Question : If $(d+e+f)=14$, $(d^2+e^2+f^2)=96$, then find the value of $(de+ef+fd)$.

Option 1: 75

Option 2: 25

Option 3: 50

Option 4: 100

Question : In a triangle DEF, DP is the bisector of $\angle D$, meeting EF at P. If DE = 14 cm, DF = 21 cm and EF = 9 cm, find EP.

Option 1: 3.6 cm

Option 2: 5.4 cm

Option 3: 6.3 cm

Option 4: 2.7 cm

Question : If A : B = 2 : 3, B : C = 6 : 7, C : D = 14 : 3, then find A : B : C : D.

Option 1: 12 : 12 : 4 : 6

Option 2: 7 : 2 : 10 : 4

Option 3: 8 : 12 : 14 : 3

Option 4: 8 : 5 : 14 : 6

Question : If $2a+3b=14$ and $2a-3b=10$, then find the value of ' $ab$ '.

Option 1: 5

Option 2: 3

Option 3: 4

Option 4: 2

Question : If $p^2+\frac{1}{p^2}=14$, then find the value of $\left(p^3+\frac{1}{p^3}\right)$.

Option 1: 56

Option 2: 60

Option 3: 48

Option 4: 52

Question : The quotient when $10^{100}$ is divided by $5^{75}$ is:

Option 1: $2^{25}×10^{75}$

Option 2: $10^{25}$

Option 3: $2^{75}$

Option 4: $2^{75}×10^{25}$