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Test: Ratio And Proportion, Indices, Logarithms - 2

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Ratio And Proportion, Indices, Logarithms - 2

Description

Attempt Test: Ratio And Proportion, Indices, Logarithms - 2 | 40 questions in 40 minutes | Mock test for CA Foundation preparation | Free important questions MCQ to study Quantitative Aptitude for CA CPT for CA Foundation Exam | Download free PDF with solutions

QUESTION: 1

Division of Rs. 750 into 3 parts in the ratio 4 : 5 : 6 is

A.
(200, 250, 300)
B.
(250, 250, 250)
C.
(350, 250, 150)
D.
none of these

Solution:

QUESTION: 2

The sum of the ages of 3 persons is 150 years. 10 years ago their ages were in the ratio 7 : 8 : 9. Their present ages are

A.
(45, 50, 55)
B.
(40, 60, 50)
C.
(35, 45, 70)
D.
none of these

Solution:

QUESTION: 3

The numbers 14, 16, 35, 42 are not in proportion. The fourth term for which they will be in proportion is

A.
45
B.
40
C.
32
D.
none of these

Solution:

QUESTION: 4

If x/y = z/w, implies y/x = w/z, then the process is called

A.
Dividendo
B.
Componendo
C.
Alternendo
D.
none of these

Solution:

QUESTION: 5

If p/q = r/s = p–r/q–s, the process is called

A.
Subtrahendo
B.
Addendo
C.
Invertendo
D.
none of these

Solution:

QUESTION: 6

If a/b = c/d, implies (a+b)/(a–b) = (c+d)/(c–d), the process is called

A.
Componendo
B.
Dividendo
C.
Componendo and Dividendo
D.
none of these

Solution:

QUESTION: 7

If u/v = w/p, then (u–v)/(u+v) = (w–p)/(w+p). The process is called

A.
Invertendo
B.
Alternendo
C.
Addendo
D.
none of these

Solution:

QUESTION: 8

12, 16, *, 20 are in proportion. Then * is

A.
25
B.
14
C.
15
D.
none of these

Solution:

QUESTION: 9

4, *, 9, 13½ are in proportion. Then * is

A.
6
B.
8
C.
9
D.
none of these

Solution:

QUESTION: 10

The mean proportional between 1.4 gms and 5.6 gms is

A.
28 gms
B.
2.8 gms
C.
3.2 gms
D.
none of these

Solution:

Let 1.4 gms, x gms and 5.6 gms be in continuous proportion.

(Mean proportional terms)^2 = Product of extremes.

Therefore x^2 = 1.4 x 5.6

therefore x^2 = 7.84

therefore x= 2.8 gms.

QUESTION: 11

A.
4
B.
2
C.
7
D.
none of these

Solution:

QUESTION: 12

Two numbers are in the ratio 3 : 4; if 6 be added to each terms of the ratio, then the new ratio will be 4 : 5, then the numbers are

A.
14, 20
B.
17, 19
C.
18 and 24
D.
none of these

Solution:

QUESTION: 13

A.
B.
C.
D.
none of these

Solution:

QUESTION: 14

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

A.
2 : 5
B.
3 : 5
C.
4 : 5
D.
6 : 7

Solution:

QUESTION: 15

if then (b-c)x + (c-a)y+(a-b)z is

A.
1
B.
0
C.
5
D.
none of these

Solution:

Let X=(b+c-a);y=(c+a-b);z=(a+b-c)

=(b-c)(b+c-a)+(c-a)(c+a-b)+(a-b)(a+b-c)

=b^2-c^2-ab+ac+c^2-a^2-bc+ab+a^2-b^2-ac+bc

=0

QUESTION: 16

4x^–1/4 is expressed as

A.
-4x^–1/4
B.
x^–1
C.
4/x^1/4
D.
none of these

Solution:

QUESTION: 17

The value of 8^1/3 is

A.
B.
4
C.
2
D.
none of these

Solution:

