Problems Based on Numbers
The counting and exchanging of the articles had been felt by man as a necessity in life since the birth of our civilization. As the counting numbers N = 1, 2, 3,………. has become a natural part of our life, they are simply called the ‘natural numbers’. The smallest natural number is 1 whereas there is no upper limit for the largest number. Further, if we count zero as the beginning number of N, the whole set viz. 0, 1, 2, 3,………… is called the ‘whole Numbers’.
If we add or multiply any two natural the result is a natural number. On the other hand, the result of the subtraction or division of two natural numbers may not be a natural number.
1. Integers : The positive, zero and the negative natural constitute INTEGERS i.e.
I= -3,-2,-1, 0, 1, 2, 3,...
2. Prime Numbers : Any number which cannot be divided by any other number without the remainder. For instance, there are twenty six prime numbers in the first hundred viz. 2, 3, 5, 7, 11,13,17,19, 23, 29, 31,37,41,43,47,53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Thus, there are 25 prime numbers in the first hundred.
3. Composite Numbers : All non-prime numbers are referred as the composite numbers.
3. (a) Even Numbers : The numbers divisible by two e.g. 2, 4, 6, 8, 10, 12,……….
3. (b) Odd Numbers : The numbers which are not divisible by 2, e.g. 3, 5, 7, 9, 11, 13, 15, 17, 19, 21,……..
4. Consecutive Numbers : A series of numbers in which each number is greater OR smaller than its succeeding or proceeding number by unity e.g. if x is a number, its consecutive are x-1, x, x+1.
5. Rational Numbers : If p is any integer and q is a non-zero integer, then R = p/q is called a rational number e.g. 2/3,5/6,11/12…….
In general, p can be positive, zero OR negative integers but q > 0. q cannot be zero i.e. q≠0, otherwise R becomes infinite.
1. The sum of the squares of first ten natural numbers is
(a) 281
(b) 402
(c) 385
(d) 502
2. The sum of the first seventeen prime number is
(a) 440
(b) 329
(c) 498
(d) 382
3. The sum of the prime number below 100 is
(a) 1061
(b) 1058
(c) 1160
(d) None of these
4. The number of prime numbers upto the counting 100 is
(a) 26
(b) 24
(c) 25
(d) 23
5. The multiplication of seven first odd numbers divided by the sum of nine even numbers provides the answer as
(a) 1501.5
(b) 1877.2
(c) 2413.1
(d) None of these
6. The product of two odd prime numbers is
(a) even
(b) odd
(c) either even or odd
(d) It depends upon the numbers chosen
7. Zero is counted as
(a) Whole number
(b) Prime number
(c) Integer
(d) a and c both are correct
8. Search the prime numbers from the given list
2, 12, 21, 37, 53, 101, 72,
(a) 2, 21, 53
(b) 12, 37, 53, 101
(c) 2, 37, 53, 101
(d) 2, 72, 101
9. Two rational numbers lying between 4/5 and 6/7 are
(a) 71/35,5/6
(b) 29/21,5/6
(c) 29/35,57/70
(d) None of these
10. The square root of a number which is divisible by 2, 4, 5 and 8 is
(a) 900
(b) 800
(c) 1600
(d) 400
Answer Key:
1.c
2.a
3.d
4.c
5.a
6.b
7.d
8.c
9.c
10.c
1.c
2.a
3.d
4.c
5.a
6.b
7.d
8.c
9.c
10.c
No comments:
Post a Comment