If f is a function satisfying f(x+y)=f(x)f(y) for all x,y∈N such that f(1)=3 and ∑x=1nfx=120 then find the value of n.
Fill in the blanks -If f(x) is discontinuous at only x=1 such that f2(x)=4 ∀x∈R , then the number of points f(x) is discontinuous are [[1]]..
If α, β ∈ C are the distinct roots of the equation x2 – x + 1 = 0, then find the value of α101 + β107.
State whether the given statement is true or false.If a, b, c ∈ R and a, b, c are in AP. a2, b2, c2 are in AP then a = b = c.
Given that n A.M.s are inserted between two sets of numbers a, 2b and 2a, b where a, b ∈R if the mth mean between these sets of numbers, is the same, then the ratio a: b =
For some a, b, c∈N, let f(x)=ax−3 and g(x)=xb+c, x∈R. If fog−1x=x−7213 then (fog) (ac) + (gof) (b) is equal to …….
If the real part of the complex number z=3+2icosθ1−3icosθ,θ∈(0,π2) is zero, then the value of sin23θ+cos2θ is equal to _________.