Question : If $\small a^{3}+3a^{2}+9a=1$, then what is the value of $a^{3}+\frac{3}{a}$?
Option 1: 31
Option 2: 26
Option 3: 28
Option 4: 24
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Correct Answer: 28
Solution : $a^{3}+3a^{2}+9a=1$ .......(i) Multiply the equation by $\frac{3}{a}$ both sides, ⇒ $3a^{2}+9a+27=\frac{3}{a}$ ......(ii) Subtracting (ii) from (i), ⇒ $a^{3}-27=1-\frac{3}{a}$ $\therefore a^{3}+\frac{3}{a}=28$ Hence, the correct answer is 28.
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Question : The value of $1 \frac{3}{4}+1 \frac{5}{7} \div 2 \frac{3}{7} \times 2 \frac{3}{7}=$?
Option 1: $1 \frac{11}{28}$
Option 2: $2 \frac{13}{28}$
Option 3: $3 \frac{13}{28}$
Option 4: $4 \frac{23}{28}$
Question : If $2x-\frac{1}{2x}=5,x\neq0$, then the value of $(x^2+\frac{1}{16x^2}-2)$is:
Option 1: $\frac{19}{4}$
Option 2: $\frac{23}{4}$
Option 3: $\frac{27}{4}$
Option 4: $\frac{31}{4}$
Question : If $a=26$ and $b=22$, then the value of $\frac{a^3-b^3}{a^2-b^2}-\frac{3 a b}{a+b}$ is_______.
Option 1: $\frac{5}{3}$
Option 2: $\frac{13}{11}$
Option 3: $\frac{1}{3}$
Option 4: $\frac{11}{13}$
Question : If $a^2+1=9a$ and $a\neq0$, then the value of $a^2+\frac{1}{a^2}$ is:
Option 1: 81
Option 2: 18
Option 3: 79
Option 4: 83
Question : If $\sin A = \frac{4}{5}$, then what is the value of $\sin^2 A$?
Option 1: $\frac{26}{25}$
Option 2: $\frac{36}{25}$
Option 3: $\frac{48}{25}$
Option 4: $\frac{16}{25}$
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