JEE Advanced questions
3844 published questions with worked solutions.
- If a, b, c are in AP then a+ 1 bc , b+ 1 ca , c+ 1 ab are in
- The AM of two given positive numbers is 2. If the larger number is increased by 1, the GM of the numbers becomes equal to the AM...
- Let a, b be two positive numbers, where a>b and 4 GM =5 HM for the numbers. Then a is
- Let a_1=0 and a_1, a_2, a_3, , a_n be real numbers such that |a_i|=|a_ i-1 +1| for all i then the AM of the numbers a_1, a_2,...
- If the first and the (2n-1)th terms of an AP, a GP and an HP are equal and their nth terms are a, b and c respectively then
- a^n+b^n a^ n-1 +b^ n-1 is the HM between a and b if n is
- If the harmonic mean between P and Q be H then H ( 1P+ 1Q ) is equal to
- Let x be the AM and y, z be two GMs between two positive numbers. Then y^3+z^3 xyz is equal to
- If a, b, c are in AP, and p, p' are the AM and GM respectively between a and b, while q, q' are the AM and GM respectively...
- If - 2< < 2 then the minimum value of ^3 + ^3 is
- If a>1, b>1 then the minimum value of _b a+ _a b is
- If a_n>1 for all n N then _ a_2 a_1+ _ a_3 a_2+ + _ a_n a_ n-1 + _ a_1 a_n has the minimum value
- The product of n positive numbers is 1. Their sum is
- If x, y, z are three real numbers of the same sign then the value of xy+ yz+ zx lies in the interval
- The least value of 2 _ 100 a- _a0.0001, a>1 is
- If 0<x< /2 then the minimum value of ( x+ x+ cosec 2x)^3 is
- If x, y, z are positive then the minimum value of x^ y- z +y^ z- x +z^ x- y is
- a, b, c are three positive numbers and abc^2 has the greatest value 1 64 . Then
- If a>0, b>0, c>0 and the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is abc then is
- The value of _ n=1 ^ 10 _0^n x ,dx is