A. $2 a^{2} - a + 2$
B. $2 a^{2} - a - 2$
C. $a - 2$
D. $a^{2} - 1$

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Answer: Option A

Explanation:

6175 . If Michael can shovel all the snow of a standard driveway in 12 minutes, and Emon can shovel all the snow of a standard driveway in 36 minutes, then working together, how many minutes would it take for them both to shovel all the snow of a standard driveway?

A. 5
B. 9
C. 15
D. 18

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Answer: Option B

Explanation:

To find how long it would take for Michael and Emon to shovel the snow together, you can use the concept of their combined work rates.

Let M be Michael's work rate (driveways per minute) and E be Emon's work rate (driveways per minute).

Michael can shovel one driveway in 12 minutes, so his work rate is:

M = 1 driveway / 12 minutes = 1/12 driveways per minute

Emon can shovel one driveway in 36 minutes, so his work rate is:

E = 1 driveway / 36 minutes = 1/36 driveways per minute

When they work together, their combined work rate is the sum of their individual work rates:

Combined Work Rate = M + E = (1/12 + 1/36) driveways per minute

Now, find a common denominator to add the fractions:

Combined Work Rate = (3/36 + 1/36) driveways per minute = 4/36 driveways per minute

Simplify the fraction:

Combined Work Rate = 1/9 driveways per minute

Now that you know their combined work rate, you can calculate how long it would take for them to shovel one standard driveway together:

Time = 1 driveway / Combined Work Rate = 1 / (1/9) = 9 minutes

So, it would take Michael and Emon 9 minutes to shovel all the snow of a standard driveway together.

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

6176 . If m is an even integer and n is an odd integer and both are positive numbers then which of following must be even?

A. $m^{2} + n^{2}$
B. $m n + n^{2}$
C. $m^{3} + n^{2}$
D. $m n + m^{2}$

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Answer: Option D

Explanation:

6177 . If m and n are whole numbers such that m " = 121, then the value of ${(m - n)}^{n + 1} i s :$

A. 1
B. 10
C. 121
D. 1000

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Answer: Option D

Explanation:

m^{n} = 121 = {(11)}^{2} ∴ m = 11; n = 2 ∴ {(m - 1)}^{n + 1} = {(11 - 1)}^{2 + 1} = 10^{3} = 1000

6178 . If f is a function defined from R is given by f (x) = 3x -5, then $f^{- 1} (x)$ is given by :

A. 1/(3x-5)
B. (x +5)/3
C. does not exist since it is not a bisection
D. (3x + 5)/3

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Answer: Option B

Explanation:

Assit. Programmer | Sonali Bank- Rubali Bank- BD Krishi Bank - 16.11.2018

6179 . If a+b=13 and a-b=3 , then find the value of $a^{2} + b^{2}$

A. 69
B. 79
C. 89
D. 91

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Answer: Option C

Explanation:

(a^{2} + b^{2}) = 1 / 2 \{{(a + b)}^{2} + {(a - b)}^{2}\} = \frac{1}{2} \{{(13)}^{2} + {(3)}^{2}\} = \frac{1}{2} (169 + 9) = \frac{1}{2} \times 178 = 89

6180 . If a+b =8 and ab =15, what is the value of $a^{2} + b^{2} ?$

A. 94
B. 79
C. 34
D. 30

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Answer: Option C

Explanation:

আমরা জানি, {(a + b)}^{2} = a^{2} + 2 a b + b^{2} \Rightarrow {(8)}^{2} = a^{2} + b^{2} + 2 a b \Rightarrow 64 = a^{2} + b^{2} + (2 \times 15) \Rightarrow a^{2} + b^{2} + (2 \times 15) = 64 \Rightarrow a^{2} + b^{2} = 64 - 30 = 34

6175 . If Michael can shovel all the snow of a standard driveway in 12 minutes, and Emon can shovel all the snow of a standard driveway in 36 minutes, then working together, how many minutes would it take for them both to shovel all the snow of a standard driveway?

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