Mathematics questions
18011 published questions with worked solutions.
- The mean of the coefficients of x,x^2, ,x^7 in the binomial expansion of (2+x)^9 is
- Let [ 3n-1 2 ] be the constant term in the binomial expansion of _ j=0 ^2a_ 2j+1 = 12 (f(1)-f(-1) )=0. If the sum of the...
- The remainder, when =924 is divided by 17, is
- Let [t] denote the greatest integer t. If the constant term in the expansion of (3x^2- 1 2x^5 )^7 is , then [ ] is equal to
- If the coefficient of x^9 in ( x^3+ 1 x )^ 11 and the coefficient of x^ -9 in ( x- 1 x^3 )^ 11 are equal, then ( )^2 is equal to
- Let the coefficients of three consecutive terms in the binomial expansion of (1+2x)^n be in the ratio 2:5:8. Then the coefficient...
- The remainder when (2023)^ 2023 is divided by 35 is
- Let the sum of the coefficients of the first three terms in the expansion of (x- 3 x^2 )^n, x 0, n N, be 376. Then the...
- Let the sixth term in the binomial expansion of ( 2^ _2 (10-3^x ) + [5] 2^ (x-2) _23 )^m, in the increasing powers of 2^ (x-2)...
- If the term without x in the expansion of 10^ 100 =x is 7315, then (1+ 1x )^x (2,e) is equal to
- The coefficient of x^4 in the expansion of (1+x+x^2 )^ 10 is
- The total number of two digit numbers 'n', such that 3^n+7^n is a multiple of 10, is
- The number of rational terms in the binomial expansion of (4^ 14 +5^ 16 )^ 120 is
- If the constant term, in binomial expansion of (2x^r+ 1 x^2 )^ 10 is 180, then r is equal to
- If _ k=1 ^ 10 K^2 ( ^ 10 C_K )^2=22000L, then L is equal to
- The coefficient of x^ 18 in the expansion of (x^4- 1 x^3 )^ 15 is
- If a,b,c be in arithmetic progression, then the value of (a+2b-c)(2b+c-a)(a+2b+c) is
- If the sum to 2n terms of the AP 2,5,8,11, is equal to the sum to n terms of the AP 57,59,61,63, , then n is equal to
- If 1, _3 3^ 1-x +2 , _3 (4 3^x-1 ) are in AP, then x equals
- If twice the 11^ th term of an AP is equal to 7 times its 21^ st term, then its 25^ th term is equal to