CBSE - Number Systems

1 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 

2 Number Systems 

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

3 Number Systems 

If   , then the value of x² + 2x + 3 is:

(1) 3 
(2) 0 
(3) 4 
(d) 1

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 

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

6 Number Systems 

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

(1) 3x 
(2) 3 / x
(3)  
(4)  

7 Number Systems 

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x²  + bx + q = 0 has equal roots, then q = 

(1)  8  
(2)  – 8
(3)  16
(4)  – 16 

 

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 

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