Let [x] denote the greatest integer less that or equal to x. If `f(x) = [x sin pi x]`, then f(x) is
(a) Continuous at x = 0
(b) Continuous in (-1, 0)
(c) Differentiable at x = 1
(d) Differentiable in (-1, 1)

If f(x)=|3-x|+[3+x] , where [x] denotes the least integer greater than or equal to x , then f(x) is:(a) continuous and differentiable at x=3. (b) continuous but not differentiable at x=3. (c)differentiable but not continuous at x=3. (d)neither differentiable nor continuous at x=3..

The function f(x)=sin^(-1)(cosx) is (a) discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

The function f(x)=sin^(-1)(cosx) is (a) . discontinuous at x=0 (b). continuous at x=0 (c) . differentiable at x=0 (d) . non of these

If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than or equal to x, then f(x) is continuous and differentiable at x=3 (b) continuous but not differentiable at x=3 (b) differentiable but not continuous at x=3 (d) neither differentiable nor continuous at x=3

The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuous at x=0 (c) differentiable at x=0 (d) none of these

The function f(x)=sin^(-1)(cos x) is discontinuous at x=0 (b) continuous at x=0( c) differentiable at x=0 (d) none of these

Let [x] denote the greatest integer less than or equal to x , then int_0^(pi/4) sinx d(x-[x])= (A) 1/2 (B) 1-1/sqrt(2) (C) 1 (D) none of these

Let [x] denote the greatest integer less than or equal to x , then int_0^(pi/4) sinx d(x-[x])= (A) 1/2 (B) 1-1/sqrt(2) (C) 1 (D) none of these

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is(a) continuous at x = 0 ,(b) continuous at x = 1 (c)differentiable at x = 0

The function f(x)=1+|cosx| is (a) continuous no where (b) continuous everywhere (c) not differentiable at x=0 (d) not differentiable at x=npi,\ \ n in Z