State which of the following sets are finite or infinite :
(i) {`x : x ∈ N and (x – 1) (x –2) = 0`}
(ii) {`x : x ∈ N and x^(2) = 4`}
(iii) {`x : x ∈ N and 2x –1 = 0`}
(iv) {`x : x ∈ N and x` is prime}
(v) {`x : x ∈ N and x` is odd}

Identify the following sets as finite or infinite. B = {x:x^(2)-5x+6=0,x inNN}

State which of the following sets are finite and which are infinite. 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}

Identify the following sets as finite or infinite. (i) X=The set of all districts in Tamilnadu. (ii) Y=The set of all straight lines passing through a point. (iii) A={x : x in Z and x lt 5} (iv) B={x: x^(2)-5x+6=0, x in N}

State the reasons for the following : (i) {1,2,3.....10} ne {x : x ∈ N and 1 lt x lt 10} (ii) {2,4,6,8,10} ne {x: x =2n+1 and x ∈ N} (iii) {5,15,30,45} ne {x : x is a multiple of 15} (iv) {2,3,5,7,9} ne {x : x is a prime number}

Which of the following pairs of sets are equal? Justify your answer. (i) X, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”. (ii) A = {n : n ∈ Z and n^(2) ≤ 4} and B = {x : x ∈ R and x^(2) – 3x + 2 = 0} .

which of the following are quadratic equations? "(i) " x-5/x=3x-9 " (ii) " (x+3)(x-4)=0 "(iii) " 5/x-3=x^(2) " (iv) " n^(3)-n+4=n^(3) (v) x-3=4x^(2)

Find the cardinal number of the following sets (i) M={p,q,r,s,t,u} (ii) P={x: x=3n+2, n in W and x lt 15} (iii) Q={y: y=(4)/(3n), n in N and 2 lt n le 5} (iv) R={"x : x is an integer, "x in Z and -5 le x lt 5} (v) S= The set of all leap years between 1882 and 1906.

sin (n +1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x

The n t h derivative of x e^x vanishes when (a) x=0 (b) x=-1 (c) x=-n (d) x=n