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JEE Advanced2009MathematicsFunctionsActual

Match the statements/expressions given in Column I with the values given in Column II.

Options

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

Correct answer

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

Step-by-step solution

(a) Let f(x)=x e^ x - x f^ (x)=e^ x +x e^ x x+ x 0 For interval x (0, 2 ) , f is strictly increasing. f(0)=-1 and f ( 2 )= 2 e one solution (b) Since, | array lll k & 4 & 1 4 & k & 2 2 & 2 & 1 array |=0 k(k-4)-4(0)+1(8-2 k)=0 k^2-6 k+8=0 k=2,4 (c) Let y=|x-1|+|x-2|+|x+1|+|x+2| For solutions, 4 k 6 k 3 / 2 Integer values of k are 2,3,4,5 . (d) Given, d y d x =y+1 |(y+1)|=x+C 2=C |y+1|=x+ 2 Put x= 2 (y+1)= 2+ 2= 4y+1=4 y=3

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