Rational number | R.S Aggarwal

Let Q be the set of rational numbers and R be a relation on Q defined by R {":"x,y inQ,x^2+y^2=5} is

Write.(i) The rational number that does not have a reciprocal.(ii) The rational numbers that are equal to their reciprocals.(iii) The rational number that is equal to its negative.

If f: R->Q (rational numbers), g: R->Q (Rational number ) are two continuous functions such that sqrt(3)f(x)+g(x)=4, then (1-f(x))^3+(g(x)-3)^3 is equal to a. 1 b. 2 c. 3 d. 4

If f : R->Q (Rational numbers), g : R ->Q (Rational numbers) are two continuous functions such that sqrt(3)f(x)+g(x)=4 then (1-f(x))^3+(g(x)-3)^3 is equal to (1) 1 (2) 2 (3) 3 (4) 4

State true or false: (i) Between any two distinct integers there is always an integer. (ii) Between any two distinct rational numbers there is always a rational number. (iii) Between any two distinct rational numbers there are infinitely many rational numbers.

If S be a non - empty subset of R. Consider the following statement p . There is a rational number x in S such that x gt 0 .Write the negation of the statement p.

Fill in the blanks : The product of two positive rational number is always .. The product of a positive rational number and a negative rational number is always .... The product of two negative rational numbers is always ...... The reciprocal of a positive rational number is ...... The reciprocal of a negative rational number is ...... Zero has .... reciprocal The product of rational number and its reciprocal is ....... The numbers.... and .... are their own reciprocal If a is reciprocal of b, then the reciprocal of b is .... The number 0 is .... the reciprocal of any number. Reciprocal of 1/a , a\ !=0\ i s ddot (17 x 12)^(-1)=17^(-1)x

Every rational number is a fraction.

Every rational number is an integer.

The multiplication of a rational number 'x' and an irrational number 'y' is