Minimum vlaue of `|x-p| + |x-15| +|x-p-15|.` If `p le x le 15 and 0 lt p lt 15` :

3y - 5x lt 15

The minimum value of the expression |x-p|+|x-15|+|x-p-15| for ' x ' in the range plt=xlt=15 where x

The minimum value of the expression |x-p+|x-15|+|x-p-15| for ' x ' in the range plt=xlt=15 where x

Solve 0 lt | x-3| le 5

If x is a real number and |5-(x-3)|+8lt15 , then (i) 1 le x le 15 (ii) 1lt x lt 15 (iii) 1 lt x le 15 (iv) 1 le x le 15

Let 0 lt A_(i) lt pi for i = 1,2,"……"n . Use mathematical induction to prove that sin A_(1) + sin A_(2)+ "….." + sin A_(n) le n sin ((A_(1) + A_(2) + "……" + A_(n))/(n)) where n ge 1 is a natural number. [You may use the fact that p sin x + (1-p) sin y le sin [px+(1-p)y] , where 0 le p le 1 and 0 le x , y le pi ]

If 0 lt x lt 2 pi and |cos x| le sin x , then

Let f (x) be defined as f (x) ={{:(|x|, 0 le x lt1),(|x-1|+|x-2|, 1 le x lt2),(|x-3|, 2 le x lt 3):} The range of function g (x)= sin (7 (f (x)) is :

Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis(a) R = {(x, y) : 0 le x le a, 0 le y le b} (b) R = {(x,y) : 0 le x lt a, 0 le y le b} (c) R = {(x,y): 0 le x le a, 0 lt y lt b} (d) R = {(x,y): 0 lt x lt a, 0 lt y lt b}

Given P = {x:9 lt 2x - 1 le 13, x in R} and Q = { x : - 5 le 3+ 4x lt 15, x in I} Where R={Real Numbers} and I={Integers}.Represent P and Q on number lines. Write down the elements of P nnQ