Let `f:R->R;f(x)={(-1)^n if x=1/(2^(2^n)), n=1,2,3.......... and 0` otherwisw then identity the correct statement (s).

Let f(n)=sum_(r=1)^(n)r^(2)C_(r)^(2)* Then ,f(5)=

Let f(x)={x^n sin (1/x) , x!=0; 0, x=0; and n>0 Statement-1: f(x) is continuous at x=0 and AA n>0. and Statement-2: f(x) is differentiable at x=0 AA n>0 (1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (2) Statement-1 is True, Statement-2 is True Statement-2 is NOT a correct explanation for Statement-1. (3) Statement-1 is True, Statement-2 is False (4) Statement-1 is False, Statement-2 is True.

Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1) . If the range of this function is [-4,3], then the value of (m^(2)+n^(2))/(4) is ….

Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1) . If the range of this function is [-4,3] , then the value of (m^(2)+n^(2))/(4) is ….

Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1) . If the range of this function is [-4,3] , then the value of (m^(2)+n^(2))/(4) is ….

Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1) . If the range of this function is [-4,3], then the value of (m^(2)+n^(2))/(4) is ….

Let f: R rarr R be defined by f(x)=|x-2n| if x in [2 n -1, 2n+1], (n in Z) . Then show that for any positive integer n, int_(0)^(2n) f(x)dx=n . Hint : f in continuous and periodic with period 2.

Statement 1: sum_(r=0)^n(r+1)^n c_r=(n+2)2^(n-1)dot Statement 2: sum_(r=0)^n(r+1)^n c_r=(1+x)^n+n x(1+x)^(n-1)dot (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1 (3) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1. (4) Statement 1 is true, Statement 2 is false.

Let f(x)=((2sinx+sin2x)/(2cosx+sin2x)*(1-cosx)/(1-sinx)): x in R. Consider the following statements. I. Domain of f is R. II. Range of f is R. III. Domain of f is R-(4n-1)pi/2, n in I. IV. Domain of f is R-(4n+1)pi/2, n in I. Which of the following is correct?