Mathematics questions
18011 published questions with worked solutions.
- Let S_n= _ n=1 ^ 15 T_n= 15 16 2=120 be an A.P., A_n=r(3) and p,q, R. If f(x) and =(x-p)^2-q, x R, then a_ 10 is equal to
- If a,b and c be three distinct real numbers in G.P. and a+b+c=xb, then x cannot be
- The sum of the following series 1+6+ 9 (1^2+2^2+3^2 ) 7+ 12 (1^2+2^2+3^2+4^2 ) 9+ 15 (1^2+2^2+ +5^2 ) 11 + up to 15 terms, is
- Let a,b and c be the 7^ th , 11^ th and 13^ th terms respectively of a non-constant A.P. If these are also the three consecutive...
- The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is _ k=1 ^ 10 k k^4+k^2+1...
- If the sum of the 33^ rd , 11^ th and 9^ th term of a non-zero A.P. is zero, then its 53^ rd term: 1 2 3 4 + 1 3 4 5 + 1 4 5 6 +...
- Let S_n=1+q+q^2+ +q^n and T_n=1+ ( q+1 2 )+ ( q+1 2 )^2+ + ( q+1 2 )^n where q is a real number and q 1. If ^ 101 C_1+ ^ 101 C_2...
- The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the...
- Let S_k= 1+2+3+ +k k. If S_1^2+S_2^2+ +S_ 10 ^2= 5 12 A, then A is equal to
- If the sum of the first 15 terms of the series ( 34 )^3+ (1 12 )^3+ (2 14 )^3+3^3+ (3 34 )^3+ is equal to 225k, then k is equal to
- The sum of all natural numbers n such that 100<n<200 and H.C.F. (91,n)>1 is
- The sum _ k=1 ^ 20 k 1 2^k is equal to
- Let the sum of the first n terms of a non-constant A.P., a_1,a_2,a_3, be 50n+ n(n-7) 2A, where A is a constant. If d is the...
- The sum of the series 1+2 3+3 5+4 7+ upto 11^ th term is
- If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its 11^ th term is
- If a_1,a_2,a_3, ,a_n are in A.P. and a_1+a_4+a_7+ +a_ 16 =114, then a_1+a_6+a_ 11 +a_ 16 is equal to
- The sum 3 1^3 1^2 + 5 (1^3+2^3 ) 1^2+2^2 + 7 (1^3+2^3+3^3 ) 1^2+2^2+3^2 + upto 10^ th term, is
- The sum 1^3 1+ 1^3+2^3 1+2 + 1^3+2^3+3^3 1+2+3 + + 1^3+2^3+3^3+ +15^3 1+2+3+ +15 - 12(1+2+3+ +15) is equal to
- Let a,b and c be in G.P. with common ratio r, where a 0 and 0<r 12. If 3a,7b and 15c are the first three terms of an A.P., then...
- Let a_1,a_2,a_3, be an A.P. with a_6=2. Then the common difference of this A.P., which maximises the product a_1a_4a_5, is