Mathematics questions
18011 published questions with worked solutions.
- Let S_k, where k=1,2, ,100, denotes the sum of the infinite geometric series whose first term is k-1 k! and the common ratio is...
- Let a,b,c be positive integers such that ba is an integer. If a,b,c are in geometric progression and the arithmetic mean of a,b,c...
- A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers...
- Let a_1,a_2,a_3, ,a_ 11 be real numbers satisfying a_1=15, 27>2a_2>0 and a_k=2a_ k-1 -a_ k-2 for k=3,4, ,11. If a_1^2+a_2^2+ +a_...
- Let a_1,a_2,a_3, ,a_ 100 be an arithmetic progression with a_1=3 and S_p= _ i=1 ^pa_i, 1 p 100. For any integer n with 1 n 20,...
- If x_1,x_2, ,x_n are any real numbers and n is any positive integer, then
- Let b_i>1 for i=1,2, ,101. Suppose _eb_1, _eb_2, , _eb_ 101 are in Arithmetic Progression (A.P.) with the common difference _e2....
- If the 2^ nd , 5^ th and 9^ th terms of a non-constant AP are in GP, then the common ratio of this GP is
- Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then the...
- If (10)^9+2(11)^1(10)^8+3(11)^2(10)^7+ +10(11)^9=k(10)^9, then k is equal to
- The sum of first 20 terms of the sequence 0.7,0.77,0.777, , is
- If a_1,a_2,a_3, are in a harmonic progression with a_1=5 and a_ 20 =25. Then, the least positive integer n for which a_n<0, is
- If the sum of the first ten terms of the series (1 35 )^2+ (2 25 )^2+ (3 15 )^2+4^2+ (4 45 )^2+ , is 16 5m, then m is equal to
- The sum of first 9 terms of the series 1^3 1+ 1^3+2^3 1+3 + 1^3+2^3+3^3 1+3+5 + is
- If a,b,c,d are positive real numbers such that a+b+c+d=2, then M=(a+b)(c+d) satisfies the relation
- Let a,b and c be three real numbers satisfying bmatrix a&b&c bmatrix bmatrix 4&7&3 7&4&3 6&5&3 bmatrix = bmatrix 0&0&0 bmatrix ....
- Let p and q be the roots of x^2-3x+m=0 and r and s be the roots of x^2-23x+n=0. If p<q<r<s are in A.P., then find the value of...
- If the sum of the first n terms of the series 5+ 125 + 405 + 845 + is 276 5, then find the value of n.
- Let a,b and c be the 4^ th , 8^ th and 16^ th terms respectively of a non-constant A.P. If a,b,c are three consecutive terms of a...
- Find the value of 1+ 1^3+2^3 1+2 + 1^3+2^3+3^3 1+2+3 + + 1^3+2^3+3^3+ +12^3 1+2+3+ +12 - 15 (1^2+2^2+3^2+ +12^2 ).