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106 . যদি $x^{4} - x^{2} + 1 = 0$ হয়, তবে $x^{3} + \frac{1}{x^{3}} = ?$ ..

A. ৩
B. ২
C. ১
D. ০

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Answer: Option D

Explanation:

x^{4} - x^{2} + 1 = 0 o r, x^{2} + \frac{1}{x^{2}} = 1 o r, x + \frac{1}{x} = \sqrt{3} এখন , x^{3} - \frac{1}{x^{3}} = {(x + \frac{1}{x})}^{3} - 3 . x . \frac{1}{x} . (x + \frac{1}{x}) = 3 \sqrt{3} - 3 \sqrt{3} = 0

107 . X+Y=6 এবং XY=6 হলে, ${(X - Y)}^{2}$ এর মান কত ? ..

A. -12
B. 12
C. 8
D. 10

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Answer: Option B

Explanation:

108 . যদি $x^{4} - x^{2} + 1 = 0$ হয়, তবে $x^{2} + \frac{1}{x^{2}} = ক ত ?$ ..

A. 4
B. 2
C. 1

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Answer: Option C

Explanation:

x^{4} - x^{2} + 1 = 0 \Rightarrow x^{4} + 1 = x^{2} \Rightarrow x^{2} + \frac{1}{x^{2}} = 1 [x^{2} দ্বারা ভাগ করে]

109 . x+y=4, xy=5 হলে, ${(x^{3} + y^{3})}^{2}$ এর মান কত ? ..

A. 16
B. 4
C. 8
D. 10

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Answer: Option A

Explanation:

110 . x2-4x-1=0 হলে , $x - \frac{1}{x}$ এর মান কত? ..

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

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Answer: Option A

Explanation:

x^{2} - 4 x - 1 = 0 \Rightarrow x^{2} - 1 = 4 x \Rightarrow x - \frac{1}{x} = 4

111 . $x^{2} + y^{2} = x y$ হলে, ${(x + y)}^{4}$ এর মান কত? ..

A. $x^{2} y^{2}$
B. xy
C. ${(x^{2} + y^{2})}^{2}$
D. $9 x^{2} y^{2}$

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Answer: Option D

Explanation:

পররাষ্ট্র মন্ত্রণালয় ব্যক্তিগত কর্মকর্তা ২৭.০৯.২০১৯

112 . $2 x + \frac{2}{y} = 4$ হলে x এর মান কত? ..

A. 2
B. 1
C. $\frac{1}{2}$
D. $\frac{1}{0}$

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Answer: Option B

Explanation:

There is wrong on this question.write question will be 2X + (2/X) = 4.As here only given one equation thats why unknown parameter must be 1.Then what will be the value of X = ? if we put X = 1,then LHS = 4 & RHS = 4 Ans:1

113 . $a^{2} - 6 a + 1 = 0$ হলে $a + \frac{1}{a} = ?$ ..

A. $\sqrt{3}$
B. $3 \sqrt{3}$
C. 6
D. 9

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Answer: Option C

Explanation:

দেওয়া আছে, a^{2} -6a+1=0 \Rightarrow a^{2} + 1 = 6 a \Rightarrow \frac{a^{2} + 1}{a} = \frac{6 a}{a} \Rightarrow \frac{a^{2}}{a} + \frac{1}{a} = 6 \Rightarrow a + \frac{1}{a} = 6

114 . $x^{y} = y^{x}, x = 2 y (x \neq 0, y \neq 0)$ হলে,(x,y) = কত? ..

A. (8,4)
B. ( 6,3)
C. (2,1)
D. (4,2)

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Answer: Option D

Explanation:

115 . $4^{x + 1} = 2^{x - 2}$ হলে , x এর মান কত? ..

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

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Answer: Option C

Explanation:

4^(x+1)=2^(x-2)

Or, 2^(2x+2)=2^(x-2)

Or, 2x+2=x-2

Or, x=-4

(ans)

বাংলাদেশ পাবলিক সার্ভিস কমিশন (BPSC) || জুনিয়র ইন্সট্রাক্টর (18-03-2023) ||

116 . ${(x^{2})}^{3}$ কে $x^{3}$ দ্বারা গুণ করলে কত হবে? ..

A. $x^{9}$
B. $x^{18}$
C. $x^{27}$
D. $x^{24}$

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Answer: Option A

Explanation:

117 . $a^{5} . a . a^{- 6}$ = কত? ..

A. a
B. $a^{2}$
D. 1

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Answer: Option D

Explanation:

118 . $x^{2} - x - 6 = 0$ সমীকরণের মূলদ্বয় হবে- ..

A. 3,2
B. 3,-2
C. -3,2
D. -3,-2

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Answer: Option B

Explanation:

x^{2} - x - 6 = 0 \Rightarrow x^{2} - 3 x + 2 x - 6 = 0 \Rightarrow x (x - 3) + 2 (x - 3) = 0 \Rightarrow (x - 3) (x + 2) = 0 x - 3 = 0 ∴ x = 3 x + 2 = 0 ∴ x = - 2 ∴ x = 3, - 2

119 . $\frac{x}{a} + a = \frac{x}{b} + b$ হলে ,x এর মান কত ? ..

A. ab
B. a
C. b
D. a/b

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Answer: Option A

Explanation:

\frac{x}{a} + a = \frac{x}{b} + b \Rightarrow \frac{x}{a} - \frac{x}{b} = b - a \Rightarrow \frac{b x - a x}{a b} = b - a \Rightarrow \frac{x (b - a)}{a b} = b - a \Rightarrow x = \frac{a b (b - a)}{(b - a)} ∴ x = a b

120 . $2^{x} + 2^{1 - x} = 3$ হলে, x = কত? ..

A. (1,2)
B. (0,2)
C. (1,3)
D. (0,1)

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Answer: Option D

Explanation:

2^{x} + 2^{1 - x} = 3 \Rightarrow 2^{x} + \frac{2^{1}}{2^{x}} = 3 \Rightarrow a + \frac{2}{a} = 3 [2^{x} = a] \Rightarrow a^{2} + 2 = 3 a \Rightarrow a^{2} - 3 a + 2 = 0 \Rightarrow a^{2} - 2 a - a + 2 = 0 \Rightarrow a (a - 2) - 1 (a - 2) = 0 \Rightarrow (a - 1) (a - 2) = 0 এখন, a-2=0                             আবার, a-1=0 a = 2 a = 1 \Rightarrow 2^{x} = 2^{1} \Rightarrow 2^{x} = 2^{0} \Rightarrow x = 1 \Rightarrow x = 0 ∴ x = 1, 0

রেলপথ মন্ত্রণালয় ।। কম্পিউটার অপারেটর (12-06-2021)

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