CDS II 2020 Elementary Mathematics Previous Year Paper (08-Nov-2020)

Question 1

x3 +  x 2 + 16 is exactly divisible by x, where x is a positive integer. The number of all such possible values of x is

Accepted Answer

5

Answer

3

Answer

4

Answer

6

Question 2

The number of (a,b,c), where a,b,c are positive integers such that abc = 30, is

Accepted Answer

27

Answer

30

Answer

9

Answer

8

Question 3

If the roots of the quadratic equation x 2 - 4x - log 10  N = 0 are real, then what is the minimum value of N ?

Accepted Answer

$\frac{1}{10000}$

Answer

1

Answer

$\frac{1}{10}$

Answer

$\frac{1}{1000}$

Question 4

The number of different solutions of the equations x + y + z = 12, where each of x,y and z is a positive integer, is

Accepted Answer

55

Answer

53

Answer

54

Answer

56

Question 5

If I = a 2 + b2 + c 2, where a and b are consecutive integers and c = ab, then I is

Accepted Answer

square of an odd integer

Answer

an even number and it is not a square of an integer

Answer

an odd number and it is not a square of an integer

Answer

square of an even integer