Question : In $\triangle X Y Z, P$ is a point on side YZ and XY = XZ. If $\angle X P Y=90°$ and $Y P=9\ \text{cm}$, then what is the length of $YZ$?

Option 1: 17 cm

Option 2: 18 cm

Option 3: 12 cm

Option 4: 15 cm

Question : If $xy+yz+zx=0$, then $(\frac{1}{x^2–yz}+\frac{1}{y^2–zx}+\frac{1}{z^2–xy})$$(x,y,z \neq 0)$ is equal to:

Option 1: $3$

Option 2: $1$

Option 3: $x+y+z$

Option 4: $0$

Question : If $x : y$ is the ratio of two whole numbers and $z$ is their HCF, then the LCM of those two numbers is:

Option 1: $yz$

Option 2: $\frac{xz}{y}$

Option 3: $\frac{xy}{z}$

Option 4: $xyz$

Question : In $\triangle A B C,$ P and Q are the middle points of the sides AB and AC, respectively. R is the point on the segment PQ such that PR : RQ = 1 : 3. If PR = 6 cm, then BC is:

Option 1: 46 cm

Option 2: 48 cm

Option 3: 44 cm

Option 4: 50 cm

Question : In $\triangle X Y Z, \angle YXZ=90°$, P is a point on side YZ such that XP is perpendicular to YZ. If XP = YP = 10 cm then what will be the value of PZ?

Option 1: 8 cm

Option 2: 9 cm

Option 3: 12 cm

Option 4: 10 cm