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""

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.)

Greatest integral x satisfying sqrt(4-x^(2))+(|x|)/(x)>=0

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

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

Consider the function f defines by f(x) = x-[x] , where[x] denotes the greatest integral function. Show that the function is discontinous for integral values of x and continous for all other values.

If only the 4^("th") term in the expansion of (2+(3pi)/(8))^(10) has the greatest numerical value, then the integral values of x are

The set of values of x for which the inequality [x]^(2)-5[x]+6<=0 (where [.] denote the greatest integral function) hold good is?

If [sin^(-1)x]^(2)+[sin^(-1)x]-2 le 0 (where, [.] represents the greatest integral part of x), then the maximum value of x is