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8326 . ${(\sqrt{3} \times \sqrt{5})}^{4}$ এর মান কত?

A. 30
B. 60
C. 225
D. 115

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Answer: Option C

Explanation:

(√3×√5)⁴

=(√15)⁴

=225

(Ans)

8327 . $△ A B C$ এর $∠ A = x, ∠ B = 2 x$ এবং $∠ C = 3 x$ হলে ত্রিভুজটি কী ত্রিভুজ?

A. সুক্ষ্মকোণী ত্রিভুজ
B. স্থুলকোণী ত্রিভুজ
C. সমকোণী ত্রিভুজ
D. সমদ্বিবাহু ত্রিভুজ

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Answer: Option C

Explanation:

আমরা জানি, ত্রিভুজের তিন কোণের সমষ্টি ১৮০°

সুতরাং, A+B+C=180°

⇨ x+2x+3x=180°

⇨6x=180°

⇨x=30°

সুতরাং B=2x =2×30° =60°

C=3x =3×30°=90°

এখানে ত্রিভুজটির একটি কোণ, C=90°

সুতরাং ত্রিভুজটি সমকোণী ত্রিভুজ।

১৭ তম শিক্ষক নিবন্ধন পরীক্ষা (স্কুল সমপর্যায়-২) (30-12-2022)

8328 . কোন শর্তে $a^{0} = 1 ?$

A. $a = 0$
B. $a ≢ 0$
C. $a > 0$
D. $a ≢ 1$

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Answer: Option B

Explanation:

8329 . $3^{x} + 3^{x} + 3^{x} =$ কত ?

A. $9^{x}$
B. $3^{x + 1}$
C. $3^{3 x}$
D. $3^{x^{3}}$

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Answer: Option B

Explanation:

3x + 3x + 3x = 3x(1 + 1 + 1) = 3x.3 = 3x + 1.

8330 . 9x+9x+9x= কত ?

A. $27^{x}$
B. $3^{2 x + 1}$
C. $9^{3 x}$
D. $3^{x 3}$

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Answer: Option B

Explanation:

9^{x} + 9^{x} + 9^{x} = 3 . 9^{x} = 3 . 3^{2 x} = 3^{2 x + 1}

8331 . $3^{- 3}$ এর মান কত ?

A. $\frac{1}{9}$
B. $\frac{1}{3}$
C. $\frac{1}{27}$
D. $\sqrt{3}$

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Answer: Option C

Explanation:

3^{- 3} = \frac{1}{3^{3}} = \frac{1}{27}

8332 . $5^{x} + 8 . 5^{x} + 16 . 5^{x} = 1$ হলে x এর মান কত?

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

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Answer: Option C

Explanation:

দেওয়া আছে, 5^{x} {+8×5}^{x} {+16×5}^{x} =1 \Rightarrow 5^{x} (1 + 8 + 16) = 1 \Rightarrow 5^{x} \times 25 = 1 \Rightarrow 5^{x} = \frac{1}{25} \Rightarrow 5^{x} = (\frac{1}{5^{2}}) \Rightarrow 5^{x} = 5^{- 2} ∴ x = - 2

8333 . x+y=8, xy==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} - 4 x y = 8^{2} - 4 \times 15 = 64 - 60 = 4 ∴ x - y = 2 ∴ (x + y) + (x - y) = 8 + 2 \Rightarrow 2 x = 10 ∴ x = 5 ∴ y = 8 - 5 = 3 ∴ {(x - y)}^{4} = {(5 - 3)}^{4} = 2^{4} = 16

8334 . $x + \frac{1}{x} = 3$ হলে $x^{3} + \frac{1}{x^{3}}$ এর মান কত?

A. 16
B. 18
C. 22
D. 1

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Answer: Option B

Explanation:

দেওয়া আছে, x + \frac{1}{x} = 3 এখন, x^{3} + \frac{1}{x^{3}} = {(x + \frac{1}{x})}^{3} - 3 . x . \frac{1}{x} (x + \frac{1}{x}) = 3^{3} - 3.3 = 27 - 9 = 18

8335 . $\frac{x}{y} + \frac{y}{x} = 6$ হলে $\frac{x^{2}}{y^{2}} + \frac{y^{2}}{x^{2}}$ এর মান কত?

