Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202124 Sep 2021Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC with usual notations a =2, ~b =3 , then value of 2 A a^2 - 2 B b^2 is

Options

  1. A5 36
  2. B1 4
  3. C1 9
  4. D13 19

Correct answer

A. 5 36

Step-by-step solution

aligned & 2 ~A a ^2 - 2 ~B ~b ^2 & = 1-2 ^2 ~A a ^2 - 1-2 ^2 ~B ~b ^2 = ( 1 a ^2 - 1 ~b ^2 )-2 ( ^2 ~A a ^2 - ^2 ~B ~b ^2 ) aligned From sine rule, we know that aligned & a A = b B & Given Expression = ( 1 a ^2 - 1 ~b ^2 )-0= 1 2^2 - 1 3^2 = 1 4 - 1 9 = 5 36 aligned

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In A B C , if A, B, C are in arithmetic progression then a ^2- ac + c ^2 ( ~A - C 2 )= 2025If in A B C, B=45^ , a=2( 3 +1) and area of A B C is 6+2 3 sq.units, then the side b = 2025In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025In a triangle ABC, if r ₁: r ₂=3: 4 and r ₂: r ₃=2: 3 , then a : b : c = 2025 Full Properties of Triangles list All MHT CET PYQs