Evaluate :
`"^10P_3`.

Find the value of "^4P_3 .

Prove that : ^10P_3= "^9P_3+3^9P_2 .

Evaluate (10!)/(3! 2! 2!)

If p = – 10, find the value of p^2 – 2p – 100

Find r if : "^10P_r= 2^9P_r .

Evaluate p=sum_(p=1)^(32)(3p+2)(sum_(q=1)^(10)(sin""(2qpi)/(11)-icos""(2qpi)/(11)))^(p) , where i=sqrt(-1)

If p = – 2, find the value of – 2p^3 – 3p^2 + 4p + 7

If P is the number of natural number whose logarithms to the base 10 have the characteristic p and Q is the number of natural numbers logarithms of whose reciprocals to the base 10 have the characteristic -q, then find the value of log_(10)P-log_(10) Q .

If p = – 2, find the value of – 3p^2 + 4p + 7