A. 30
B. 32
C. 34
D. 36

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Answer: Option C

Explanation:

{(x/y) + (y + x)}² = 6²

= > (x²/y²) + 2.(x/y).(y/x) + (y²/x²) = 6²

= > (x²/y²) + (y²/x²) = 36 - 2 = 34

8336 . $x^{2} - 4 x + 1 = 0$ হলে $x \div (x^{2} - 3 x + 1)$ এর মান কত?

B. 1
C. 2
D. 4

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Answer: Option B

Explanation:

x² - 4x + 1 = 0

বা, x² + 1 = 4x

x/( x² - 3x + 1)

বা, x / 4x - 3x

∴x/x = 1

8337 . $\frac{a^{3} - b^{3}}{a + b}$ কে $\frac{a^{4} + b^{4} + a^{2} b^{2}}{a^{3} + b^{3}}$ দ্বারা ভাগ করলে ভাগফল কত হবে?

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

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Answer: Option A

Explanation:

\frac{a^{3} - b^{3}}{a + b} \div \frac{a^{4} + b^{4} + a^{2} b^{2}}{a^{3} + b^{3}} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \div \frac{{(a^{2})}^{2} + 2 . a^{2} . b^{2} + {(b^{2})}^{2} - {(a b)}^{2}}{(a + b) (a^{2} - a b + b^{2})} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \times \frac{(a + b) (a^{2} - a b + b^{2})}{{(a^{2} + b^{2})}^{2} - {(a b)}^{2}} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \times \frac{(a + b) (a^{2} - a b + b^{2})}{(a^{2} + b^{2} + a b) (a^{2} + b^{2} - a b)} = (a - b)

8338 . $4 x^{2} - 2$ হতে কত বিয়োগ করলে রাশিটি পূর্ণবর্গ হবে?

A. $- \frac{1}{4 x^{2}}$
B. $- \frac{1}{2 x^{2}}$
C. $\frac{1}{4 x^{2}}$
D. $\frac{1}{2 x^{2}}$

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Answer: Option A

Explanation:

4 x^{2} - 2 = {(2 x)}^{2} - 2.2 x . \frac{1}{2 x} + {(\frac{1}{2 x})}^{2} - {(\frac{1}{2 x})}^{2} = {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} {সুতরাং, 4x}^{2} -2 হতে - \frac{1}{4 x^{2}} বিয়োগ করলে রাশিটি পূর্ণবর্গ হবে। {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} - (- \frac{1}{4 x^{2}}) = {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} + \frac{1}{4 x^{2}} = {(2 x - \frac{1}{2 x})}^{2}

8339 . $a^{4} - 51 a^{2} + 1 = 0$ হলে $a - \frac{1}{a}$ এর মান কত?

A. $\pm 9$
B. $\pm 7$
C. $\pm 5$
D. $\pm 3$

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Answer: Option B

Explanation:

দেওয়া আছে, a^{4} - 51 a^{2} + 1 = 0 \Rightarrow a^{4} + 1 = 51 a^{2} \Rightarrow \frac{a^{4} + 1}{a^{2}} = \frac{51 a^{2}}{a^{2}} \Rightarrow \frac{a^{4}}{a^{2}} + \frac{1}{a^{2}} = 51 \Rightarrow a^{2} + \frac{1}{a^{2}} = 51 এখন, {(a - \frac{1}{a})}^{2} = {(a + \frac{1}{a})}^{2} - 4 . a . \frac{1}{a} = a^{2} + 2 . a . \frac{1}{a} + \frac{1}{a^{2}} - 4 = a^{2} + \frac{1}{a^{2}} - 2 = 51 - 2 = 49 ∴ a - \frac{1}{a} = \sqrt{49} = \pm 7

8340 . $x^{2} + y^{2} + x^{2} = 5, x + y + z = 3$ হলে yz + zx -xy এর মান কত?

A. -5
B. -4
C. -3
D. -2

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Answer: Option D

Explanation:

কোর্স ক্যাটাগরি

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