Solve the following: Select the rational numbers from the list which are also the integers.
`(9)/(4), (8)/(4), (7)/(4), (6)/(4), (9)/(3), (8)/(3), (7)/(3), (6)/(3), (5)/(2), (4)/(2), (3)/(1), (3)/(2), (1)/(1), (0)/(1), (-1)/(1), (-2)/(1), (-3)/(2), (-4)/(2), (-5)/(2), (-6)/(2)`,

(7)/(8)-:(7(1)/(2)-5(1)/(6)-:2(3)/(4))+4(1)/(2)

1(5)/(6)+[2(2)/(3)-{3(3)/(4)(3(4)/(5)-:9(1)/(2))}]

The greatest of the numbers 2(1)/(2),3^((1)/(3)),4^((1)/(4)),5^((1)/(5)),6^((1)/(6)) and 7^((1)/(7)) is

(5)/(6)-:(6)/(7)xx?-(8)/(9)-:1(3)/(5)+(3)/(4)xx3(1)/(3)=2(7)/(9)(7)/(6)(b)(6)/(7)(c)1(d) None of these

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range: (i) {(2,1), (3,1),(4,2)} (ii) {(2,2),(2,4),(3,3),(4,4)} (iii) {(2,1),(5,1),(8,1),(11,2),(14,2),(17,2)} (iv) {(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} (v){(2,1),(4,2),(6,3),(8,4),(10,5)} (vi) {(1,2),(2,3),(3,4),(3,5),(3,7),(4,8)}

Using integration, find the area of the region bounded by : (i) (1,0), (4,5) and (6,3) (ii) (1,0) ,(2,2) and (3,1) (iii) (-1,2), (1,5) and (3,4) (iv) (2,3), (3,5) and (3,4) (v) (-1,0) ,(1,3) and (3,2) (vi) (1,3) , (2,5) and (3,4) (vii) (4,1), (6,6) and (8,4) (viii) (2,5), (4,7) and (6,2) (ix) (-2,1) ,(0,4) and (2,3) (x) (2,1), (3,4) and (5,2).

The sum of the slopes of the tangents to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 drawn from the point (6,-2) is 1) 0 2) (3)/(4) 3) (-6)/(7) 4) (-8)/(9)

Solve (a) 2/3 + 1/7 (b) 3/10 + 7/15 (c) 4/9 + 2/7 (d) 5/7 + 1/3 (e) 2/5 + 1/6 (f) 4/5 + 2/3 (g) (3/4) (1/3) (h) (5/6) (1/3) (1) 2/3 + 3/4 + 1/2 (1) 1/2 + 1/3 = 1/6 (k) (1) 1/3 + (3) 2/3 (1) (4) 2/3 +(3) 1/4 (m) ((16)/5))(7/5)