CA Foundation Quantitative Aptitude Important Question

  • By Team Koncept
  • 9 January, 2025
CA Foundation Quantitative Aptitude Important Question

CA Foundation Quantitative Aptitude Important Question

Most Expected Questions | CA Foundation Quantitative Aptitude

With the January 2025 CA Foundation exams fast approaching, we've created a blog featuring important practice questions for each chapter of the Quantitative Aptitude syllabus. Whether you're tackling topics like Statistics, Probability, or Time Value of Money, this curated question bank is designed to help you strengthen your problem-solving skills and boost exam confidence. Dive into the most exam-relevant questions to fine-tune your preparation and achieve success in the Quantitative Aptitude paper. Start practicing now and stay ahead of the competition!

Table of Content

Buisness Mathematics 

  1. Ratio and Proportion, Indices, Logarithms
  2. Equations
  3. Linear Inequalities
  4. Mathematics of Finance 
  5. Basic Concepts of Permutations and Combinations
  6. Sequence and Series - Arithmetic and Geometric Peogressions
  7. Sets, Relations and Functions, Basics of Limits and Continuity functions
  8. Basic Concepts of Diffrential and Integral Calculus

Logical Reasoning

  1. Number Series, Coding and Decoding and Odd Man Out
  2. Direction Tests
  3. Seating Arrangements
  4. Blood Relations

Statistics

  1. Statistical Representation of Data
  2. Sampling
  3. Measures of Central Tendency and DIspersion
  4. Probability
  5. Theorectical Distributions
  6. Correlation and Regression
  7. Index Number

CA Foundation Jan 25 Important Question Other Subjects Blogs :

  1. Important Question Jan 25 Paper 1 : Accounting
  2. Important Question Jan 25 Paper 2 : Business Laws 
  3. Important Question Jan 25 Paper 4 : Business Economics 
  4. CA Foundation Syllabus (New Updates)

CA Foundation Quantitative Aptitude Important Question - 5

Buisness Mathematics 

Chapter 1: Ratio and Proportion, Indices, Logarithms

Question 1. 

On simplification {\left( {\frac{{{x^{ab}}}}{{{x^{{a^2} + {b^2}}}}}} \right)^{(a + b)}} \times {\left( {\frac{{{x^{^{{b^2} + {c^2}}}}}}{{{x^{bc}}}}} \right)^{(b + c)}} \times {\left( {\frac{{{x^{ca}}}}{{{x^{{c^2} + {a^2}}}}}} \right)^{(c + a)}}   reduces to

  1. {x^{ - 2{a^3}}}
  2. {x^{2{a^3}}}
  3. {x^{ - 2({a^3} + {b^3} + {c^3})}}
  4. {x^{2({a^3} + {b^3} + {c^3})}}

Answer: a. {x^{ - 2{a^3}}}

Description: The expression = {({x^{ab - {a^2} - {b^2}}})^{a + b}} \times {({x^{{b^2} + {c^2} - bc}})^{b + c}} \times {({x^{ca - {c^2} - {a^2}}})^{c + a}}

= {x^{ - (a + b)({a^2} - ab + {b^2})}} \times {x^{(b + c)({b^2} + {c^2} - bc)}} \times {x^{(c + a)(ca - {c^2} - {a^2})}}

= {x^{ - {a^3} - {b^3} + {b^3} + {c^3} - {c^3} - {a^3}}} = {x^{ - 2{a^3}}}

Question 2. 

If xyz=1 then the value of \frac{1}{{1 + x + {y^{ - 1}}}} + \frac{1}{{1 + y + {z^{ - 1}}}} + \frac{1}{{1 + z + {x^{ - 1}}}} is

  1. 1
  2. 0
  3. 2
  4. None

Answer: a. 1

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Question 3. 

If  x = \sqrt 3 + \frac{1}{{\sqrt 3 }}  and y = \sqrt 3 - \frac{1}{{\sqrt 3 }}  then {x^2} - {y^2} is

  1. 5
  2. \sqrt 3
  3. \frac{1}{{\sqrt 3 }}
  4. 4

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Question 4. 

