JEE Advanced questions
3844 published questions with worked solutions.
- The sum of the coefficients of x^ 2r , r=1,2,3, , in the expansion of (1+x)^ n is
- The sum of the coefficients in the polynomial expansion of (1+x-3x^ 2 )^ 2163 is
- The sum of the coefficients of all the integral powers of x in the expansion of (1+2 x)^ 40 is
- If (1+x-2x^ 2 )^ 8 =a_0+a_1x+a_2x^2+ +a_ 16 x^ 16 then the sum a_1+a_3+a_5+ +a_ 15 is equal to
- The sum ^ 20 C_0+ ^ 20 C_1+ ^ 20 C_2+ + ^ 20 C_ 10 is equal to
- If (1+x)^ 10 =a_0+a_1x+a_2x^2+ +a_ 10 x^ 10 then (a_0-a_2+a_4-a_6+a_8-a_ 10 )^2+(a_1-a_3+a_5-a_7+a_9)^2 is equal to
- The sum 12 , ^ 10 C_0- ^ 10 C_1+2 ^ 10 C_2-2^2 ^ 10 C_3+ +2^9 ^ 10 C_ 10 is equal to
- 1 ^ n C_1+2 ^ n C_2+3 ^ n C_3+ +n ^ n C_n is equal to
- If a_n= _ r=0 ^ n 1 ^ n C_r then _ r=0 ^ n r ^ n C_r equals
- The sum of the series _ r=1 ^ n (-1)^ r-1 ^ n C_r(a-r) is equal to
- Let (1+x)^ n = _ r=0 ^ n a_rx^ r . Then (1+ a_1 a_0 ) (1+ a_2 a_1 ) (1+ a_n a_ n-1 ) is equal to
- The value of _ r=1 ^ 10 r ^ n C_r ^ n C_ r-1 is equal to
- The sum _ r=1 ^ n r ^ 2n C_r is equal to
- The sum 1 ^ 20 C_1-2 ^ 20 C_2+3 ^ 20 C_3- -20 ^ 20 C_ 20 is equal to
- The coefficient of a^ 8 b^ 6 c^ 4 in the expansion of (a+b+c)^ 18 is
- The term independent of x in the expansion of (1+x)^ n (1- 1x )^ n is
- The coefficient of the (r+1)th term of (x+ 1x )^ 20 when expanded in the descending powers of x is equal to the coefficient of...
- If (1+x)^ 2n =a_0+a_1x+a_2x^2+ +a_ 2n x^ 2n then
- In the expansion of ( [3] 4 + 1 [4] 6 )^ 20 ,
- Let n N. If (1+x)^ n =a_0+a_1x+a_2x^2+ +a_nx^ n , and a_ n-3 ,a_ n-2 ,a_ n-1 are in AP then