Mathematics questions
18011 published questions with worked solutions.
- If ^1P_1+2 ^2P_2+3 ^3P_3+ +15 ^ 15 P_ 15 = ^4P_r-s,
- Let a_1,a_2, ,a_ 10 be an AP with common difference -3 and b_1,b_2, ,b_ 10 be a GP with common ratio 2. Let c_k=a_k+b_k, k=1,2,...
- The mean of 10 numbers 7 8, 10 10, 13 12, 16 14, is
- If a_1(>0),a_2,a_3,a_4,a_5 are in a G.P., a_2+a_4=2a^1+1 and 3a_2+a_3=2a, then a_4+a^2+2a^4 is equal to
- If the sum of the first ten terms of the series 15+ 2 65 + 3 325 + 4 1025 + 5 2501 + is mn, where m and n are co-prime numbers,...
- Let for n=1,2, ,50, S be the sum of the infinite geometric progression whose first term is n^2 and whose common ratio is 1...
- Let 3,6,9,12, upto 78 terms and 5,9,13,17, upto 59 terms be two series. Then, the sum of terms common to both the series is equal...
- Let a,b be two non-zero real numbers. If p and r are the roots of the equation x^2-8ax+2a=0 and q and s are the roots of the...
- Let a_1=b_1=1, a_n=a_ n-1 +2 and b_n=a_n+b_ n-1 for every natural number n 2. Then _ n=1 ^ 15 a_n b_n is equal to
- The series of positive multiples of 3 is divided into sets: 3 , 6,9,12 , 15,18,21,24,27 , . Then the sum of the elements in the...
- 2^3-1^3 1 7 + 4^3-3^3+2^2-1^3 2 11 + 6^3-5^3+4^3-3^3+2^3-1^3 3 15 + + 30^3-29^3+28^3-27^3+ +2^3-1^3 15 63 is equal to
- For p,q R, consider the real valued function f(x)=(x-p)^2-q, x R and q>0. Let a_1,a_2,a_3 and a_4 be in an arithmetic progression...
- Let x_1,x_2,x_3, ,x_ 20 be in geometric progression with x_1=3 and the common ratio 12. A new data is constructed replacing each...
- Let the ratio of the fifth term from the beginning to the fifth term from the end in the binomial expansion of ( [4]2+ 1 [4]3...
- If _ k=1 ^ 10 k k^4+k^2+1 = mn, where m and n are coprime, then m+n is equal to
- Let a_1,a_2,a_3, be an A.P. If _ r=1 ^ a_r 2^r =4, then 4a_2 is equal to
- Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the...
- If 1 2 3 4 + 1 3 4 5 + 1 4 5 6 + + 1 100 101 102 = k 101 , then 34k is equal to
- The 4^ th term of a G.P. is 500 and its common ratio is 1m, m N. Let S_n denote the sum of the first n terms of this G.P. If...
- Let a_1,a_2,a_3, be a G.P. of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and...