JEE Advanced2006MathematicsProperties of TrianglesActual
Match the following.
Options
- A(i) (a), (ii) (b), (iii) (c)
- B(i) (b), (ii) (a), (iii) (c)
- C(i) (a), (ii) (c), (iii) (b)
- D(i) (b), (ii) (c), (iii) (a)
Correct answer
B. (i) (b), (ii) (a), (iii) (c)
Step-by-step solution
aligned & (i) _ i=1 ^ ⁻¹ ( 1 2 i^2 )=t _ i=1 ^ ⁻¹ ( 2 4 i^2-1+1 ) & _ i=1 ^ ⁻¹ (2 i+1)-(2 i-1) 1+(2 i-1)(2 i+1) & ( ⁻¹ 3- ⁻¹ 1 )+ ( ⁻¹ 5- ⁻¹ 3 )+ + ⁻¹(2 n+1)- ⁻¹(2 n-1) & t= _ n ( ⁻¹(2 n+1)- ⁻¹ 1 )= _ n ⁻¹ ( 2 n 1+2 n+1 )= 4 & t=1 . aligned (ii) We have, ₁= 1- ^2 ₁ 2 1+ ^2 ₂ 2 = a b+c ^2 2 = b+c-a b+c+a Also, ₃= 1- ^2 ₃ 2 1+ ^2 ₃ 2 = c a+b ^2 ₃ 2 = a+b-c a+b+c ^2 ₁ 2 + ^2 ₃ 2 = 2 b a+b+c = 2 b 3 b = 2 3 , [as, a, b, c are in AP 2 b=a+c ] (iii) Line through (0,1,0) and perpendicular to plane x+2 y+2 z=0 is given by