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Solution


Q.

Match the range of functions given in Column I with Column II.

  Column I   Column II
A f(x)=|sinx|, x∈R p [0, 2]
B f(x)=|3-x|+|2+x|, x∈[0,4] q [5, 7]
C f(x)=x4+2x2+5, x∈[-1,1] r [0, 1]
D f(x)=cos2x, x∈R s [5, 8]

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

Ans.

(4)

A) f'(x)=(1-x)(2x+1)ex(1-x)≥0, range is [0,1]

B) f(x)={1-2x,x<-25,-2≤x<32x-1,x≥3         Min. value of f(x)=5

     Max. value of f(x)=2(4)-1=7

C) f(x)=(x2+1)2+4, Minimum at x=0

D) f'(x)=2x3(2-x2)e-x2⇒Decreasing in [-1,0]