All India Engineering / Architecture Entrance Examination (AIEEE)

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AIEEE 2009 Maths

 Q. 13. Let  f (x) = x |x| and g (x) = sinx.

Statement-1: is differentiable at x = 0 and its derivative is continuous at that point.

Statement-2: is twice differentiable at x = 0.

1. Statement-1 is false, Statement-2 is true.
   
   
2. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
   
   
3. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
   
   
4. Statement-1 is true, Statement-2 is false.

Sol:  

Answer: (4)

Q. 14. Given p(x) = x⁴ + ax³+ bx² + cx + d such that x = 0 is the only real root of p` (x) = 0. If p(-1) < p(1), then in the interval [-1, 1]

1. neither p (-1)is the minimum nor p(1)is the maximum of p
   
   
2. p (-1)is the minimum and p(1) is the maximum of p
   
   
3. p (-1)  is not minimum but p(1) is the maximum of p
   
   
4. p (-1) is the minimum but p(1) is not the maximum of p

Sol: 

Answer: (3)

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