JEE Advanced2024MathematicsMatricesActual
Let and be the distinct roots of the equation x^2+x-1=0 . Consider the set T= 1, , . For a 3 3 matrix M= (a_ i j )_ 3 3 , define R_i=a_ i 1 +a_ i 2 +a_ i 3 and C_j=a_ 1 j +a_ 2 j +a_ 3 j for i=1,2,3 and j=1,2,3 . Match each entry in List-I to the correct entry in List-II. The correct option is
Options
- A( P ) (4) ( Q ) (2) ( R ) (5) ( S ) (1)
- B( P ) (2) ( Q ) (4) ( R ) (1) ( S ) (5)
- C( P ) (2) ( Q ) (4) ( R ) (3) ( S ) (5)
- D( P ) (1) ( Q ) (5) ( R ) (3) ( S ) (4)
Correct answer
C. ( P ) (2) ( Q ) (4) ( R ) (3) ( S ) (5)
Step-by-step solution
aligned & , are roots of x ^2+ x -1=0 & + =-1 1+ + =0 & M= [ array lll a ₁₁ & a ₁₂ & a ₁₃ a ₂₁ & a ₂₂ & a ₂₃ a ₃₁ & a ₃₂ & a ₃₃ array ] aligned (P) M= [ array lll 1 & & & & 1 & 1 & array ] 3! 2=12 For one arrangement of row 1 we can arrange other two rows exactly in two ways and row 1 can be arranged in 3 ! ways 3! 2=12 ways (Q) M= [ array lll x & a & b a & y & c b & c & z array ] Consider one such arrangement with a= , b= , c=1M= [ array lll 1 & & & & 1 & 1 & array ] a, b, c can be arranged in 3 ! ways and corresp