Write the set {x : x is a positive integer and `x^(2) < 40`} in the roster form.

Prove that : If n is a positive integer and x is any nonzero real number, then prove that C_(0)+C_(1)(x)/(2)+C_(2).(x^(2))/(3)+C_(3).(x^(3))/(4)+….+C_(n).(x^(n))/(n+1)=((1+x)^(n+1)-1)/((n+1)x)

Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form : (i) {P, R, I, N, C, A, L} (a) { x : x is a positive integer and is a divisor of 18} (ii) { 0 } (b) { x : x is an integer and x^(2) – 9 = 0 } (iii) {1, 2, 3, 6, 9, 18} (c) {x : x is an integer and x + 1= 1 } (iv) {3, –3} (d) {x : x is a letter of the word PRINCIPAL}

Which of the following pairs of sets are disjoint { x : x is an even integer } and { x : x is an odd integer}

Match roster forms with the set builder form. (i) {p,r,I,n,c,a,l} (a) {x : x is a positive integer and is a divisor of 18} (ii) {0} (b) {x : x is an integer and x^(2)-9=0} (iii) {1,2,3,6,9,18} (c) {x : x is an integer and x+1=1} (iv) {3,-3} (d) {x : x is a letter of the word PRINCIPAL}

In the following, state whether A = B or not: A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10 }

If the first three terms in the expansion of (1 -ax)^n where n is a positive integer are 1,-4x and 7x^2 respectively then a =

List all the elements of the following sets : C = {x : x is an integer, x^(2) ≤ 4 }

If f(x)=(a-x^(n))^(1//n) , where a gt 0 and n is a positive integer, then f[f(x)]=

If two consecutive terms in the expansion of (x+a)^n are equal to where n is a positive integer then ((n+1)a)/(x+a) is