Statement 1: The number of distinct terms in `(1+x+x^2+x^3+x^4)^(1000) is 4001.`
Statement 2: The number of distinct terms in expansion `(a_1+a_2++a_m)^ni s^(n+m-1)C_(m-1)^dot`
Only conclusion I follows Only
conclusion II follows
Either I or II follows
Neither I nor II follows

Statement 1: 1^(99)+2^(99)++100^(99) is divisible by 10100. Statement 2: a^n+b^n is divisible by a+bifn is odd. Only conclusion I follows Only conclusion II follows Either I or II follows Neither I nor II follows

The total number of terms in the expansion of (1+2x+x^2)^2 is

Statement 1 : Let the vertices of a A B C be A(-5,-2),B(7,6), and C(5,-4) . Then the coordinates of the circumcenter are (1,2)dot Statement 2 : In a right-angled triangle, the midpoint of the hypotenuse is the circumcenter of the triangle. Only conclusion I follows Only conclusion II follows Either I or II follows Neither I nor II follows

Total number of terms in the expansion of (1-x-x^(2))^(5) is -

Statement-l: If the diagonals of the quadrilateral formed by the lines px+ qy+ r= 0, p'x +q'y +r'= 0 , are at right angles, then p^2 +q^2= p' ^2+q' ^2 . Statement-2: Diagonals of a rhombus are bisected and perpendicular to each other. Only conclusion I follows Only conclusion II follows Either I or II follows Neither I nor II follows

Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(1-3sqrt(2)x)^9dot

The number of distinct terms in the expansion of is (x^(3)+(1)/(x^(3))+1)^(n) is (a) 2n (b) 3n (c) 2n+1 (d) 3n+1

The number of terms in the expansion of (x^2+1+1/x^2)^n, n in N , is:

Statement -I : Number of terms in the expansion of (x+y+z+w)^(50) is .^(53)C_(3) . Statement -II : Number of non- negative solution of the equation p+q+r+s=50 is .^(53)C_(3) .

Find the third term in the expansion of (1-2x)^(3//2)""dot