If `a_1,a_2,a_3,a_4` are positive real numbers such that `a_1 + a_2 + a_3 + a_4 = 16` then find maximum value of `(a_1 + a_2)(a_3+a_4)`.

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+....+a_(n-1)+3a_n is

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+....+a_(n-1)+3a_n is

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+....+a_(n-1)+3a_n is

If a_1, a_2, a_3,...a_20 are A.M's inserted between 13 and 67 then the maximum value of the product a_1 a_2 a_3...a_20 is

The number of ordered quadruples (a_1,a_2,a_3,a_4) of positive odd integers that satisfy a_1+a_2+a_3+a_4=32 is equal to (a)31 C_3 (b) 17 C_3 (c)4495 (d) (17C_3)-(17C_4)

The number of ordered quadruples (a_1,a_2,a_3,a_4) of positive odd integers that satisfy a_1+a_2+a_3+a_4=32 is equal to (a)31 C_3 (b) 17 C_3 (c)4495 (d) (17C_3)-(17C_4)

Three distinct numbers a_1 , a_2, a_3 are in increasing G.P. a_1^2 + a_2^2 + a_3^2 = 364 and a_1 + a_2 + a_3 = 26 then the value of a_10 if a_n is the n^(th) term of the given G.P. is:

If a_1+a_2+a_3+......+a_n=1 AA a_1 > 0, i=1,2,3,......,n, then find the maximum value of a_1 a_2 a_3 a_4 a_5......a_n.