Mathematics questions
18011 published questions with worked solutions.
- In the expansion of (1+3x+2x^2 )^6 the coefficient of x^ 11 is
- The coefficient of a^3b^4c in the expansion of (1+a-b+c)^9 is equal to
- If a,b,c,d be four consecutive coefficients in the binomial expansion of (1+x)^n, then the value of the expression ( b b+c )^2-...
- The coefficient of the term independent of x in the expansion of (1+x+2x^3 ) ( 32x^2- 1 3x )^9 is
- If T_0,T_1,T_2, ,T_n represents the terms in the expansion of (x+a)^n, then (T_0-T_2+T_4- )^2+ (T_1-T_3+T_5- )^2 is equal to
- The coefficients of x^2y^2, yzt^2 and xyzt in the expansion of (x+y+z+t)^4 are in the ratio
- If (1+x)^n= _ r=0 ^na_rx^r and b_r=1+ a_r a_ r-1 and _ r=1 ^nb_r= (101)^ 100 100! , then n is
- 1 1! ,(n-1)! + 1 3! ,(n-3)! + 1 5! ,(n-5)! + is equal to
- If (1+x)^ 15 =C_0+C_1x+C_2x^2+ +C_ 15 x^ 15 , then C_2+2C_3+3C_4+ +14C_ 15 is equal to
- If a,b,c are in AP, then the sum of the coefficients of 1+ (ax^2-2bx+c ) ^ 1973 is
- The coefficient of x^n in the polynomial (x+ ^nC_0 ) (x+3 , ^nC_1 ) (x+5 , ^nC_2 ) [x+(2n+1) , ^nC_n ]
- If (1+x)^n=C_0+C_1x+C_2x^2+ C_nx^n, then C_0^2+C_1^2+C_2^2+C_3^2+ +C_n^2 is equal to
- If n is even, then the middle term in the expansion of (x^2+ 1x )^n is 924x^6, then n is equal to
- If the coefficient of 7^ th and 13^ th term in the expansion of (1+x)^n are equal, then n is equal to
- The sum of the coefficients in the expansion of (1+2x+3x^2+ +nx^ n-1 )^2 is
- The first 3 terms in the expansion of (1+ax)^n (n 0) are 1, 6x and 16x^2. Then, the value of a and n are respectively
- The 6^ th term in the expansion of (2x^2- 1 3x^2 )^ 10 is
- If the 6^ th term in the expansion of ( 1 x^ 8/3 +x^2 _ 10 x )^8 is 5600, then value of x is
- The r^ th terms in the expansion of (a+2x)^n is
- The (r+1)^ th term in the expansion of (1-x)^ -4 will be