 If x:y:z = 2: 3:5 if x+ y+ z = 60 ,then the value of z

  1. 30
  2. 15
  3. 9
  4. 12

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 2: Equations

Question 1. 

Solving equation \sqrt {{y^2} + 4y - 21} + \sqrt {{y^2} - y - 6} = \sqrt {6{y^2} - 5y - 39} following roots are obtained

  1. 2, 3, 5/3
  2. 2, 3, -5/3
  3. -2, -3, 5/3
  4. -2, -3, -5/3

Answer: b. 2, 3, -5/3

Description: 

By the method of verification

{y^2} + 4y - 21 = (y + 7)(y - 3),

{y^2} - y - 6 = (y - 3)(y + 2),

6{y^2} - 5y - 39 = (6y + 13)(y - 3)

\therefore y=3 satisfies the equation.

y=2 also satisfies the equation. 

y=-5/3 also satisfies the equation. 

Question 2. 

Solve {x^3} + 3{x^2} - x - 3 = 0 given that the roots are in arithmetical progression 

  1. -1, 1, 3
  2. 1, 2, 3
  3. -3,-1,1
  4. -3,-2,-1

Answer: c. -3,-1,1

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Question 3. 

Solve {x^3} - 7{x^2} + 14x - 8 = 0 given that the roots are in geometrical progression

  1. \frac{1}{2}, 1, 2

  2. 1, 2, 4

  3. \frac{1}{2}, -1, 2

  4. -1, 2, -4

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Question 4.

If 2x -3y = 1 and 5x +2y = 50, then what is the value of (x-2y)? 

  1. -2
  2. 6
  3. 7
  4. 10

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 3: Linear Inequalities

Question 1. 

On solving the inequalities 2x + 5y ≤ 20, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0, we get the following situation

  1. (0, 0), (0, 4), (4, 0) and (20/11, 36/11)
  2. (0, 0), (10, 0), (0, 6) and (20/11,36/11)
  3. (0, 0), (0, 4), (4, 0) and (2, 3)
  4. (0, 0), (10, 0), (0, 6) and (2, 3)

Answer: a. (0, 0), (0, 4), (4, 0) and (20/11, 36/11)

Description: 

Here, 2x + 5y ≤ 20,

         3x + 2y ≤ 12,

         x ≥ 0,  

         y ≥ 0

The easiest and the quickest way to fin the answer is to use the values of x & y given in the options to solve the equation.

Situation (i) (0,0),(0,4),(4,0) and (\frac{{20}}{{11}},\frac{{36}}{{11}})

here x & y both the values can be zero hence it rules out (0,0) because it is true.

now x = 0 & y = 4

equation 1=  2x + 5y ≤ 20 

               =  2(0) + 5(4) ≤ 20

               =  0+20 ≤ 20

               = 20 = 20

This can be done for all the values and for both the equation. By Doing so we will find that values in option A satisfies both the inequalities hence it is the right answer.

Question 2.

The solution of the inequality (5-2x / 3) < x / 6 -  is 

  1.  x>8
  2.  x≤ 8 
  3. x=8
  4. none of these

Answer: a.  x>8

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Question 3.

The shaded region represents:

  1. 3x + 2y< 24,x + 2y> 16, x + y< 10x,x> 0,y>0
  2. 3x+2y<24, x+2y < 16, x+y > 10, x>0,y >0
  3. 3x + 2y < 24, x + 2y < 16, x + y < 10, x > 0, y > 0
  4. None of these.

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Question 4. 

 If the roots of (k-4)x2-26x+(k+5)=0are coincident . Then the value of k ?

  1. 14
  2. 20
  3. 18
  4. 22

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 4: Mathematics of Finance 

Question 1.

