All India Engineering / Architecture Entrance Examination (AIEEE)
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AIEEE 2008 MATHEMATICS
Q. 17. Let p be the statement 'x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.
Statement-1: r is equivalent to either q or p.
- Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
- Statement-1 is true, Statement-2 is false.
- Statement-1 is false, Statement-2 is true.
- Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Sol. P : x is an irrational number
~ p : x is rational number
q : y is a transcendental number
r : x is a rational number iff y is a transcendental number
| p | q | ~p | ~q |  |
s1: q or p |
 |
 |
| T | T | F | F | F | T | F | T |
| T | F | F | T | T | T | T | F |
| F | T | T | F | T | T | T | F |
| F | F | T | T | F | F | F | T |
We see that s, and r are not equivalent 
Also s2 and r are not equivalent 
Q. 18. In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement-1: The number of different ways the child can buy the six ice-creams is 
.
Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.
- Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
- Statement-1 is true, Statement-2 is false.
- Statement-1 is false, Statement-2 is true.
- Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Sol. The number of different ways the child can buy the b ice-creams
t1 + t2 + t3 + t4 + t5 = 6
= 6 + 5 - 1C5-1 = 10C4
