The term independent of `a` in the expansion of `(1+sqrta+ 1/(sqrta-1))^-30` is (a) `30C_20` (b) `0` (c) `30C_10` (d) non of these

Find the term independent of x in the expansion of (2^(x) + 2^(-x)+log_(e)e^(x+2)))^(30) .

The number of terms in the expansion of (a + b + c)^(10) is

The coefficient of x^(28) in the expansion of (1+x^3-x^6)^(30) is 1 b. 0 c. 30 C_6 d. ^30 C_3

The coefficient of the term independent of x in the exampansion of ((x+1)/(x^(2//3)-x^(1//3)+1)-(x-1)/(x-x^(1//2)))^(10) is 210 b. 105 c. 70 d. 112

If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, then k equals 2,-2 b. 3,-3 c. 4,-4 d. 1,-1

The coefficient x^5 in the expansion of (1+x)^(21)+(1+x)^(22)++(1+x)^(30) is a. "^51 C_5 b. "^9C_5 c. "^31 C_6 -"^(21)C_6 d. "^30 C_5 + "^(20)C_5

If the lines a x+y+1=0,x+b y+1=0, and x+y+c=0(a , b , c being distinct and different from 1) are concurrent, then (1/(1-a))+(1/(1-b))+(1/(1-c))= (a)0 (b) 1 (c) 1/((a+b+c)) (d) none of these

Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, 10 passengers enter the train during the journey with 10 different ticket of two class. The number of different sets of tickets they may have is a. ^15 C_(10) b. ^20 C_(10) c. ^30 C_(10) d. none of these

In a "DeltaA B C"," "/_"C"=60" "&\ /_A=75. If D is a point on A C such that area of the "DeltaB A D" is sqrt(3) times the area of the "DeltaB C D", then the /_"A B D"= 60^0 (b) 30^0 (c) 90^0 (d) none of these

For r = 0, 1,"…..",10 , let A_(r),B_(r) , and C_(r) denote, respectively, the coefficient of x^(r ) in the expansion of (1+x)^(10), (1+x)^(20) and (1+x)^(30) . Then sum_(r=1)^(10) A_(r)(B_(10)B_(r ) - C_(10)A_(r )) is equal to