The set of values of p for which the equation `|lnx| -px =0` possess three distinct roots is (A) `(0,1/e)` (B) `(0,1)` (C) `(1,e)` (D) `(0,e)`

The set of values of p for which the equation |ln x|-px=0 possess three distinct roots is

The set of values of p for which the equation |ln x|-px=0 possess three distinct roots is (A) (0,(1)/(e))(B)(0,1)(C)(1,e)(D)(0,e)

The number of values of k for which the equation x^(3)-3x+k=0 has two distinct roots lying in the interval (0,1) is three (b) two (c) infinitely many (d) zero

The number of values of k for which the equation x^3-3x+k=0 has two distinct roots lying in the interval (0,1) is (a) three (b) two (c) infinitely many (d) zero

If the equation a x^2+2x+a=0 has two distinct roots, if a=+-1 (b) a=0 (c) a=0,\ 1 (d) a=-1,\ 0

If the equation a x^2+2x+a=0 has two distinct roots, if (a) a=+-1 (b) a=0 (c) a=0,\ 1 (d) a=-1,\ 0

The function f(x)=x^x decreases on the interval (a) (0,\ e) (b) (0,\ 1) (c) (0,\ 1//e) (d) (1//e ,\ e)

If (1-p) is a root of the quadratic equation x^(2)+px+(1-p)=0 , then its roots are (a) 0,-1 (b) -1,1 (c) 0,1 (d) -1,2

f(x)=|x log_e x| monotonically decreases in (a) (0,1/e) (b) (1/e ,1) (c) (1,oo) (d) (1/e ,oo)

Between any two real roots of the equation e^xsinx-1=0 , the equation e^xcosx+1=0 has :