Mathematics questions
18011 published questions with worked solutions.
- If 3^6 4^4 k is the term, independent of x, in the binomial expansion of ( x4- 12 x^2 )^ 12 , then k is equal to
- If the coefficient of a^7b^8 in the expansion of (a+2b+4ab)^ 10 is K 2^ 16 , then K is equal to
- If (2021)^ 3762 is divided by 17, then the remainder is
- 3 7^ 22 +2 10^ 22 -44 when divided by 18 leaves the remainder
- Let n N and [x] denote the greatest integer less than or equal to x. If the sum of (n+1) terms ^nC_0,3 ^nC_1,5 ^nC_2,7 ^nC_3, is...
- The remainder on dividing 1+3+3^2+3^3+ +3^ 2021 by 50 is
- Let C_r denote the binomial coefficient of x^r in the expansion of (1+x)^ 10 . If for , R, C_1+3 2 ,C_2+5 3 ,C_3+ upto 10 terms =...
- If the sum of the co-efficients of all the positive even powers of x in the binomial expansion of (2x^3+ 3x )^ 10 is 5^ 10 - 3^9,...
- If ( ^ 40 C_0 )+ ( ^ 41 C_1 )+ ( ^ 42 C_2 )+ + ( ^ 60 C_ 20 )= mn , ^ 60 C_ 20 and m and n are coprime, then m+n is equal to
- If the coefficient of x^ 10 in the binomial expansion of ( x 5^ 1/4 + 5 x^ 1/3 )^ 60 is 5^k l, where l,k N and l is co-prime to...
- If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of (x^n+ 2 x^5 )^7 is 939, then the sum...
- The number of positive integers k such that the constant term in the binomial expansion of (2x^3+ 3 x^k )^ 12 , x 0 is 2^8 ,...
- Let the coefficients of x^ -1 and x^ -3 in the expansion of (2x^ 15 - 1 x^ 15 )^ 15 , x>0, be m and n respectively. If r is a...
- If the maximum value of the term independent of t in the expansion of (t^2x^ 15 + (1-x)^ 1 10 t )^ 15 , x 0 is K, then 8K is...
- If the coefficients of x and x^2 in the expansion of (1+x)^p(1-x)^q, p,q 15, are -3 and -5 respectively, then the coefficient of...
- Let for the 9^ th term in the binomial expansion of (3+6x)^n, in the increasing powers of 6x, to be the greatest for x= 32, the...
- Let the coefficients of the middle terms in the expansion of ( 1 6 + x )^4, (1-3 x)^2 and (1- 2x )^6, >0, respectively form the...
- If 1+ (2+ ^ 49 C_1+ ^ 49 C_2+ + ^ 49 C_ 49 ) ( ^ 50 C_2+ ^ 50 C_4+ + ^ 50 C_ 50 ) is equal to 2^n m, where m is odd, then n+m is...
- Suppose _ r=0 ^ 2023 r^2 , ^ 2023 C_r=2023 2^ 2022 . Then the value of is
- The largest natural number x such that 3^x divides 66! is