Mathematics questions
18011 published questions with worked solutions.
- If y=3^ x-1 +3^ -x-1 (x real), then the least value of y is
- If AM and GM of x and y are in the ratio p:q, then x:y is
- GM and HM of two numbers are 10 and 8 respectively. The numbers are
- In a sequence of 21 terms, the first 11 terms are in AP with common difference 2 and the last 11 terms are in GP with common...
- Let a,b,c be in AP and |a|<1, |b|<1, |c|<1. If x=1+a+a^2+ to , y=1+b+b^2+ to and z=1+c+c^2+ , then x,y,z are in
- The HM of two numbers is 4. Their AM is A and GM is G. If 2A+G^2=27, then A is equal to
- If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots of x^2-2ax+a^2=0 respectively, then
- The difference between two numbers is 48 and the difference between their arithmetic mean and their geometric mean is 18. Then,...
- Let a,b,c be in GP and 4a,5b,4c are in AP such that a+b+c=70, then value of b is
- Let a be a positive number such that the arithmetic mean of a and 2 exceeds their geometric mean by 1. Then, the value of a is
- Three numbers whose sum is 15 are in AP. If they are added by 1,4 and 19 respectively they are in GP. The numbers are
- Let , , and be four positive real numbers such that their product is unity, then the least value of (1+ )(1+ )(1+ )(1+ ) is
- If a,b,c are distinct positive real numbers and a^2+b^2+c^2=1, then 3 (a^2b^2c^2 )^ 1/3 is
- If A_1,A_2; G_1,G_2 and H_1,H_2 be two AM's, GM's and HM's between two quantities, then the value of G_1G_2 H_1H_2 is
- If AM of two numbers is twice of their GM, then the ratio of greatest number to smallest number is
- The number of divisors of 3 7^3, 7 11^2 and 2 61 are in
- The harmonic mean between two numbers is 14 25 and the geometric mean is 24. The greater number between them is
- If a,b,c are in AP, b-a,c-b and a are in GP, then a:b:c is
- If a,a_1,a_2, ,a_ 2n ,b are in arithmetic progression and a,g_1,g_2, ,g_ 2n ,b are in geometric progression and h is the harmonic...
- If the AM and GM between two numbers are in the ratio m:n, then the numbers are in the ratio