Question : Simplify the following expression: $[(1 + p)(1 + p^2)(1 + p^4)(1 + p^8)(1 + p^{16})(1 - p) - 1]$
Option 1: $-p^{32}$
Option 2: $p^{32}$
Option 3: $(1 + p^{32})$
Option 4: $(1 - p^{32})$
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Correct Answer: $-p^{32}$
Solution : Given: $[(1+p)(1+p^2)(1+p^4)(1+p^8)(1+p^{16})(1 - p) - 1]$ = $[(1+p)(1-p)(1+p^2)(1+p^4)(1+p^8)(1+p^{16})-1]$ = $[(1-p^2)(1+p^2)(1+p^4)(1+p^8)(1+p^{16})-1]$ = $[(1-p^4)(1+p^4)(1+p^8)(1+p^{16})-1]$ = $[(1-p^8)(1+p^8)(1+p^{16})-1]$ = $[(1-p^{16})(1+p^{16})-1]$ $ = [(1 - p^{32}) -1]$ $ = -p^{32}$ Hence, the correct answer is $-p^{32}$.
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Question : Simplify the following expression: [$\sqrt{25}$ + 12 ÷ 3 – {20 + (16 of 8 ÷ 16) – (54 ÷ 18 of $\frac{1}{2}$}]
Option 1: –13
Option 2: 12
Option 3: 22
Option 4: 0
Question : Simplify the following expression. $(4 x + 1)^2 - (4 x + 3)(4 x - 1)$
Option 1: $(4 x + 1)$
Option 2: $4$
Option 3: $(4x- 3)$
Option 4: $4x$
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Option 1: 2
Option 2: 1
Option 3: 3
Question : Simplify the following expression. $(2 \times 7-5+9 \div 3) \div(4+2)^2 \times 2$
Option 1: $2$
Option 2: $\frac{3}{2}$
Option 3: $\frac{2}{3}$
Option 4: $1.5$
Question : Simplify the following expression. 120 ÷ 15 of 4 + [11 × 4 ÷ 4 of {4 × 2 – (8 – 11)}]
Option 1: $\frac{120}{61}$
Option 2: $\frac{61}{120}$
Option 3: $3$
Option 4: $-3$
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