If `x` satifies `|x-1|+|x-2|+|x-3|geq6,` then (a)`0lt=xlt=4` (b). `xlt=-2orgeq4` (c). `xlt=0orxgeq4` (d). None of these

The range of the function f(x)=|x-1|+|x-2|,-1lt=xlt=3, is [1,3] (b) [1,5] (c) [3,5] (d) none of these

The roots of the equation a x^2+b x+c=0, a in R^+, are two consecutive odd positive (A) |b|lt=4a (B) |b|geq4a (C) |b|geq2a (D) none of these

Redefine the function f(x)=|x-2|+|2+x|,-3lt=xlt=3

Solve the equation (sinx+cosx)^(1+sin2x)=2, when 0lt=xlt=pi

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these

The vectors (x,x+1,x+2),(x+3,x+3,x+5) and (x+6,x+7,x+8) are coplanar for (A) all values of x (B) xlt0 (C) xgt0 (D) none of these

Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(x)=x|x| is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these

Let A={x in R :-1lt=xlt=1}=B . Then, the mapping f: A->B given by f(x)=x|x| is (a) injective but not surjective (b) surjective but not injective (c) bijective (d) none of these

if f(x) ={{:(x+2 ,if xlt0),(-x^(2)-2 ,if 0le xlt1),( x ,if xge1):} then the number of points of discontinuity of |f(x)|is (a) 1 (b) 2 (c) 3 (d) none of these