346 . $2 x^{4} + x - 15$ এর উৎপাদক কোনটি ?

A. (x-3)(2x-5)
B. $(x + 3) (2 x + 5)$
C. $(x + 3) (2 x - 5)$
D. $(x - 3) (2 x + 5)$

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Answer: Option B

Explanation:

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347 . 2y = 2x-4 এবং 4x-5y=3 হলে x ও y এর মান কত?

A. x = 5, y = 7
B. x = 2, y = 5
C. x = 3, y = 7
D. x = 7, y = 5

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Answer: Option D

Explanation:

দেওয়া আছে,

২y=2x-4…….(1)

এবং

4x-5y=3…….(2)

(1)*2-(2) =>y=5

y এর মান(1)নং এ বসিয়ে পাই, 10=2x-4 বা, x=7

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উপজেলা/থানা শিক্ষা অফিসার (19-03-2004)

348 . $9 x^{2} - 9 x - 4$ এর একটি উৎপাদক 3x + 1 হলে অপরটি কত?

A. (3x+1)
B. (3x-4)
C. (3x+4)
D. কোনোটিই নয়

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Answer: Option B

Explanation:

9 x^{2} - 9 x - 4 = 9 x^{2} - 12 x + 3 x - 4 = 3 x (3 x - 4) + 1 (3 x - 4) = (3 x - 4) (3 x + 1)

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বাংলাদেশ বেসামরিক বিমান চলাচল কর্তৃপক্ষ || নিরাপত্তা অপারেটর (01-10-2021)

349 . a+b=4 এবং a-b=2 হলে, $a^{2} + b^{2}$ এর মান কত ?

A. 5
B. 10
C. 15
D. 20

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Answer: Option B

Explanation:

a^{2} + b^{2} = \frac{1}{2} \{{(a + b)}^{2} + {(a - b)}^{2}\} = \frac{1}{2} (4^{2} + 2^{2}) = \frac{1}{2} (16 + 4) = \frac{1}{2} \times 20 = 10

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তথ্য মন্ত্রণালয়ের অধীন বিটিভি-এর সহকারী প্রকৌশলী (সিভিল) - 27.08.2017

350 . a+b+c =21 এবং ab+be+ca=143 হলে $a^{2} + b^{2} + c^{2}$ এর মান কত?

A. 160
B. 175
C. 165
D. 155

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Answer: Option D

Explanation:

Given: a + b + c = 21 ab + bc + ca = 143

We want to find: a^2 + b^2 + c^2

Now, let's use the following identity: (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + ac + bc)

We know that (a + b + c)^2 = 21^2 = 441 and ab + bc + ca = 143.

Now, plug these values into the identity: 441 = a^2 + b^2 + c^2 + 2(143)

Simplify the equation: 441 = a^2 + b^2 + c^2 + 286

Now, isolate a^2 + b^2 + c^2: a^2 + b^2 + c^2 = 441 - 286 = 155

So, we have a^2 + b^2 + c^2 = 155.

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351 . $x + y = 8, x y = = 15$ হলে ${(x - y)}^{4} = ?$

A. 4
B. 8
C. 9
D. 16

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Answer: Option D

Explanation:

আমরা জানি,
(x – y)² = (x + y)² - 4xy
= (8)² - 4×15
= 64 - 60 = 4
∴ x - y = 2
∴(x + y) + (x - y) = 8 + 2
= > 2x = 10
∴ x = 5
∴y = 8 - 5 = 3
সুতরাং, (x - y)⁴ = (5 - 3)⁴ = 24 = 16.

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352 . a=1. b=2, c=3 হলে $a^{2} + 2 a b - c$

A. 1
B. 2
C. 4
D. 6

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Answer: Option B

Explanation:

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353 . $a^{2} - a - 56$ হলে a এর মান কত?

A. 7, -8
B. 8, -7
C. 5, -6
D. 14, -4

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Answer: Option B

Explanation:

a^{2} - a - 56 = 0 \Rightarrow a^{2} - 8 a + 7 a - 56 = 0 \Rightarrow a (a - 8) + 7 (a - 8) = 0 \Rightarrow (a - 8) + (a + 7) = 0 a = 8, - 7

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354 . $|2 x - 5| < 7$ অসমতাটির সমাধান কত?

A. -3
B. -2
C. 1< x< 5
D. -1 < x <6

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Answer: Option D

Explanation:

|2 x - 5| < 7 = 7 < 2 x - 5 < 7 = 7 + 5 < 2 x - 5 + 5 < 7 + 5 = 2 < 2 x < 12 = 1 < x < 6

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355 . $(a + b) = \sqrt{7}$ এবং $(a - b) = \sqrt{5}$ হলে, $8 a b (a^{2} + b^{2}) =$ কত?

A. 12
B. 24
C. 36
D. 40

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Answer: Option B

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356 . $4 x^{2} - 13 x - 12$ এর উৎপাদক কত ?

A. $(x - 4) (4 x + 3)$
B. $(2 x - 4) (2 x - 3)$
C. $(2 x - 4) (2 x + 3)$
D. $(x + 4) (4 x - 3)$

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Answer: Option A

Explanation:

4x²-13x-12

=4x²-16x+3x-12

=4x(x-4)+3(x-4)

=(x-4)(4x+3)

(ans)

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প্রাথমিক বিদ্যালয় সহকারী শিক্ষক নিয়োগ পরীক্ষা-2012-(যমুনা-05) (26-02-2012)

A. 57
B. 46
C. 35
D. 24

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Answer: Option D

Explanation:

৪ - ২ = ২
৪২ = ২৪x২ - ৬

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সহকারী উপজেলা/থানা শিক্ষা অফিসার (15-04-2005)

A. ৬১
B. ৯৪
C. ৭২
D. ৮৩

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Answer: Option C

Explanation:

ধরি, একক স্থানীয় অঙ্ক x

দশক স্থানীয় অঙ্ক x + 5

সংখ্যাটি = 10(x + 5) + x

= 11x + 50

প্রশ্নমতে,

11x + 50 - 5(2x + 5) = 10x + x + 5

= 11x + 50 - 10x - 25 = 11x + 5

= x + 25 = 11x + 5 = 10x = 20

x = 2

সংখ্যাটি = 11 × 2 + 50 = 72

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সহকারী উপজেলা/থানা শিক্ষা অফিসার (15-04-2005)

359 . a+b+c=9 , ab + bc + ca =31 হলে , $a^{2} + b^{2} + c^{2} =$ কত?

A. 49
B. 39
C. 29
D. 19

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Answer: Option D

Explanation:

a + b + c = 9,

ab + bc + ca = 31,

a² + b² + c² = ?

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

বা, a² + b² + c² = (a + b + c)² - 2(ab + bc + ca)

= 9² - (2×31)

= 81 - 62

= 19.

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360 . |x-4| = 2 এর সমাধান হবে

A. x = 3, 6
B. 6, -2
C. 2, 6
D. -2, -6

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Answer: Option C

Explanation:

|x - 4| = 2

x - 4 = + - 2 [ মডুলাস উঠায় নিলে + - হয় ]

x - 4 = + 2

বা, x = + 2 + 4

x = 6

আবার, x - 4 = - 2

বা, x = - 2 + 4

x = 2

অতএব, x = 2, 6

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সহকারী উপজেলা/থানা শিক্ষা অফিসার (24-12-2010)

347 . 2y = 2x-4 এবং 4x-5y=3 হলে x ও y এর মান কত?

360 . |x-4| = 2 এর সমাধান হবে

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