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JEE Advanced2011MathematicsFunctionsActual

Match the statements given in Column I with the intervals/union of intervals given in Column II.

Options

  1. A(A) q, (B) r, (C) s, (D) t
  2. B(A) s, (B) t, (C) r, (D) q
  3. C(A) q, (B) r, (C) s, (D) r
  4. D(A) s, (B) t, (C) r, (D) r

Correct answer

D. (A) s, (B) t, (C) r, (D) r

Step-by-step solution

(A) Given, |z|=1 z z =1 2 i z 1-z^2 = 2 i z z z -z^2 = 2 i z -z , Let z=x+i y z- z =2 i y= 2 i -2 i y =- 1 y where, y= 1-x^2 -1 y 1 -1 y and y 1 -1 1 y and 1 y 1 Re ( 2 i z 1-z^2 ) (- ,-1] [1, ) (B) f(x)= ⁻¹ ( 8 (3^ x-2 ) 1-3^ 2(x-1) ) , aligned & For domain, -1 8 (3^ x-2 ) 1-3^ 2(x-1) 1 & -1 9 (3^ x-2 )- (3^ x-2 ) 1-3^ 2(x-1) 1 & -1 3^x-3^ x-2 1-3^x 3^ (x-2) 1 & 3^x-3^ x-2 1-3^x 3^ x-2 -1 & (3^x-1 ) (3^ x-2 -1 ) (3^ x-1 +1 ) (3^ x-1 -1 ) 0 & x (- , 0] (1, ) & and 3^x-3^ x-2 1-3^x 3^ x-2 1 & (3^ x-2 -1 ) (3^x+1 ) (

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