For any two integers say 3 and 4 we know that `3lt4` Is it true to say `-3lt-4`?give nay reason.

Do you know you are living being ? How can you say that ?give reasons

We know that any real number x can be expressed as followig x=[x]+{x} , where [x] is an integer and 0 le {x} lt 1 . We define [x] as the greatest integer less than or equal to x or integer part of x and [x] as the fractional part of x. Suppose for any real number x, we write x=(x)-(x) , where (x) is integer and 0 le (x) lt 1 . We define (x) as the least integer greater than (or) equal to x. For example (3.26) =4(-14.4)= - 14(5)=5 elearly, if x in I then (x)=[x] . If x !in I , then (x)=[x]+1 we can also define that x in ( n , in +1) rArr (x)=n+1 , where n in I The domain of defination of the function f(x)=(1)/(sqrt(x-(x))) is

We know that any real number x can be expressed as followig x=[x]+{x} , where [x] is an integer and 0 le {x} lt 1 . We define [x] as the greatest integer less than or equal to x or integer part of x and [x] as the fractional part of x. Suppose for any real number x, we write x=(x)-(x) , where (x) is integer and 0 le (x) lt 1 . We define (x) as the least integer greater than (or) equal to x. For example (3.26) =4(-14.4)= - 14(5)=5 elearly, if x in I then (x)=[x] . If x !in I , then (x)=[x]+1 we can also define that x in ( n , in +1) rArr (x)=n+1 , where n in I The range of the function f(x)=(1)/(sqrt((x)-[x])) is

Which of the following statements are true and which are false? In each case give a valid reason for saying so. s: If x and y are integers such that x gt y , then -x lt -y .

Observe that as the number we subtract from 3 is decreasing the result obtained is increasing. Do say is it true for all integers.3 - 3 =0, 3 - 2=1,3 - 1=2,3 - 0=3,3 - (-1)=4,3 - (-2)=5,3 - (-3)=6.

Simplify and give reasons : 4^-3

Manasa says, "Each angle in any pair of complementary angles is always acute".Do you agree? Give reason.

If I, n are positive integers , 0 lt f lt 1 and if (7 + 4sqrt3)^n = I +f , then show that I is an odd integer

If cos theta cos 2 theta cos 3theta = 1//4 for 0 lt theta lt pi then theta =

Two integers x and y are chosen one by one with replacement from 1, 2, 3, 4, 5,…., 10. Find the probability that 0 lt |x"- "y| lt 5 .