If `f(x)=^nsqrtx^m ,n in N ,` is an even function, then `m` is (a)even integer (b) odd integer any integer (d) `f(x)-e v e n i s not pos s i b l e`

If (4+sqrt(15))^n=I+f,w h r en is an odd natural number, I is an integer and 0

f: Rvec[-1,oo)a n df(x)=1n([|s in2x|+|cos2x|]) (where [.] is the greatest integer function.) Then, (a) f(x)h a sr a ngZ (b) f(x)i sp e r iod i c function (c) f(x)i sin v e r t i b l ein[0,pi/4] (d) f(x) is into function

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

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1) f(x) has two points of extrema

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a) G(x) is an odd function (b) G(x)i s an even function (c) G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

If f(x)={x^2sin(pix)/2,|x|<1x|x|,|x|geq1,t h e nf(x)i s an even function (b) an odd function a periodic function (d) none of these

If alpha,beta are the roots of x^2+p x+q=0a d nx^(2n)+p^n x^n+q^n=0and lf(alpha//beta),(beta//alpha) are the roots of x^n+1+(x+1)^n=0,t h e nn( in N) a. must be an odd integer b. may be any integer c. must be an even integer d. cannot say anything

Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A ,A+B ,a n dC are all integer. Conversely, prove that if the number 2A ,A+B ,a n dC are all integers, then f(x) is an integer whenever x is integer.