RATIO PROPORTION INDICES AND LOGARITHMS CA FOUNDATION QUESTIONS

Problem 1 :

In 40 litres mixture of glycerine and water, the ratio of glycerine and water is 3 : 1. The quantity of water added in the mixture in order to make this ratio 2 : 1 is

(a) 15 litres    (b) 10 litres        (c) 8 litres     (d) 5 litres

Solution:

The ratio of glycerine to water = 3 : 1

New ratio = 2 : 1

So, option (d) is correct.

Problem 2 :

p^a-b × p^b-c × p^c-a is equal to

(a) p                (b) 1           (c) 0         (d) none of these

Solution:

= p^a-b × p^b-c × p^c-a

= p^a-b+b-c+c-a

= p⁰

= 1

So, option (b) is correct.

Problem 3 :

(a) m + n = 1     (b) m/n = 1      (c) m - n = 1    (d) m² - n² = 1

Solution:

So, option (a) is correct.

Problem 4 : 

The compounded into of 4 : 9, the duplicate ratio of 3 : 4, the triplicate ratio of 2 : 3 and sub duplicate ratio of 9 : 64 is

(a) 2 : 7      (b) 7 : 2      (c) 1 : 36        (d) none of these

Solution:

Now, we have 4 ratios:

So, option (d) is correct.

Problem 5 :

If 2^x - 2^x-1 = 32, then the value of x is

(a) 4     (b) 5     (c) 6     (d) 7

Solution:

So, option (c) is correct.

Problem 6 :

The integral part of a logarithm is called _____, and the decimal part of a logarithm is called _____.

(a) Mantissa, Characteristic       (b) Characteristic, Mantissa

(c) Whole, Decimal         (d) None of these

Solution:

The integral part of a logarithm is called Characteristic, and the decimal part of a logarithm is called Mantissa.

So, option (b) is correct.

Problem 7 :

Given log 2 = 0.3010 and log 3 = 0.4771 then the value of log 24

(a) 1.3081     (b) 1.1038     (c) 1.3801      (d) 1.8301

Solution:

We know that,

log(ab) = log a + log b

Therefore, log 24 = log(2 x 2 x 2 x 3)

= log 2 + log 2 + log 2 + log 3

= 0.3010 + 0.3010 + 0.3010 + 0.4771

= 1.3801

So, option (c) is correct.

Problem 8 :

(a) 3    (b) 0      (c) 2      (d) 1

Solution:

So, option (b) is correct.

Problem 9 :

In a ratio, which is equal to 3 : 4, if the antecedent is 12, then the consequent is :

(a) 9      (b) 16       (c) 20        (d) 24

Solution:

So, option (b) is correct.

Problem 10 :

(a) 2         (b) 3          (c) 4         (d) 6

Solution:

So, option (a) is correct.