QUESTION: 18

The value of 2 × (32) ^1/5 is

A.
2
B.
10
C.
4
D.
none of these

Solution:

QUESTION: 19

The value of 4/(32)^1/5 is

A.
8
B.
2
C.
4
D.
none of these

Solution:

QUESTION: 20

The value of (8/27)^1/3 is

A.
2/3
B.
3/2
C.
2/9
D.
none of these

Solution:

QUESTION: 21

2^½ .4^¾ is equal to

A.
a fraction
B.
a positive integer
C.
a negative integer
D.
none of these

Solution:

QUESTION: 22

has simplified value equal to

A.
xy²
B.
x²y
C.
9xy²
D.
none of these

Solution:

QUESTION: 23

x^a–b × x^b–c × x^c–a is equal to

A.
x
B.
1
C.
0
D.
none of these

Solution:

QUESTION: 24

The value of is equal to

A.
0
B.
2/3
C.
1
D.
none of these

Solution:

QUESTION: 25

{(3³)² × (4²)³ × (5³)²} / {(3²)³ × (4³)² × (5²)³} is

A.
3/4
B.
4/5
C.
4/7
D.
1

Solution:

QUESTION: 26

Which is True ?

A.
2⁰ > (1/2)⁰
B.
2⁰< (1/2)⁰
C.
2⁰ = (1/2)⁰
D.
none of these

Solution:

QUESTION: 27

If x^1/p = y^1/q = z^1/r and xyz = 1, then the value of p+q+r is

A.
1
B.
0
C.
1/2
D.
none of these

Solution:

QUESTION: 28

The value of y^a–b × y^b–c × y^c–a × y–^a–b is

A.
y^a+b
B.
y
C.
1
D.
1/y^a+b

Solution:

QUESTION: 29

The True option is

Solution:

QUESTION: 30

The simplified value of 16x^–3y²× 8^–1x³y^–2 is

A.
2xy
B.
xy/2
C.
2
D.
none of these

Solution:

QUESTION: 31

The value of (8/27)^–1/3 × (32/243)^–1/5 is

A.
9/4
B.
4/9
C.
2/3
D.
none of these

Solution:

QUESTION: 32

The value of {(x+y)^2/3 (x–y)^3/2/√x+y × √ (x–y)³}⁶ is

A.
(x+y)²
B.
(x–y)
C.
x+y
D.
none of these

Solution:

QUESTION: 33

Simplified value of (125)^2/3 × √25 × ³√5³× 5^1/2 is

A.
5
B.
1/5
C.
1
D.
none of these

Solution:

QUESTION: 34

[{(2)^1/2 . (4)^3/4 . (8)^5/6 . (16)^7/8 . (32)^9/10}4]^3/25 is

A.
A fraction
B.
an integer
C.
1
D.
none of these

Solution:

QUESTION: 35

[1–{1–(1–x²)^–1}^–1]^–1/2 is equal to

A.
x
B.
1/x
C.
1
D.
none of these

Solution:

ANSWER :- a

Solution :- [1–{1–(1–x²)^–1}^–1]^–1/2

=[1 - { 1- x² -1/(1-x²) }^-1]^-1/2 here we used a^-n = 1/aⁿ

= [1 - {(-x^2)/(1-x^2)}^-1]^-1/2

= [ 1 - { x^2 /( x^2 -1) }^-1]^-1/2

= [ 1- (x²-1)/ x²]^-1/2

= [ (x² -x²+1)/ x²]^-1/2

= [1/x²]^-1/2

= [x²]^1/2

= x ^2*1/2

= x

QUESTION: 36

Ajay and Raj together have Rs. 1050. On taking Rs. 150 from Ajay, Ajay will have same amount as what Raj had earlier. Find the ratio of amounts with Ajay and Raj initially.

A.
3:4
B.
7:1
C.
1:3
D.
4:3