Home
Class 11
MATHS
The number of ordered pairs (x,y) satisf...

The number of ordered pairs (x,y) satisfying `|x|+|y|=2 and sin""((pix^(2))/(3))=1 ` is/are

A

2

B

3

C

4

D

6

Text Solution

Verified by Experts

`|x|+|y|=2, sin ((pi x^(2))/3)=1`
`rArr |x|, |y| in [0, 2], (pi x^(2))/3=(4n+1) pi/2, n in Z`
`rArr x^(2)=(3(4n+1))/2=3/2`, as `|x| le 2`
`rArr |a|=sqrt(3/2), |y|=4-sqrt(3/2)`
Thus, there are four ordered pairs.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Find the number of redered pairs (x,y) satisfying x^2+1=y and y^2+1=x

If x, y in [0,2pi] then find the total number of order pair (x,y) satisfying the equation sinx .cos y = 1

The number of ordered pairs of integers (x ,y) satisfying the equation x^2+6x+y^2=4 is a. 2 b. 8 c. 6 d. none of these

For 0ltx ,yltpi, the number of ordered pairs (x, y) satisfying system equations cot^2(x-y)-(1+sqrt(3))cot(x-y)+sqrt(3)="0 and cosy="(sqrt(3))/2 is

The number of all possible ordered pairs (x, y), x, y in R satisfying the system of equations x+y=(2pi)/3, cosx+cosy=3/2 is

If x in (0,2pi)a n dy in (0,2pi) , then find the number of distinct ordered pairs (x , y) satisfying the equation 9cos^2x+sec^2y-6cosx-4secy+5=0

The number of ordered pairs which satisfy the equation x^2+2xsin(x y)+1=0 are (where y in [0,2pi] ) (a) 1 (b) 2 (c) 3 (d) 0

Find the number ordered pairs (x ,y)ifx ,y in {0,1,2,3, , 10}a n dif|x-y|> 5.

The number of ordered pairs (x,y) , where x , y in N for which 4 , x , y are in H.P. , is equal to

The locus of the point P(x,y) satisfying the relation sqrt((x-3) ^(2) +(y-1)^(2))+ sqrt((x+3) ^(2) +(y-1)^(2))=6 is-

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. The equation tan^4x-2sec^2x+a=0 will have at least one solution if

    Text Solution

    |

  2. A tower P Q stands at a point P within the triangular park A B C such ...

    Text Solution

    |

  3. The number of ordered pairs (x,y) satisfying |x|+|y|=2 and sin""((pi...

    Text Solution

    |

  4. If tanbeta=(tanalpha+tangamma)/(1+tanalphatangamma)dot prove that sin...

    Text Solution

    |

  5. Prove that a(bcosC-c cosB)=b^2-c^2

    Text Solution

    |

  6. If 4sin^4x+cos^4x=1,then x is equal to (n in Z) (a)npi (b) npi+-...

    Text Solution

    |

  7. If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/...

    Text Solution

    |

  8. If in a triangle acos^2(C/2)+ c cos^2(A/2)=(3b)/2, then find the rela...

    Text Solution

    |

  9. Evaluate cosacos2acos3a......... cos 999 a , where a=(2pi)/(1999)dot

    Text Solution

    |

  10. If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z)

    Text Solution

    |

  11. Let ABC be a triangle of area 24sq.units and PQR be the triangle forme...

    Text Solution

    |

  12. Find the number of pairs of integer (x , y) that satisfy the followin...

    Text Solution

    |

  13. Prove that (4cos^2 9^0-3)(4cos^2 27^0-3)=tan9^0dot

    Text Solution

    |

  14. Let A D be a median of the A B Cdot If A Ea n dA F are medians of ...

    Text Solution

    |

  15. Find the value of cos12^0+cos84^0+cos156^0+cos132^0

    Text Solution

    |

  16. If no solution of 3siny+12sin^3x=a lies on the line y=3x , then a in ...

    Text Solution

    |

  17. If in a triangle P Q R ,sinP ,sinQ ,sinR a r e i n AdotPdot , then ...

    Text Solution

    |

  18. Find the angle theta whose cosine is equal to its tangent.

    Text Solution

    |

  19. If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,np...

    Text Solution

    |

  20. If in a triangle the angles are in the ratio as 1:2:3 , prove that the...

    Text Solution

    |