If `(a^(3)-3a-2)x^(2)+(a^(2)-a-2)x=(2a^(4)-10a+b)` is true for all real values of x where `a, b in R` then find the value of b.

If (sqrt 2+sqrt 3)^2=a+bsqrt 6 where a,b in theta ,then find the value of a and b.

If the variance of 1, 2, 3, 4, 5, ... , x is 10, then the value of x is

p(x)= ax^2+bx+5 :- If (x^2-1) is a factor of p(x),then find the value of a and b?

Let f(x) be a function such that f'(x) = log_(1//3) [log_(3) (sin x + a)] .If f(x) is decreasing for all real values of x, then a) a in (1, 4) b) a in (4, oo) c) a in (2, 3) d) a in (2, oo)

If * is defined by a * b=a-b^2 and oplus is defined by a oplus b = a^2+b ,where a and b are integers.Then find the value of ( 3 oplus 4 ) * 5