If x ∈ R and the numbers `(5 ^ (1−x) +5^ (x+1) , a/2, (25^ x +25^ −x ))` form an A. P. then a must lie in the interval ............ .

If x in R , the numbers 2^(1+x)+2^(1-x), b//2,36^x+36^(-x) form an A.P., then b may lie in the interval [12 ,oo) b. [6,oo) c. (-oo,6] d. [6, 12]

If ln^(2)x+3lnx-4 is non negative, then x must lie in the interval :

If log_(1/3)((3x-1)/(x+2)) is less than unity, then 'x' must lie in the interval :

If x and y are integers, what is x + y ? (1) 3^x = 81 (2) 5^x = (25)/(5^y)

If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then fin the interval in which y lies.

Consider a quadratic expression f (x) =tx^(2) -(2t -1) x+ (5x -1) If f (x) can take both positive and negative values then t must lie in the interval

The values of x satisfying x^("log"_(5)) gt5 lie in the interval

If 25 ^(x+1) = (125)/( 5^(x)) , find the value of x.

The least value of a for which 5^(1+x)+5^(1-x),a//2,25^(x)+25^(-x) are three consecutive terms of an A.P., is

If x+1/x=5, then x^2+1/(x^2)=? (a)25 (b) 10 (c) 23 (d) 27