The compound interest on half-yearly rests on ₹ 10000 the rate for the first and second years being 6% and for the third year 9% p.a. is ₹______

  1. 2200
  2. 2287
  3. 2285
  4. None

Answer: d. None

Description: Relevant Data: 

Principal (P) = ₹ 10,000

Rate of interest for first and second year (R) = 6% p.a, compounded half yearly

Rate of interest for third year (R) = 9% p.a, compounded half yearly

Time (T) = 3 years

Number of conversion (N) = 6

Relevant Solution :

Amount at the end of second year: 

A = P\left[ {{{\left( {1 + \frac{R}{2}} \right)}^N}} \right]

A = 10000\left[ {{{\left( {1 + \frac{6}{2}} \right)}^4}} \right] 

A = ₹ 11,255 

Amount at the end of third year: 

A = P\left[ {{{\left( {1 + \frac{R}{2}} \right)}^N}} \right]

A = 11255{\left( {1 + \frac{9}{2}} \right)^2} 

A = ₹ 12,290.74

Total interest earned:

C.I = A - P

     = 12290.74 - 10000

     = ₹ 2,290.74

Question 2.

A sinking fund is created for redeming debentures worth ₹ 5 lkhs at the end of 25 years. How much provision needs to be made out of profits each year provided sinking fund investments can earn interest at 4% p.a.?

  1. 12,006
  2. 12,040
  3. 12,039
  4. 12,035

Answer: a. 12,006

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Question 3.

A = ₹ 5200, R =5% p.a, T =6 years, P will be

  1. ₹ 2000
  2. ₹ 3880
  3. ₹ 3000
  4. None of these

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Question 4. 

Find the future value of annuity ₹.1000 made annually for 7 years at interest rate of 14% compounded  annually is _______ Given (1.14) 6= 2.5023

  1. ₹ 10730.71
  2. ₹ 10735 
  3. ₹ 10734
  4. ₹ 10237

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 5: Basic Concepts of Permutations and Combinations

Question 1. 

In how many ways can 6 boys and 6 girls be seated around a table so that no 2 boys are adjacent?

  1. 4! × 5!
  2. 5! × 6!

  3. {}^6{P_6}

  4. 5 \times {}^6{P_6}

Answer: b. 5! × 6!

Description: 6 boys and 6 girls are to be seated around a table such that no 2 boys are adjacent to each other.

There is a boy between two girls. 6 girls are arranged in a circular arrangement.

This can be done in (6-1)!= 5! ways. Now there 6 positions for 6 boys. Therefore these 6 boys are arranged in 6P6 =6!^6{P_6} = 6! ways.

Hence the required number of arrangements is 5! × 6!.

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Question 2.

In how many ways 6 men can sit at a round table so that all shall not have the same neighbours in any two occasions?

  1. 5! ÷ 2
  2. 5!

  3. {(7!)^2}

  4. 7!

Answer: a. 5! ÷ 2

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Question 3.

How many combinations can be formed of 8 counters marked 1 2 …8 taking 4 at a time there being at least one odd and even numbered counter in each combination?

  1. 68
  2. 66
  3. 64
  4. 62

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Question 4. 

nC1+nC2+nC3+………….=

  1. 2n-1
  2.  2n
  3.  2n+1
  4. none of these

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 6: Sequence and Series - Arithmetic and Geometric Peogressions

Question 1. 

The sum of n terms of the series 2.4.6 + 4.6.8 + 6.8.10 + ………. is

  1. 2n(n³+6n²+11n+6)
  2. 2n(n³–6n²+11n–6)
  3. n(n³+6n²+11n+6)
  4. n(n³+6n²+11n– 6)

Answer: a. 2n(n³+6n²+11n+6)

Description: The required sum of n terms of The series 

=2.4.6 + 4.6.8+ ………. uo to n terms

\begin{array}{l} = \Sigma (2n)(2n + 1)(2n + 4)\\ = \Sigma (8{n^3} + 24{n^2} + 16{n^2})\\ = 8\left[ {{n^3} + 24\Sigma {n^2} + 16n} \right]n \end{array}

= 8\frac{{{n^2}{{(n + 1)}^2}}}{4} + 24\frac{{n(n + 1)(2n + 1)}}{6} + 16\frac{{n(n + 1)}}{2}

= 2n({n^3} + 6{n^2} + 11n + 6) 

Question 2.

If a, b, c are in A.P. as well as in G.P. then –

  1. They are also in H.P. (Harmonic Progression)
  2. Their reciprocals are in A.P.
  3. Both (A) and (B) are true
  4. Both (A) and (B) are false

Answer: c. Both (A) and (B) are true

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Question 3.

