The value of `(30,0)(30,10)-(30,1)(30,11)+(30,2)(30,12)-.............+(30,20)(30,30)`, where `(n,r)=nC_r` is a. `(30,10)` b. `(30,15)` c. `(60,30)` d. `(31,10)`

The value of ((30), (0))((30), (10))-((30), (1))((30),( 11)) +(30 2)(30 12)++(30 20)(30 30)= a. ^60 C 20 b. ^30 C 10 c. ^60 C 30 d. ^40 C 30

Find the value of : sin30^(@)cos30^(@)

Find the value of : sin30^(@)cos30^(@)

Find the value of 2sin30^(@)cos30^(@) .

The value of sum_(r=0)^(10)r^(10)C_r3^r(-2)^(10-r) is 20 b. 10 c. 300 d. 30

Find the vlaue of (2tan30^(@))/(1-tan^(2) 30^(@)) .

If ((n),(r )) "denotes " ""^nC_r then (a) Evalutae : 2^(15)((30),(0))((30),(1))-2^(14)((30),(1))((29),(14))+2^(13)((30),(2))((28),(13)).......-((30),(15))((15),(0)) ( b) Prove that : Sigma_(r=1)^(n) ((n-1),(n-r))((n),(r))=((2n-1),(n-1)) ( c) Prove that : ((n),(r))((r),(k))=((n),(k))((n-r),(r-k))

Find the value of sin60^(@)cos30^(@)+cos60^(@)sin30^(@) .

The value of sum_(r=0)^(40) r""^(40)C_(r)""^(30)C_(r) is (a) 40.^(69)C_(29) (b) 40.^(70)C_(30) (c) .^(60)C_(29) (d) .^(70)C_(30)

In Figure, the value of x is (a) 12 (b) 15 (c) 20 (d) 30