376 . $(a - 5) (a + x) = a^{2} - 25$ হলে x এর মান কত?

A. 5
B. 6
C. 7
D. 8

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Answer: Option A

Explanation:

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377 . a+b=3 এবং ab=2 হলে, $a^{3} + b^{3}$ এর মান নির্ণয় কর?

A. 9
B. 27
C. 18
D. 12

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Answer: Option A

Explanation:

a^{3} + b^{3} = {(a + b)}^{3} - 3 a b (a + b) = 3^{3} - 3.2 . (3) = 27 - 18 9

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378 . 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}

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379 . $\frac{2 x + 2 y + x^{2} - y^{2}}{x + y} = ?$

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

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Answer: Option C

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380 . (x+3) (x-3) কে $x^{2} - 6$ দিয়ে ভাগ করলে ভাগশেষ কত?

A. -3
B. -6
C. 6
D. 3

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Answer: Option A

Explanation:

(x + 3) - (x - 3) = x^{2} - 3 x + 3 x - 9 = x^{2} - 9 = 6 - 9 = - 3

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381 . (a + b) = 4 হলে ${(a + b)}^{3}$ কত?

A. 16
B. 64
C. 12
D. 24

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Answer: Option B

Explanation:

Given data, a + b = 4 Then, {(a + b)}^{3} = 4^{3} = 4 \times 4 \times 4 = 64

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382 . $\frac{3}{x} + \frac{4}{x + 1} = 2$ হলে x এর মান কত?

A. 2
B. 4
C. 1
D. 3

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Answer: Option D

Explanation:

3/x + 4/(x + 1) = 2

= > {3(x + 1) + 4x }/x(x + 1) = 2

= > {3x + 3 + 4x} = 2 (x2 + x)

= > 7x + 3 = 2x2 + 2x

= > 2x2 - 5x - 3 = 0

= > 2x2 - 6x + x - 3 = 0

= > 2x(x - 3) + 1(x - 3) = 0

= > (2x + 1) (x - 3) = 0

if,

x - 3 = 0

= > x = 3

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383 . $x^{2} + y^{2} = 25$ এবং xy = 12 হলে x + y = ?

A. 6
B. 7
C. 8
D. 9

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Answer: Option B

Explanation:

দেওয়া আছে - x^{2} + y^{2} = 25 এবং xy = 12 {(x + y)}^{2} = x^{2} + 2 xy + y^{2} = x^{2} + y^{2} + 2 xy = 25 + 2.12 = 25 + 24 {(x + y)}^{2} = 49 x + y = 7

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384 . If $8^{2 x + 3} = 2^{2 x + 6},$ then x=?

A. -3
B. -1
C. 8
D. None of these

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Answer: Option D

Explanation:

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385 . x + y =2 এবং y = 3x - 2 হলে, x ও y এর মান হবে যথাক্রমে-

A. 1, 1
B. 1, 2
C. 2, 2
D. 2, 1

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Answer: Option A

Explanation:

x + y = 2

বা, x + 3x - 2 = 2

বা, 4x = 2 + 2

বা, x = 4/4

x = 1

আবার,

y = 3x - 2

বা, y = 3 *1 - 2

বা, y = 3 - 2

সুতরাং y = 1

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386 . (a-b)=3 এবং ab=4 হলে $a^{2} + b^{2}$ এর মান কত?

A. 25
B. 17
C. 11
D. 1

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Answer: Option B

Explanation:

দেওয়া আছে (a - b) = 3 এবং ab = 4 a^{2} + b^{2} = {(a - b)}^{2} + 2 ab = 3^{2} + 2 \times 4 = 9 + 8 = 17

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387 . $(x^{2} - 16)$ কে উৎপাদকে বিশ্লেষণ করলে কোনটি পাওয়া যায়?

A. $(x^{2} - 4) (x^{2} - 4)$
B. (x+4) (x-4)
C. (x+2)(x-2)
D. $(x^{2} + 16) (x^{2} - 16)$

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Answer: Option B

Explanation:

x^{2} - 16 = x^{2} - 4^{2} = (x + 4) (x - 4)

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388 . $x^{3} + 1$ এবং $x^{2} - 1$ এর গ.সা.গু কত?

A. X+1
B. X-1
C. (X+1)( X-1) (X2-X+1)
D. X( X-1)

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Answer: Option A

Explanation:

x³ + 1 = (x + 1)(x² - x + 1)

x² – 1 = (x + 1)(x - 1)

∴ নির্ণেয় গ.সা.গু = x + 1.

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389 . $a + \frac{1}{a} = 3$ হলে $a^{2} + \frac{1}{a^{2}} =$ কত?

A. 11
B. 13
C. 7
D. 9

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Answer: Option C

Explanation:

a2 + 1/a2 = (a + 1/a)2_2*a*1/a

= 32_2

= 9_2

= 7.

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390 . $a^{2} + 2 a b - 2 b - 1$ বীজগাণিতিক রাশিটির একটি উৎপাদক

A. a+1
B. b+1
C. a-2
D. a-1

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Answer: Option D

Explanation:

আমরা জানি . a^{2} + ab - 2 b - 1 = a^{2} + ab + b^{2} - b^{2} - 2 b - a = {(a + b)}^{2} - (b^{2} + 2 \times b \times 1 + 1^{2}) = {(a + b)}^{2} - {(b + 1)}^{2} = (a + b + b + 1) \{(a + b) - (b + 1)\} = (a + 2 b + 1) (a + b - b - 1) = (a + 2 b + 1) (a - 1)

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385 . x + y =2 এবং y = 3x - 2 হলে, x ও y এর মান হবে যথাক্রমে-

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