If (b – c)2 , (c – a)2 , (a – b)2 are in A.P. then (b – c), (c – a), (a – b) are in _______.

  1. A.P.
  2. G.P.
  3. H.P.
  4. None

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Question 4.

The nth term of the sequence -1,2, -4, 8,.is  

  1. (-1) n 2n-1
  2. 2n-1
  3. 2n
  4. none of these

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 7: Sets, Relations and Functions, Basics of Limits and Continuity functions

Question 1.

On a survey of 100 boys it was found that 50 used white shirt 40 red and 30 blue. 20 were habituated in using both white and red shirts 15 both red and blue shirts and 10 blue and white shirts. Find the number of boys using all the colours.

  1. 20
  2. 25
  3. 30
  4. None

Answer: b. 25

Description: 

Let A be the set of boys using white shirt,

Let B be the set of boys using red shirt,

Let C be the set of boys using blue shirt,

n(A) = 50, n(B) = 40, n(C) = 30, n(A ∩ B) = 20, n(B ∩ C) = 15,  n(C ∩ A) = 10, we have to determine n(A ∩ B ∩ C).

Now n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) - n(A ∩ B ∩ C)

\therefore  100 = 120 - 45 + n(A ∩ B ∩ C)

\therefore n(A ∩ B ∩ C) = 25.

Question 2.

Out of 60 students 25 failed in paper (1), 24 in paper (2), 32 in paper (3), 9 in paper (1) alone, 6 in paper (2) alone, 5 in papers (2) and (3) and 3 in papers (1) and (2) only. Find how many failed in all the three papers.

  1. 10
  2. 60
  3. -50
  4. None

Answer: a. 10

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Question 3. 

In his report an Inspector of an assembly line showed in respect of 100 units the following which you are require to examine

Defect No.of pieces
Strength 35
Flexibility 40
Radius 18
Strength & Flexibility 7
Strength & Radius 11
Flexibility & Radius 12
Strength Flexibility Radius 3
  1. No. of pieces with radius defect alone was –2 which was impossible
  2. Report may be accepted
  3. Cannot be determined due to data insufficiency
  4. none

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Question 4.

The set having no element is called 

  1.  Singleton set 
  2.  null set
  3.  finite set
  4. Infinite set 

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 8: Basic Concepts of Diffrential and Integral Calculus

Question 1.  

If y =2x+4/x, then x2d2y/dx2+xdy/dx- − yields

  1. 3
  2. 1
  3. 0
  4. 4

Answer: c. 0

Description:

Step 1: Find the First Derivative dy/dx

Given:

y=2x+4x-1

Differentiating with respect to x:

dy/dx=d/dx (2x)+d/dx(4x-1)=2-4x-2 = 2-4/x2

Step 2: Find the Second Derivative d2y/dx2

Now, differentiate dy/dx:

d2y/dx2 = d/dx(2-4/x2)=0+8x-3=8/x3

Step 3: Substitute into the Expression

Now, we have:

The first derivative: dy/dx

Question 2.

∫1/xlogx dx = ?

  1.  log|x| + c 
  2.  log |logx| + c
  3. (logx)2 + c 
  4. none of these

Answer: b.  log |logx| + c

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Question 3.

fex (x2 + 2x)dx

  1.  x2.ex+c 
  2.  x.ex+c
  3. -x.ex+c
  4. e-x+c

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CA Foundation Quantitative Aptitude Important Question - 5

Logical Reasoning

Chapter 1: Number Series, Coding and Decoding and Odd Man Out

Question 1.

If 'DELHI' is coded '73541' and 'CALCUTTA' as '82589662', How can 'CALICUT' be coded?

  1. 5279431
  2. 5978213
  3. 8251896
  4. 8543962

Answer: c. 8251896

Description:  

Here as per the details in the question all alphabets are assigned specific numbers, like

D=7 E=3 L=5 H=4 I=1 C=8 A=2 U=9 T=6

 

∴ So CALICUT would be coded as 8251896.

