RATIO PROPORTION INDICES AND LOGARITHMS CA FOUNDATION TEST

Problem 1 :

(a) 4x² : 5y²    (b) 16x² : 25y²    (c) 25x² : 16y²

(d) none of these

Solution:

So, option (c) is correct.

Problem 2 :

(a) 2    (b) 3    (c) 5    (d) 6

Solution:

So, option (b) is correct.

Problem 3 :

If a^1/3 + b^1/3 + c^1/3 = 0 then the value of (a + b + c)³ is 

(a) abc    (b) 9bac      (c) 27abc     (d) 1/27abc

Solution:

So, option (c) is correct.

Problem 4 :

(a) 0      (b) 1      (c) -1       (d) None

Solution:

So, option (b) is correct.

Problem 5 :

(a) 3         (b) 3/2        (c) 1          (d) 2/3

Solution:

So, option (b) is correct.

Problem 6 :

Ratio between 25 hours and 45 minutes is

(a) 5 : 9           (b) 100 : 3       (c) cannot be determined

(d) None

Solution:

1 hour = 60 minutes

25 hours = 60 × 25

= 1500 minutes

Ratio of 1500 minutes and 45 minutes is

= 1500 : 45

= 100 : 3

So, option (b) is correct.

Problem 7 :

The logarithm of 21952 to the base of 2√7 and 19683 to the base of 3√3 are

(a) Equal      (b) Not equal       (c) have a difference of 2269

(d) None

Solution:

So, option (a) is correct.

Problem 8 :

(a) 116 : 31     (b) 19 : 37      (c) 11 : 43     (d) 18 : 35

Solution:

Given, a  = 4, b = 3 and x = 7, y = 5

So, option (c) is correct.

Problem 9 :

If 2^x × 3^y × 5^z = 360 Then what is the value of x, y, z ?

(a) 3, 2, 1     (b) 1, 2, 3      (c) 2, 3, 1     (d) 1, 3, 2

Solution:

2^x × 3^y × 5^z = 360

2^x × 3^y × 5^z = 36 × 10

= 2 × 2 × 3 × 5 × 2

So, 2^x × 3^y × 5^z = 2³ × 3² × 5¹

x = 3, y = 2, z = 1

So, option (a) is correct.

Problem 10 :

Solution:

So, option (b) is correct.