Evaluate :

`| [ a , b ] , [ c , d ] |` + `| [ b , q ] , [ p , c ] | `+ `| [ p , d ] , [ a , q ] |` is equal to

If p+q+r=0=a+b+c , then the value of the determnalnt |p a q b r c q c r a p b r b p c q a|i s 0 b. p a+q b+r c c. 1 d. none of these

Match the coloumn {:(,A to Q, B to R, C to P, D to S),(,A to Q, B to R, C to S, D to P),(,A to R, B to Q, C to S, D to P),(,A to R, B to Q, C to P, D to S):}

In Fig. 4.177, A C B A P Q . If B C=10 c m , P Q=5c m , B A=6. 5 c m and A P=2. 8 c m find C A and A Q . Also, find the area ( A C B): a r e a ( A P Q) . (FIGURE)

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

In a A B C , P and Q are point on the sides A B and A C respectively, such that P Q B C . If A P=2. 4 c m , A Q=2c m , Q C=3c m and B C=6c m , find A B and P Q .