Do thenre exist integers x such that 12x =5 (mod 8)?

Let x and x+2 be two consecutive even positive integers, such that xgt12 and the sum of the integers is less than 39. Find all possible pairs of such integers.

Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not greater than xdot Then (A) ("lim")_(x->5)f(x)=1 (B) ("lim")_(x->5)f(x)=0 (C) ("lim")_(x->5)f(x) does not exist. (D)none of these

Let [x] denotes the greatest integer less then or equal to x. If x=(sqrt3+1)^5 , then [x] is equal to

If [x]^2-5[x]+6=0 (where [.] denotes the greatest integer function), then x belongs to

If f (x)=[x] , where [x] denotes greatest integer less than or equal to x ,show that , underset(xrarr2)"lim"f(x) does not exist .

Evaluate the following limits (if exists), where {,} denotes the fractional part of x and [,] denotes the greatest integer part lim_(x rarr 0) [(1+x)^(1/x)+e(x-1)]/x

Which of the following function is/are periodic? A. f(x)={1,0,x is rationalx is irrational B. f(x)={x−[x],12,2n≤x<2n+12n+1≤x<2n+2 where [.] denotes the greatest integer function n∈Z C. f(x)=(−1)[2xπ, where [.] denotes the greatest integer function D. f(x)=x−[x+3]+tan(πx2), where [.] denotes the greatest integer function, and a is a rational number

Let f(x) =x[1/x]+x[x] if x!=0 ; 0 if x =0 where[x] denotes the greatest integer function. then the correct statements are (A) Limit exists for x=-1 (B) f(x) has removable discontinuity at x =1 (C) f(x) has non removable discontinuity at x =2 (D) f(x) is non removable discontinuous at all positive integers

Does there exist a GP containing 27,8 and 12 as three of its terms ? If it exists, how many such progressions are possible ?