Home
Class 12
MATHS
Consider a triangle PQR having sides of ...

Consider a triangle PQR having sides of lengths p,q,r opposite to the angles P,Q,R respectively. Then which of the following statements is (are) true?

A

`cosP ge 1 −p^2/(2qr)`

B

`cosR ge ((q−r)/(p+q)) cos P + ((p−r)/(p+q))cos Q`

C

`(q+r)/p lt 2(sqrt(sinQ sinR))/sin P`

D

if `p lt q and p lt r`, then `cosQ gt p/r and cosR gt p/q`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE ADVANCED

    JEE ADVANCED PREVIOUS YEAR|Exercise MATHS|36 Videos

  • JEE ADVANCED 2022

    JEE ADVANCED PREVIOUS YEAR|Exercise MATHEMATICS (SECTION -3)|4 Videos

Similar Questions

Explore conceptually related problems

Given that P+Q+R=0 . Which of the following statement is true?

If p,q,r have truth values T,F,T respectively, which of the following is true ?

In a triangle P Q R , let /_P Q R=30o and the sides P Q and Q R have lengths 10sqrt(3) and 10, respectively. Then, which of the following statement(s) is (are) TRUE? /_Q P R=45o (b) The area of the triangle P Q R is 25sqrt(3) and /_Q R P=120o (c) The radius of the incircle of the triangle P Q R is 10sqrt(3)-15 (d) The area of the circumcircle of the triangle P Q R is 100 pi

If p, q are true and r is false statement then which of the following is true statement?

In a non right angled triangle DeltaPQR , let p,q,r denote the lengths of the sides opposite to the angle P,Q,R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. if p=sqrt(3),q=1 and the radius of the circumcircle of the DeltaPQR equals to 1, then which of the followign options is/are correct?

Let PQR be a triangle of area Delta with a = 2, b = 7//2 , and c = 5//2 , where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R, respectively. Then (2 sin P - sin 2P)/(2 sin P + sin 2P) equals

Let PQR be a triangle of ! area with a = 2 , b = 7/2 and c = 5/2 , where a , b and c are the lengths of the sides of the triangle opposite to the angles P , Q and R respectively. Then , (2sinP-sin2P)/(2sinP+sinP) equals

JEE ADVANCED PREVIOUS YEAR-JEE ADVANCED 2021-QUESTION
  1. Let vecu , vecv and vecw be vectors in three-dimensional space, where ...

    Text Solution

    |

  2. Let s1 = {(i,j, k) ∶ i,j, k ∈ {1,2, … ,10}} ,s2 = {(i,j) ∶ 1 ≤ i < j +...

    Text Solution

    |

  3. Consider a triangle PQR having sides of lengths p,q,r opposite to the ...

    Text Solution

    |

  4. Let f:[-pi/2,pi/2] to R be a continuous function such that f(0)=1 and ...

    Text Solution

    |

  5. For any real number alpha and beta , let y(alpha,beta)(x): alpha,beta ...

    Text Solution

    |

  6. Let O be the origin and vec(OA)=2hati+2hatj+hatk , vec(OB)=hati-2hatj+...

    Text Solution

    |

  7. Let E denote the parabola y^2 = 8x. Let P = (-2,4), and let Q and Q' b...

    Text Solution

    |

  8. Consider the region R = {(x, y) in R xx R : x ge 0 and y^2 le (4 − x)}...

    Text Solution

    |

  9. Consider the region R = {(x, y) in R xx R : x ge 0 and y^2 le (4 − x)}...

    Text Solution

    |

  10. Let f1 : (0, oo) to R and f2 : (0, oo) to R be defined by f1(x) = int0...

    Text Solution

    |

  11. Let f1 : (0, oo) to R and f2 : (0, oo) to R be defined by f1(x) = int0...

    Text Solution

    |

  12. Let gi:[pi/8,(3pi)/8] to R , i=1,2 , and f:[pi/8,(3pi)/8] to R be func...

    Text Solution

    |

  13. Let gi:[pi/8,(3pi)/8] to R , i=1,2 , and f:[pi/8,(3pi)/8] to R be func...

    Text Solution

    |

  14. Consider M with r=1025/513. Let k be the number of all those circle Cn...

    Text Solution

    |

  15. Consider M with r=((2^199-1)sqrt2)/2^198. The number of all those circ...

    Text Solution

    |

  16. Let psi1:[0,oo] to R , psi2:[0,oo) to R , f:[0,oo) to R and g :[0,oo) ...

    Text Solution

    |

  17. Let psi1:[0,oo] to R , psi2:[0,oo) to R , f:[0,oo) to R and g :[0,oo) ...

    Text Solution

    |

  18. A number is chosen at random from the set {1,2,3, . . . 2000} Let p be...

    Text Solution

    |

  19. Let E be the ellipse x^2/16+y^2/9=1. For For any three distinct points...

    Text Solution

    |

  20. For any real number x, let [x] denote the largest integer less than or...

    Text Solution

    |