Mathematics questions
18011 published questions with worked solutions.
- If b is very small as compared to the value of a, so that the cube and other higher powers of ba can be neglected in the identity...
- If the greatest value of the term independent of 'x' in the expansion of (x +a x )^ 10 is 10! (5!)^2 , then the value of 'a' is...
- The lowest integer which is greater than (1+ 1 10^ 100 )^ 10^ 100 is
- The sum of all those terms which are rational numbers in the expansion of (2^ 1/3 +3^ 1/4 )^ 12 is
- The remainder when (2021)^ 2023 is divided by 7 is
- If _ k=1 ^ 31 31 k 31 k-1 - _ k=1 ^ 30 30 k 30 k-1 = (60!) (30!)(31!) , where R, then the value of 16 is equal to
- The term independent of x in the expansion of (1-x^2+3x^3 ) ( 52x^3- 1 5x^2 )^ 11 , x 0 is
- If the constant term in the expansion of ger, then the value of k is equal to
- The remainder when (2021)^ 2022 +(2022)^ 2021 is divided by 7 is
- The remainder when 7^ 2002 +3^ 2022 is divided by 5 is
- The remainder when (11)^ 1011 +(1011)^ 11 is divided by 9 is
- _ i j; i,j=0 ^n ^nC_i , ^nC_j is equal to
- The remainder when 3^ 2022 is divided by 5 is
- If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of ( [4]2+ 1 [4]3 )^n is 6:1,...
- If the coefficients of three consecutive terms in the expansion of (1+x)^n are in the ratio 1:5:20, then the coefficient of the...
- 25^ 190 -19^ 190 -8^ 190 +2^ 190 is divisible by
- The absolute difference of the coefficients of x^ 10 and x^7 in the expansion of (2x^2+ 1 2x )^ 11 is equal to
- The sum of the coefficients of three consecutive terms in the binomial expansion of (1+x)^ n+2 , which are in the ratio 1:3:5, is...
- The fractional part of the number 4^ 2022 15 is equal to
- The coefficient of x^5 in the expansion of (2x^3- 1 3x^2 )^5 is