Mathematics Times – July 2019

Since x y 1  1 tan ( ) tan ( )x 1  y 1 tan ( ) tan (x 1  y 1 1) and 1 5 2 1 2   y Notice the function tant is increas ...

12.Sol: Suppose that the persons A to E are seated clockwise around the circle as shown below i.e., a b c    0   Minimum ...

SECTION-III 15.Sol: So g x cos 2 sin xvanishes only when 2 sin x is an odd multiple of 2  , i.e. 2 sin xis an odd multi ...

(I) 2 r MN  3 3 4 4 12^2 ^2    r 6 centre C of circle C 3 lies on 4 3 y x Let 4 , 3 C h h    12 3 3 2 OC MC OM  ...

For Find the smallest value of x 0 , the smallest value of   4 8 13^2 6 1 x x x    is: (a) 1 (b) 2 (c) 25 12 (d) 13 6 2 ...

  36 4.4.9 0y^2   y^2 4 0  y 2 or y 2 (extraneous because whenx y 0, 0). From y 2 ,we know the smallest value of y ...

maximum value is 9 2 when x 2. 7.Sol: Method 1: x xy y x xy y x xy y^2        ^23 ^22  2 2^22    2    3.3 2x ...

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