If `[dot]` denotes the greatest integer function, then `(lim)_(xvec0)x/a[b/x]` `b/a` b. `0` c. `a/b` d. does not exist

("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))], where [dot] denotes the greatest integer function, is equal to (a)0 (b) 1 (c) -1 (d) does not exist

Given ("lim")_(xvec0)(f(x))/(x^2)=2,w h e r e[dot] denotes the greatest integer function, then (a) ("lim")_(xvec0)[f(x)]=0 (b) ("lim")_(xvec0)[f(x)]=1 (c) ("lim")_(xvec0)[(f(x))/x] does not exist (d) ("lim")_(xvec0)[(f(x))/x] exists

Column I ([.] denotes the greatest integer function), Column II ""("lim")_(xvec0)([100(sinx)/x]+[100(tanx)/x]) , p. 198 ("lim")_(xvec0)([100 x/(sinx)]+[100(tanx)/x]) , q. 199 ("lim")_(xvec0)([100(sin^(-1)x)/x]+[100(tan^(-1)x)/x]) , r. 200 ("lim")_(xvec0)([100 x/(sin^(-1)x)]+[100(tan^(-1)x)/x]) , s. 199

("lim")_(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest integer function is equal to (a) 0 (b) -1 (c) not exist (d) none of these

("lim")_(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e greatest integer function is 5 (b) 6 (c) 7 (d) does not exist

The range of f(x)=[|sin x|+|cosx"|""]"dot Where [.] denotes the greatest integer function, is {0} (b) {0,1} (c) {1} (d) none of these

IfI=int_(-20pi)^(20pi)|sinx|[sinx]dx(w h e r e[dot] denotes the greatest integer function), then the value of I is -40 (b) 40 (c) 20 (d) -20

lim_(x->0)[(1-e^x)(sinx)/(|x|)]i s(w h e r e[dot] represents the greatest integer function). (a) -1 (b) 1 (c) 0 (d) does not exist

The sum of roots of the equation cos^(-1)(cosx)=[x],[dot] denotes the greatest integer function, is (a) 2pi+3 (b) pi+3 (c) pi-3 (d) 2 pi-3

If f(x)=sin([x]pi)/(x^2+x+1) where [.] denotes the greatest integer function, then (A) f is one-one (B) f is not one-one and not constant (C) f is a constant function (D) none of these