if a=(1 2) b=(3 -2) and p moves in the plane such that ap+bp=7 then the locus of p has two axes of symmetry.their equations are

Question : If $(a+b)=5$, then the value of $(a-3)^7+(b-2)^7$ is:

Option 1: $2^7$

Option 2: $3^7$

Option 3: $1$

Option 4: $0$

Question : In $\triangle$ABC, $\angle$A = $90^{\circ}$, BP and CQ are two medians. Then the value of $\frac{BP^2 + CQ^2}{BC^2}$ is:

Option 1: $\frac{4}{5}$

Option 2: $\frac{5}{4}$

Option 3: $\frac{3}{4}$

Option 4: $\frac{3}{5}$

Question : 8 cm and 5 cm are the radii of two circles. If the distance between the centres of the two circles is 11 cm, then the length (in cm) of the common tangent of the two circles is:

Option 1: $2 \sqrt{7}$

Option 2: $3 \sqrt{7}$

Option 3: $\sqrt{7}$

Option 4: $4\sqrt{7}$

Question : Two mixtures A and B have the following compositions:
Mixture A has copper and tin in a ratio of 1 : 2
Mixture B has copper and tin in a ratio of 1 : 3
If equal quantities of mixtures A and B are used for producing mixture C, then find the ratio of copper and tin in mixture C.

Option 1: 2 : 5

Option 2: 1 : 5

Option 3: 7 : 17

Option 4: 7 : 12

Question : If $a, b$ and $c$ are positive numbers such that $(a^2+b^2):(b^2+c^2):(c^2+a^2)=34:61:45$, then $b - a : c - b : c - a$ = _______.

Option 1: 3 : 2 : 1

Option 2: 2 : 1 : 3

Option 3: 3 : 1 : 2

Option 4: 1 : 2 : 3