CBSE - Number Systems

1 Number Systems 

If an integer a is less than integer b, then :

1) a lies on the right of b on the number line
2) b lies on the right of a on the number line
3) a lies on the left of b on the number line
4) Both (2) & (3)

2 Number Systems 

Sum of the roots of the equation x⁴ - 3(2^{x + 3}) + 128 = 0, is:

(1) 0 
(2) 7
(3) 5 
(4) 8

3 Number Systems 

Four positive integers sum to 125. If the first of these numbers is increased by 4, the second is decreased by 4, the third is multiplied by 4 and the fourth is divided by 4, we find four equal numbers, then four original integers are: 

1) 16, 24, 25, 80
2) 8, 22, 38, 57 
3) 7, 19, 46, 53
4) 12, 28, 40, 45 

4 Number Systems 

If a < b < c < d < e are consecutive positive integers, such that b + c+ d is a perfect square and a + b + c + d + e is a perfect cube. What is the smallest possible value of c?

1) 675
2) 576
3) 475
4) 384 

5 Number Systems 

What is the largest integer that is a divisor of (n +1) (n+3) (n+5) (n+7) (n+9) for all positive even integers n? 

1) 3
2) 5 
3) 11
4) 15 

6 Number Systems 

The number obtained by adding 12 to a natural number is 160 times of the multiplicative inverse of the natural number. Find the number.

1) 20
2) 16
3) 12
4) 8

7 Number Systems 

If p = x + 1/x  then the value of p – 1/p  will be -

(1) 3x 
(2) 3 / x
(3)  
(4)  

8 Number Systems 

The absolute value of an integer x is represented by :

1) [x]
2) {x} 
3) (x)
4) | x |  

9 Number Systems 

If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b is :

(1)  2  
(2)  3
(3)  5
(4)  10

10 Number Systems 

The rational form of –25.6875 is :-
1)-(411/16)
2)-(421/16)
3)-(431/16)
4)-(441/16)