Check whether the following sentences are statements. Give reasons for your answer.
`{:("(i) 8 is less than 6"," (ii) Every set is a finite set. "),("(iii) The sun is a star. ","(iv) Mathematics is fun. "),("(v) There is no rain without clouds. ","(vi) How far is Chennai from here?"):}`

State whether the following statements are true or false . Justify your answers . (i) Every irrational number is a real number . (ii) Every rational number is a real number . (iii) Every real number need not be a rational number (iv) sqrt(n) is not irrational if n is a perfect square .

Write whether the following statements are True or False. Justify your answer (i) A binomial has two terms (ii) Every polynomial is a binomial (iii) A binomial may have degree 3 (iv) Degree of zero polynomial is zero (v) The degree of x ^(2) + 2xy + y ^(2) is 2 (vi) pi r ^(2) is a monomial.

State which of the following sets are finite and which are finited. Give reasons for your answer. (i) A={ x : x in N and x lt 100} (ii) B={x : x in N and x le 5} (iii) C={1^(2), 2^(2), 3^(2),....} (iv) D={1,2,3,4} (v) {x : x is a day of the week}

Which of the following expressions are polynomials in one variable and which are not ? Give reasons for you answer. (i) 3x ^(2) - 2x + 5 (ii) x ^(2) + sqrt2 (iii) p^(2) - 3p +q (iv) y + (2)/(y) (y ne 0) (v) 5 sqrtx + x sqrt5 (vi) x ^(100) + y ^(100)

Which of the following statements regarding biodiversity hot spots are incorrect? i) High endemism ii) High levels of species richness iii) Total number is 34 in the world iv) Five of these occur in India v) High alien species invasions vi) Cover less than 2% of the earth's land area, but if properly conserved, they can reduce extinctions by about 30%

Which of the following expressions are polynomias ? Which are not? Give reasons. (i) 4x ^(2) + 5x -2 (ii) y ^(2) -8 (iii)5 (iv) 2x ^(2) + (3)/(x) -5 (v) sqrt3x ^(2) + 5y (vi 1/x + 1 (x ne 0) (vii) sqrtx (viii) 3 xyz

Check whether the following equations are quadratic or not . (i) x^(2) - 6x - 4 = 0 (ii) x^(3) - 6x^(2) + 2 x - 1 = 0 (iii) 7x = 2x^(2) (iv) x^(2) + (1)/(x^(2)) = 2 (v) (2x + 1 ) (3 x + 1 ) = 6 (x - 1) (x - 2) (vi) 3y^(2) = 192