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1246 . x + y = 10, $x^{2} - y^{2} = 10$ হলে, 12xy = ?

A. 24.75
B. 297
C. 247.5
D. 247

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Answer: Option B

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B unit (অ-বাণিজ্য শাখা) শিফট-২ (২০২৩-২০২৪) || (07-03-2024) || রাজশাহী বিশ্ববিদ্যালয়

1247 . যদি $\frac{x}{y} = \frac{3}{4}$ হয়, তবে $\frac{x + y}{x - y}$ এর মান কত?

A. $2$
B. $- 7$
C. $5$
D. $7$

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Answer: Option B

Explanation:

\frac{x}{y} = \frac{3}{4} \Rightarrow \frac{x + y}{x - y} = \frac{3 + 4}{3 - 4} = \frac{7}{- 1} = - 7

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সহকারী উপজেলা/থানা শিক্ষা অফিসার (মুক্তিযোদ্ধা ও ক্ষুদ্র নৃ-গোষ্ঠী কোটা) (21-08-2015)

1248 . ${(1 - x)}^{- 2}$ এর সাধারণ পদ কোনটি?

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

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Answer: Option D

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1249 . যদি (x - 5) (a + x) = $x^{2} - 25$ হয়, তবে a -এর মান কত?

A. 5
B. 25
C. -25
D. -5

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Answer: Option A

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1250 . $y = x^{2}$ বক্ররেখার (2,3) বিন্দুতে ঢাল কত?

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

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Answer: Option C

Explanation:

dy/dx=m=2x, in [2,3] point m=2[2]=4 .

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1251 . 9x+2=81,x=?

B. 1
C. 2
D. 3

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Answer: Option A

Explanation:

9^(x+2)=81

Or, 9^(x+2)=9²

Or, x+2=2

Or, x=0

(ans)

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1252 . a+1a=4 হলে $a^{2} + \frac{1}{a^{2}}$ এর মান কত ?

A. 14
B. 12
C. 16
D. 18

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Answer: Option A

Explanation:

a^{2} + \frac{1}{a^{2}} = a^{2} + \frac{1}{a^{2}} = {(a + \frac{1}{a})}^{2} - 2 . a . \frac{1}{a} = {(4)}^{2} - 2 = 16 - 2 = 14 a n s .

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1253 . $x + y = 3$ এবং $x y = 1 x^{3} + y^{3} + 3 x y$ এর মান কত?

A. -12
B. -48
C. 42
D. 21

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Answer: Option D

Explanation:

x^3 +y^3 + 3xy

= (x+y)^3 - 3xy(x+y) + 3xy

=(3)^3 - 3.1.3 +3.1

= 27-9+3

=21.

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1254 . $x - y = 10, x y = 5$ হলে, ${(x + y)}^{2} =$ কত ?

A. 80
B. 120
C. 110
D. 90

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Answer: Option B

Explanation:

দেওয়া আছে , x-y =10 এবং xy =5 x^{2} + y^{2} = {(x - y)}^{2} + 4 xy = 10^{2} + 4.5 = 100 + 20 = 120

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প্রাথমিক বিদ্যালয় প্রধান শিক্ষক নিয়োগ পরীক্ষা-2009-(জবা-03) (11-09-2009)

1255 . যদি ${(x - y)}^{2} = 12$ এবং xy = 1 হয়, তবে $x^{2} + y^{2} =$ কত?

A. 14
B. 11
C. 12
D. 13

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Answer: Option A

Explanation:

{(x - y)}^{2} = x^{2} - 2 x y + y^{2} {12+2 =x}^{2} {+y}^{2} So, x^{2} + y^{2} = 14

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1256 . $\frac{1}{2} \{{(a + b)}^{2} + {(a - b)}^{2}\} = কত ?$

A. $a^{2} + b^{2}$
B. $a^{2} - b^{2}$
C. $\frac{{(a + b)}^{2}}{2} - \frac{{(a - b)}^{2}}{2}$
D. ${(a + b)}^{2} + {(a - b)}^{2}$

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Answer: Option A

Explanation:

এটি একটি সুত্র।

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1257 . 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

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1258 . ${(x + y)}^{2} = 164$ এবং xy=32 হলে x-y= কত ?

A. 6
B. 9
C. 4
D. 12

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Answer: Option A

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1259 . যদি a + b = 7 এবং ab = 12 হয় তবে ${(a - b)}^{2}$ হবে--

A. 50
B. 125
C. 5
D. 1

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Answer: Option D

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প্রাথমিক বিদ্যালয় সহকারী শিক্ষক নিয়োগ পরীক্ষা-2005-(সিলেট বিভাগ-06) (21-08-2005)

1260 . $a + b + c = 9, a^{2} + b^{2} + c^{2} = 29$ হলে ab+bc+ca -এর মান কত ?

A. 52
B. 46
C. 26
D. 22

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Answer: Option C

Explanation:

a + b + c = 9, a^{2} + b^{2} + c^{2} = 29 a b + b c + c a = ? {(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) বা, ab+bc+ca = \{{(a + b + c)}^{2} - (a^{2} + b^{2})\} /2 বা, ab + bc + ca = \{{(a + b + c)}^{2} - (a^{2} + b^{2} + c^{2})\} / 2 বা, ab + bc + ca = \{{(a + b + c)}^{2} - (a^{2} + b^{2} + c^{2})\} / 2 = (81 - 29) / 2 = 26

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