Question : If $ax^{2}+bx+c=a(x-p)^{2}$, then the relation among $a, b ,$ and $c$ would be:

Option 1: $abc=1$

Option 2: $b^{2}=ac$

Option 3: $b^{2}=4ac$

Option 4: $2b=a+c$

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

Option 1: 1

Option 2: 2

Option 3: –1

Option 4: 0

Question : If $x= a-b, y=b-c, z=c-a$, then the numerical value of the algebraic expression $x^3+y^3+z^3-3xyz$ will be:

Option 1: $a + b + c$

Option 2: $0$

Option 3: $4(a + b + c)$

Option 4: $3abc$

Question : If $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}$, then $(x+y+z)$ is:

Option 1: $a+b+c$

Option 2: $0$

Option 3: $a^2+b^2+c^2$

Option 4: $2$

Question : If $a= 9.6,b= 4.44,$ and $c= 5.16$, then the value of $a^3- b^3- c^3- 3 abc$ is:

Option 1: 0

Option 2: –1

Option 3: 2

Option 4: 1

Question : If $a+b+c=1, ab+bc+ca=-1$ and $abc=-1$, then the value of $a^{3}+b^{3}+c^{3}$ is:

Option 1: 1

Option 2: – 1

Option 3: 2

Option 4: – 2