The function `f(x)=(4sin^2x−1)^n (x^2−x+1),n in N`, has a local minimum at `x=pi/6` . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number

The function f(x)=(x^2-4)^n(x^2-x+1),n in N , assumes a local minimum value at x=2. Then find the possible values of n

Prove that 4n^(2)-1 is an odd number for all n in N

What is the sum of first n odd natural numbers ?

Let f(x) = (x^2 - 1)^(n+1) + (x^2 + x + 1) . Then f(x) has local extremum at x = 1 , when n is (A) n = 2 (C) n = 4 (B) n = 3 (D) n = 5

The sum of first n odd natural numbers is always an odd number.

If composite function f_1(f_2(f_3((f_n(x))))n timesis an decreasing function and if r of f_i ' s are decreasing function while rest are increasing, then the maximum value of r(n-r) is (n^2-1)/4 , when n is an even number (n^2)/4, when n is an odd number (n^2-1)/4, when n is an odd number (n^2)/4, when n is an even number

If A = { x : x is a natural number }, B = { x : x is an even natural number} C = { x : x is an odd natural number} and D = { x : x is a prime number }, find C ∩ D

If A = { x : x is a natural number }, B = { x : x is an even natural number} C = { x : x is an odd natural number} and D = { x : x is a prime number }, find B ∩ D

If A = { x : x is a natural number }, B = { x : x is an even natural number} C = { x : x is an odd natural number} and D = { x : x is a prime number }, find B ∩ C

If A = { x : x is a natural number }, B = { x : x is an even natural number} C = { x : x is an odd natural number} and D = { x : x is a prime number }, find A ∩ D