Mathematics questions
18011 published questions with worked solutions.
- Let S_n denote the sum of the first n terms of an A.P. If S_4=16 and S_6=-48, then S_ 10 is equal to
- If a_1,a_2,a_3, are in A.P. such that a_1+a_7+a_ 16 =40, then the sum of the first 15 terms of this A.P. is
- The greatest positive integer k, for which 49^k+1 is a factor of the sum 49^ 125 +49^ 124 + +49^2+49+1, is
- Five numbers are in A.P., whose sum is 25 and product is 2520. If one of these five numbers is - 12, then the greatest number...
- Let a_1,a_2,a_3 be a G.P. such that a_1<0, a_1+a_2=4 and a_3+a_4=16. If _ i=1 ^9a_i=4 , then is equal to
- If the sum of the first 40 terms of the series, 3+4+8+9+13+14+18+19+ is (102)m, then m is equal to
- Let f:R R be such that for all x R, (2^ 1+x +2^ 1-x ), f(x) and (3^x+3^ -x ) are in A.P., then the minimum value of f(x) is
- If the 10^ th term of an A.P. is 1 20 and its 20^ th term is 1 10 , then the sum of its first 200 terms is
- Let a_n be the n^ th term of a G.P. of positive terms. If _ n=1 ^ 100 a_ 2n+1 =200 and _ n=1 ^ 100 a_ 2n =100, then _ n=1 ^ 200...
- The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in
- If the sum of first 11 terms of an A.P., a_1,a_2,a_3, is 0 (a_1 0), then the sum of the A.P., a_1,a_3,a_5, ,a_ 23 is ka_1, where...
- Let S be the sum of the first 9 terms of the series: x+ka + x^2+(k+2)a + x^3+(k+4)a + x^4+(k+6)a + where a 0 and x 1. If S= x^ 10...
- If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common...
- If the sum of the series 20+19 35+19 15+18 45+ upto n^ th term is 488 and the n^ th term is negative, then
- Let and be the roots of x^2-3x+p=0 and and be the roots of x^2-6x+q=0. If , , , form a geometric progression. Then ratio...
- If 1+ (1-2^2 1 )+ (1-4^2 3 )+ (1-6^2 5 )+ + (1-20^2 19 )= -220 , then an ordered pair ( , ) is equal to
- Let a_1,a_2, a_n be a given A.P. whose common difference is an integer and S_n=a_1+a_2+ +a_n. If a_1=1, a_n=300 and 15 n 50, then...
- If 3^ 2 2 -1 , 14 and 3^ 4-2 2 are the first three terms of an A.P. for some , then the sixth term of this A.P. is
- If 2^ 10 +2^9 3^1+2^8 3^2+ +2 3^9+3^ 10 =S-2^ 11 then S is equal to
- If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms...