CBSE - Number Systems

1 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 

2 Number Systems 

The absolute value of an integer x is represented by :

1) [x]
2) {x} 
3) (x)
4) | x |  

3 Number Systems 

What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24? . 

1) 259
2) 355
3) 255
4) none

4 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

5 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 

6 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

7 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)

8 Number Systems 

If x, y, z are positive real numbers and a, b, c are rational numbers, then the value of    is :

(1)  –1  
(2)  0 
(3)  1 
(4)  none of these 

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 

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

(1) 3x 
(2) 3 / x
(3)  
(4)