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Consider the sets A = ( x , y ) R R : x ^2+ y ^2=25 , B = ( x , y ) R R : x ^2+9 y ^2=144 , C = ( x , y ) . Z Z : x^2+y^2 4 , and D=A B . The total number of one-one functions from the set D to the set C is:

Options

  1. A15120
  2. B19320
  3. C17160
  4. D18290

Correct answer

C. 17160

Step-by-step solution

A : x ^2+ y ^2=25...(i) B : x^2 144 + y^2 16 =1...(ii) C: x^2+y^2 4...(iii) Solve (1) & (2) aligned & x^2+9 (25-x^2 )=144 & -8 x^2=144-225=-81 & x= 9 2 2 aligned By (1) y= 25-x^2 = 25- 81 8 = 119 2 2 D = A ~B = ( 9 2 2 , 119 2 2 ), ( 9 2 2 ,- 119 2 2 ), ( -9 2 2 , 119 2 2 ), ( -9 2 2 , - 119 2 2 ) No. of elements in set D=4 aligned & C= (x, y) Z Z : x ^2+ y ^2 4 & = (0,2),(2,0),(0,-2),(-2,0),(1,1),(-1,-1), & (1,-1),(-1,1),(1,0),(0,1),(-1,0),(0,-1), & (0,0) aligned No. of elements in set C =13 Total no. of one-one f

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