All India Engineering / Architecture Entrance Examination (AIEEE)

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AIEEE 2010 Mathematics

Directions: Questions number 12 to 16 are Assertion-Reason type questions. Each of these questions
contains two statements:
Statement-1 : (Assertion) and
Statement-2 : (Reason).
Each of these questions also has four alternative choices, only one of which is the correct answer.
You have to select the Answer.

Q. 12. Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ……,20}.
Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is.  
Statement-2: If the four chosen numbers form an AP, then the set of all possible values of common difference is

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

Sol :

Required probability = 
Statement -2 is false because common difference can also be ±6.

Answer: (2)

Q. 13. Statement-1: The point  is the mirror image of the point  
in the plane .
Statement-2: The plane  bisects the line segment joining  and

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

Sol : 

Statement I and II both are true but statement II is not the correct explanation.
Plane is not just bisector but it is perpendicular bisector of AB.

Answer: (1)