Let `p = 144 ^(sin^(2)x) + 144^( cos^(2)x),` then the number of integral values of such p's can take are

If p = sin^(2)x + cos^(4)x , then

if exactly one root of equation x^(2)-(p+1)x-p^(2)=0 lie between 1 and 4 then the number of integral value of p is -

Let f(x)=2x^(3)-3(2+p)x^(2)+12px If f(x) has exactly one local maxima and one local minima, then the number of integral values of p is ....

The equaton (cos p - 1) x^(2) + x (cos p ) + sin p = 0 in the veriable x, has real roots then p can take any value in the interval :

Let a,b in n ana >1. Also p is a prime number.If ax^(2)+bx+c=p for any intergral values of x, then prove that a+bx+c!=2p for any integral value of x.

If (52)/(x)=(169)/(144) , find the value of x.

Let f be a function defined from R rarr R as f(x)={ x+p^(2) x 2} If f(x) is surjective function then sum of all possible integral values of p for p in [0 ,10] is

Let P be minimum value of 9sin^2x+16cosec^2x and S be the minimum value of 16sin^2x+9cosec^2x then the value of (P+S)/2 is