286 . If x is an integer, then which of the following is always an even integer?

A. x - 1
B. x + 1
C. x + 2
D. 2x + 2

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Answer: Option D

Explanation:

287 . If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, What is the average of x, y and z in terms of m?

A. m+6
B. m+7
C. 2m+14
D. 2m+14

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Answer: Option B

Explanation:

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A. 2
B. 3
C. 4
D. 6

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Answer: Option D

Explanation:

Y/X = 1/3

বা, x = 3

এখন, x + 2y = 10

3y + 2y = 10

5y = 10

y = 10/8 = 2

x = 3 × 2 = 6

289 . $i f \frac{1}{x} > 1,$ which of the following must be true?

A. $1 < x^{2}$
B. $\frac{1}{x^{2}} > 2$
C. $x^{2} > 1$
D. $\frac{1}{x^{2}} < 1$

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Answer: Option D

Explanation:

Uttara Bank PLC || Probationary Officer (09-11-2024) || 2024

290 . $i f {(2 x - 1)}^{2}$ = 100 then which one of the following could equal x?

A. -11/2
B. -9/2
C. 11/2
D. 13/2

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Answer: Option C

Explanation:

সমন্বিত ব্যাংক অফিসার (ক্যাশ) || (02-06-2023)

291 . $i f (89^{2})$ is added to the square of a number, the answer so obtained is 16292. what is the $\frac{1}{26}$ of that number

A. 5.65
B. 2.70
C. 3.50
D. 6.66

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Answer: Option C

Explanation:

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292 . $i f a^{x} = b a n d b^{y} = a$ then find the value of xy.

A. 1
C. a
D. y

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Answer: Option A

Explanation:

বাংলাদেশ ব্যাংক || অফিসার (ক্যাশ) (21-07-2023) || 2023

293 . $i f x + \frac{1}{x} = 2, t h e n x^{3} + \frac{1}{x^{3}} e q u a l t o -$

A. 64
B. 14
C. 8
D. 2

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Answer: Option D

Explanation:

Janata Bank PLC || Officer (Rural Credit) (27-10-2023) || 2023

294 . $i f x = 10^{14}, y = 10^{0.7}$ and $x^{z} = y^{3}$ then is the value of $z$

A. $0.5$
B. $0.66$
C. $1.5$
D. $2$

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Answer: Option C

Explanation:

Uttara Bank PLC || Probationary Officer (09-11-2024) || 2024

295 . $i f x = \frac{\sqrt{3} - 2}{\sqrt{2} + 1}$ then which of the following equals to x - 4 ?

A. $- 2 \sqrt{2} + \sqrt{6} - \sqrt{3} - 2$
B. $- 2 \sqrt{2} + \sqrt{6} - \sqrt{3} + 2$
C. $\sqrt{3} - 2$
D. $\sqrt{3} + 2$

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Answer: Option A

Explanation:

Uttara Bank PLC || Probationary Officer (09-11-2024) || 2024

296 . $i f x = a + \frac{1}{a} a n d y = a - \frac{1}{a} t h e n x^{4} + y^{4} - 2 x^{2} y^{2} = ?$

A. 4
B. 8
C. 16
D. 20

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Answer: Option C

Explanation:

সমন্বিত ৮ ব্যাংক ও ১ টি আর্থিক প্রতিষ্ঠান || অফিসার জেনারেল (10-03-2023) | | 2023

297 . $i f 2 x - 1 \geq - 3, t h e n -$

A. $x \leq - 2$
B. $x \geq - 2$
C. $x \leq - 1$
D. $x \geq - 1$

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Answer: Option C

Explanation:

অফিসার (সাধারণ) ২৭.১২. ২০১৯

298 . $i f a^{2} + b^{2} = 45$ and ab = 18, $f i n d \frac{1}{a} + \frac{1}{b}$

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

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Answer: Option B

Explanation:

বাংলাদেশ ব্যাংক || অফিসার (ক্যাশ) (21-07-2023) || 2023

299 . $I f a^{x} = b^{y},$ $b y c a n d c^{z} = a,$ $w h a t i s t h e v a l u e v o f x y z ?$

A. $0$
B. $a b c$
C. $1$
D. $2$

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Answer: Option C

Explanation:

Uttara Bank PLC || Probationary Officer (09-11-2024) || 2024

300 . $i f \sec θ + \tan θ = x, t h e n \tan θ i s -$

A. $(x^{2} + 1) / x$
B. $(x^{2} - 1) / x$
C. $(x^{2} + 1) / 2 x$
D. $(x^{2} - 1) / 2 x$

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Answer: Option D

Explanation:

Step - by - step explanation:

Given : sec θ + tan θ = x …….. (1)

By using an identity , sec² θ - tan² θ = 1

(sec θ + tan θ)(sec θ - tan θ) = 1

[By using identity , a² - b² = (a + b) (a - b) ]

x (sec θ - tan θ) = 1

(sec θ - tan θ) = 1/x ……….(2)

On Subtracting eq 1 & 2,

sec θ + tan θ - (sec θ - tan θ) = (x - 1/x)

sec θ + tan θ - sec θ + tan θ) = (x - 1/x)

2 tan θ = (x - 1/x)

2 tan θ = (x² - 1)/x

tan θ = (x² - 1)/2x

Hence, the value of tan θ is (x² - 1)/2x.

অফিসার (সাধারণ) ২৭.১২. ২০১৯

286 . If x is an integer, then which of the following is always an even integer?

287 . If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, What is the average of x, y and z in terms of m?

288 . if y/x = 1/3 and x + 2y = 10, then x is--/যদি y/x = 1/3 এবং x + 2y = 10 হয় তাহলে x = ?

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