Question : If $a = 2, b = –3$, then the value of $27a^3–54a^2b+36ab^2–8b^3$ is:

Option 1: 1562

Option 2: 1616

Option 3: 1676

Option 4: 1728

Question : Directions: If 1 * 2 = 1, 2 * 3 = –1 and  3 * 4 = –5, then find the value of 7 * 9 = ?

Option 1: –47

Option 2: –29

Option 3: –2

Option 4: –9

Question : If $a=17, b=13$, then find the value of the expression $\left(a^3-b^3 – 3a^2b+3ab^2\right)$.

Option 1: – 64

Option 2: – 27000

Option 3: 27000

Option 4: 64

Question : If $(a+\frac{1}{a})=–2$, then the value of $a^{1000}+a^{–1000}$ is:

Option 1: $2$

Option 2: $0$

Option 3: $1$

Option 4: $\frac{1}{2}$

Question : If $a+\frac{1}{a-2}=4$, then the value of $(a-2)^{2}+(\frac{1}{a-2})^{2}$ is:

Option 1: 0

Option 2: 2

Option 3: –2

Option 4: 4

Question : If $p^{3}-q^{3}=(p-q)[(p+q)^{2}-xpq$, then the value of $x$ is:

Option 1: 1

Option 2: –1

Option 3: 2

Option 4: –2