If 1,

Solve the inequality 2 X−1 > 5 and graph its solution.

Find the points of local maxima and local minima of f(x) = x 3 – 6 x 2 + 9x + 2014, x ε

A tailor needs at lease 40 large buttons and 60 small buttons. In the market, buttions are available in two boxes or cards. A box contains 6 large and 2 small buttons and a card contains 2 large and 4 small buttons. If the cost of a box is $3 and cost of a card is $2, find how many boxes and cards should be purchased so as to minimize the expenditure.

Evaluate : ∫x ²√5x − 3dx

a) If pth term of an A.P is q and qth term of the A.P. is p, find its rth term.

b) Find the sum of all the integers between 100 and 1000 that are divisible by 9.

If A = 3 -1 ,
          2 1
Show that A2
- 4 A + 5 I2 = 0. Also, find A4
.