If `f(x)={kx^(2),x>=1, 4,,x<1` is continuous at `x=1,` then the value of `k` is:

The p.m.f. of a r.v. X is P(x){{:(kx^(2)","x=1","2","3","4),(0", otherwise"):} , then Var (X) =

The p.m.f. of a r.v. X is P(x)={{:(kx^(2)","x=1","2","3","4),(0", otherwise"):} , then E (X) =

If f(x) = {(2x+1,",",x le 1),(-3-kx^(2),",",x gt 1):} is continuous at x = 1, then the value of k is

If f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):} is continuous at x = 2, then the value of k is

Let f(x)=|(x^(2),kx,4+kx),(kx,4+kx),x^(2)),(4+kx),x^(2),kx)| If f(x) is positive for all x in R, the find the number of integral values in the range of k.

f:R to R is defined as f(x)= {{:(x^(2)+kx+3",",,"for "xge0),(2kx+3",",,"for "x lt0):} . If f(x) is injective, then find the values of k .

If f(x) is continuous at x=1 , where f(x)={:{(kx^(2)", for " x ge 1),(4", for " x lt 1):} , then k=

If for the function 'f', given by : f(x)=kx^(2)+7x+4, f^(')(5)=97 , find 'k'.

If f(x) = {{:(2x^(2) + 3x +4, x lt 1),(kx+9-k, x ge 1):} is differentiable at x=1, then k is equal to

If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive integral value of k is