`y lt -2`

2x-y gt 1, x-2y lt -1

f(x)= {(|x+1|",",x lt -2),(2x+3",",-2 le x lt 0),(x^(2) + 3",",0 le x lt 3),(x^(3)-15,3 le x):} . Find at which points, the function f(x) is discontinuous ?

2x-3y lt 6

x+y lt 5

x+y ge 4, 2x-y lt 0

3y-5x lt 30

State True or False, if 'false' write correct statement. The point (-x,-y) lies in the first quadrant where x lt 0, y lt 0 .

y = x sin x : xy' = y + x sqrt(x^(2) - y^(2))(x ne 0 and x gt y or x lt -y)

If alpha, beta be the roots of 4x^(2) - 16x + c = 0, c in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 , then the number of integral values of c is

Two open pipes of length L are vibrated simultaneously. If length of one of the pipes is reduced by y. then the number of beats heats per second will be if the velocity of sound is v and y lt lt L :-