If p, q, r, s are statements, where, p: A^2-B^2=(A-B)(A+B) ; A, B are matrices, A B B A q: 5 5 r: ^8 C ₁+ ^8 C ₂+ ^8 C ₃+ . .+ ^8 C ₈=256 s: Maximum value of ^8 C _ r is 70 then the statement from the following having truth value true is ....

Step-by-step solution

Statement p : A^2-B^2=(A-B)(A+B) with matrices A,B where AB BA . Expanding the right side gives (A-B)(A+B) = A^2 + AB - BA - B^2 . For A^2-B^2 to equal this expression, AB must equal BA , but by hypothesis AB BA . Thus, p is false. Statement q : 5 5 is true since equality holds. Statement r : ^8C₁ + ^8C₂ + + ^8C₈ . The full sum from k=0 to 8 is 2^8 = 256 , so the given sum is 256 - ^8C₀ = 255 . Since 255 256 , r is false. Statement s : Maximum value of ^8C_r occurs at r=4 and equals 8! 4!4! = 70 , so s is true. Eva