Mathematics questions
18011 published questions with worked solutions.
- If a_a is the greatest term in the sequence a_n= n^3 n^4+147 , n=1,2,3, , then a is equal to
- Let 0<z<y<x be three real numbers such that 1x, 1y, 1z are in an arithmetic progression and x, 2y,z are in a geometric...
- The sum of all those terms, of the arithmetic progression 3,8,13, ,373, which are not divisible by 3, is equal to
- Let S=109+ 108 5+ 107 5^2 + + 2 5^ 107 + 1 5^ 108 . Then the value of (16S-(25)^ -54 ) is equal to
- Let a_k and b_k , k N, be two G.P.s with common ratio r_1 and r_2 respectively such that a_1=b_1=4 and r_1<r_2. Let c_k=a_k+b_k,...
- The sum to 20 terms of the series 2 2^2-3^2+2 4^2-5^2+2 6^2- is equal to
- The sum _ k=1 ^ 20 (1+2+3+ +k) is
- The sum, _ n=1 ^7 n(n+1)(2n+1) 4 is
- The number of terms common to the two A.P.'s 3,7,11, ,407 and 2,9,16, ,709 is
- If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4^ th A.M. is equal to 2^...
- The minimum value of for which the equation 4 x + 1 1- x = has at least one solution in (0, 2 ) is
- The sum of first four terms of a geometric progression (G.P.) is 65 12 and the sum of their respective reciprocals is 65 18 . If...
- Let A_1,A_2,A_3, be squares such that for each n 1, the length of the side of A_n equals the length of the diagonal of A_ n+1 ....
- If the arithmetic mean and geometric mean of the p^ th and q^ th terms of the sequence -16,8,-4,2, satisfy the equation...
- Consider an arithmetic series and a geometric series having four initial terms from the set 11,8,21,16,26,32,4 . If the last...
- Let S_n(x)= _ a^ 1/2 x+ _ a^ 1/3 x+ _ a^ 1/6 x+ _ a^ 1/11 x+ _ a^ 1/18 x+ _ a^ 1/27 x+ up to n-terms, where a>1. If S_ 24...
- Let 1 16 , a and b be in G.P. and 1a, 1b,6 be in A.P., where a,b>0. Then 72(a+b) is equal to
- _ r=1 ^ 10 r! (r^3+6r^2+2r+5 )= (11!), then the value of is equal to
- Let a_n _ n=1 ^ be a sequence such that a_1=1, a_2=1 and a_ n+2 =2a_ n+1 +a_n for all n 1. Then the value of 47 _ n=1 ^ a_n 2^ 3n...
- If _32, _3 (2^x-5 ), _3 (2^x- 72 ) are in an arithmetic progression, then the value of x is equal to