Monday, February 20, 2012

Solve Examples 1

1. Which of the following is a natural number?
A) -9    B)0    C) 1    D)   5.25
Ans: Zero, negative integers & fractions are not natural numbers. Only positive integers are natural numbers. Ans: (C)

2. Which of the following is a prime number?
A) 2   B) 0   C) 1   D) 143
Ans: 143/11=13. 0&1 are not primes by definition. 2 is a prime. Hence the answer is A.

3. Which of the following is a real number?
A) -7   B) 3.5   C) -3*1\3   D)All
Ans: Any number that can be represented in the number line is a real number. Here the numbers are real. So, the answer is D.

4. Which of the following is an irrational number?
A) 5  B)  2  C) 5.75  D) 6.66666
Ans: 2 can't be expressed as the ratio of two integers. Hence this is an irrational number. So, the answer is B.

5. Which one is correct?
A) -3>-2   B) /3/>/-3/  C) 4<3   D) -3<-2
Ans: Let us plot al the numbers in the number line.

We know that as we move right along the number line, the numbers grow larger. So, options A & C are false. From the definition of absolute value we know that, /3/=3=/-3/
So, B is also false. D is correct.

6. If n is an integer, which of the following must be odd?
A) n    B) 2n   C) n+2   D) 2n+1
Ans: IN general, an odd integer can be represented as 2n +1 . So, the answer is D.

7. If an is an even integer, which of the following must be3 an odd integer
A) 7n-2   B) 5(n-2)   C) (16n+24)/8  D)  (6n+24)/3
Ans: 7n-2=7 x even -2=even
     5(n-2)=5 (even-2)=5 x even=even
(16n+24)/8= 2n+3=2 x even + odd= even+ odd=odd
Ans: C

8. What is the product of the odd integers between -8 and 8 ?
A) 0   B) 10050   C) 12025   D) 5005
Ans: The odd integers between -8 & 8 are -7,-5,-3,-1,1,3,5,7. Their product is 11025. Hence C is the answer. Zero is an even integer. 

(6n+12)/3=2n+4= 2 x even+even = even+even = even

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