Let `x=1+3a+6a^2+10 a^3+ ,|a|<1.` `y=1+4b+10 b^2+20 b^3+ ,|b|<1.` Find `S+1+3(a b)+5(a b)^2+` in terms of `xa n dydot`

Let p(x) be a real polynomial of least degree which has a local maximum at x=1 and a local minimum at x=3. If p(1)=6a n dp(3)=2, then p^(prime)(0) is_____

Let A={1, 2, 3, 4} and B=N , Let f:A to B be defined by f(x)=x^(3) then, Find the range of f.

Let X={1, 2, 3, 4} and Y={2, 4, 6, 8, 10} and R={(1, 2), (2, 4), (3, 6), (4, 8)} . Find the range =____.

Let A={1, 2, 3, 4} and B={-1 ,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} . Let R={(1, 2), (2, 6), (3, 10), (4, 9)}subsetAtimesB be a relation. Show that R is a function and find its domain, co-domain and the range of R.

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9} . Find A′.

Let A = {1, 2, 3, 4, 5, 6} . Insert the appropriate symbol ∈ or ∉ in the blank spaces: 10. . .A

Let A={1, 2, 3) and B={x|x is the prime number less than 10}. Find AtimesB and BtimesA .

Let A={1, 2, 3, 4, 5, 6}, B=W and f:A to is defined by f(x)=x^(2)-1 find the range of f.

Let f(x)=x^3-3x^2+6AAx in R and g(x)={m a x :f(t ; x+1lt=tlt=x+2,-3lt=xlt=0 1-x ,xgeq .Find continuity and differentiability of g(x) for x in [-3,1]

Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of f(x) is 0 (b) -15 (c) 3-2pi none of these