JEE Advanced2008MathematicsBasics of MathematicsActual
Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.
Options
- A(A) r, (B) q,r, (C) s, (D) p,r
- B(A) s, (B) q,s, (C) r, (D) p,q
- C(A) s, (B) q,r, (C) s, (D) p,q
- D(A) r, (B) q,s, (C) r, (D) p,r
Correct answer
D. (A) r, (B) q,s, (C) r, (D) p,r
Step-by-step solution
(A) Let y= x^2+2 x+4 x+2 aligned & x^2+(2-y) x+(4-2 y)=0 & (2-y)^2-4(4-2 y) 0 & y^2+4 y-12 0 & y -6, y 2 & aligned Minimum value of y is 2 . (B) Since, (A+B)(A-B)=(A-B)(A+B) aligned & A^2-A B+B A-B^2=A^2+A B-B A-B^2 & A B=B A & and (A B)^t=(-1)^k A B & B^t A^t=(-1)^k A B & -B A=(-1)^k A B [ B^t=-B, A^t=A ] & B A=(-1)^ k+1 A B & (-1)^ k+1 =1 & aligned k+1 is even or k is odd. (C) 1 ₂ 3>1 k>0 array From Eqs. (ii) and (iii), 0 < k < 2 k=1[ k is an integer] array rlrl (D) & & = & ( 2 - ) & = & 2 - & =2 n , n Z & & - 2