Greatest integral value

Absolute value of the difference between the greatest and smallest integral value of x ,satisfying the inequality ((log_(10)x-1))/((e^(x)-3))<=0 ,is equal to

Square of the distance between the integral points of intersection of L_1a n dL_2 for the greatest and the least integral values of m is 5 b. 20 c. 25 d. 30""

Square of the distance between the integral points of intersection of L_1 : 2x+y=50 a n dL_2 :y=mx+1 for the greatest and the least integral values of m is a. 5 b. 20 c. 25 d. 30""

In a triangle ABC,/_A=30^(@),b=6. Let CB_(1) and CB_(2) are greatest and least integral value of side a for which two triangles can be formed.It is also given angle B_(1) ,is obtuse and angle B_(2), is acute give (All symbols used have usual mening in a triangle.)

The value of lim_(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)]) (where [.] represents the greatest integral function) is

The value of lim_(xto1)({1-x+[x]+[1-x]} (where [.] donetes the greatest integral function) is

The value of lim_(xto1)({1-x+[x-1]+[1-x]} (where [.] donetes the greatest integral function) is

The value of int_0^(2pi)[2 sin x] dx , where [.] represents the greatest integral functions, is

The value of int_(0)^(2 pi)[2sin x]dx, where [.] represents the greatest integral functions,is