Question 2.

1268, 2051, 2726, 3301, 3784, ?

  1. 4183
  2. 4296
  3. 4312
  4. 4443

Answer: a. 4183

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Question 3. 

Find odd man out, 52, 51, 48, 43, 34, 27, 16

  1. 27
  2. 34
  3. 43
  4. 48

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Question 4. 

5, 7, 11, ?, 35, 67

  1. 23
  2. 28
  3. 30
  4. 19

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Question 5.

Find the sum of all natural numbers between 250 and 1,000 which are exactly divisible by 3 : 

  1. 1,56,375 
  2. 1,56,357
  3. 1,65,375
  4. 1,65,357

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 2: Direction Tests

Question 1.

Raju is standing facing north. He goes 30 meters ahead and turns left and goes for 15 meters. Now he turns right and goes for 50 meters and finally turns to his right and walks. In which direction is he heading?   

  1. North 
  2. East 
  3. South
  4. West

Answer: b. East

Description:

Hence, He is heading towards East Direction.

Question 2. 

A child walks 25 feet towards North, turns right and walks 40 feet, turns right again and walks 45 feet. He then turns left and walks 20 feet. He turns left again, walks 20 feet. Finally, he turns to his left to walks another 20 feet. In which direction is the child from his starting point?

  1. North 
  2. South 
  3. West 
  4. East

Answer: d. East

Description: 

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Question 3.

Facing towards North, Ravi walks 35 m. He then turns left and walks 55 m. He again turns left and walks 35 m. How far is from original position and towards which direction.

  1. 30m North
  2. 20m East
  3. 55m West
  4. 20m South

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 3: Seating Arrangements

Question 1.

Six persons M, N, O, P, Q and R are sitting in two row with three persons in each row. Both the rows are in front of each other. Q is not at the end of any row. P is the second the left of R. O is the neighbour of Q and diagonally opposite to P. N is the neighbour of R. Who is in front of N?

  1. R
  2. Q
  3. P
  4. M

Answer: b. Q

Description: 

Facing ↓ M Q O Facing ↓
Facing ↑ P N R Facing ↑

Hint :

Point  
Step - 1 Six persons M, N, O, P, Q and R are sitting in two row with three persons in each row.  Both the rows are in front of each other. Facing ↓ person person person Facing ↓
Facing ↑ person person person Facing ↑
Step - 2 Q is not at the end of any row Facing ↓ Q   Q Facing ↓
 
or

  
Facing ↑ Q   Q Facing ↑
Step - 3 P is the second the left of R Facing ↓ R   P Facing ↓
  or  
Facing ↑ P   R Facing ↑

Step - 4 O is the neighbour of Q and diagonally opposite to P (We can take any row for this condition in order to solve)

 Facing ↓ R   p Facing ↓
Facing ↑ O Q   Facing ↑
Step - 5 N is the neighbour of R Facing ↓ R N P Facing ↓
Facing ↑ O Q M ? Facing ↑

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Question 2.

Five friends P, Q, R, S and T are sitting in a row facing North. Here, S is between T and Q and Q is to the immediate left of R. P is to the immediate left of T. Who is in the middle?

  1. S
  2. T
  3. Q
  4. R

Answer: a. S

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Question 3.

Six girls are standing in such a way that they form a circle, facing the centre. Subbu is to the left of Pappu, Revathi is between Subbu and Nisha, Aruna is between Pappu and Keerthna. Who is to the right of Nisha?

  1. Revathi
  2. Aruna
  3. Subbu
  4. Keerthana

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 4: Blood Relations

Question 1. 

A is B's wife's husband's brother. C and D are sisters of B. How is A related to C?

  1. Brother
  2. Sister-in-law
  3. Wife
  4. Sister

Answer: a. Brother

Description: 

Hence, A is the brother of C.

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Question 2.

Six members of a family namely A,B,C,D,E and F are travelling together. 'B' is the son of C but C is not the mother of B. A and C are married couple. E is the brother of C. D is the daughter of A. F is the brother of B.How many male members are there in the family?

  1. 3
  2. 2
  3. 4
  4. 1

Answer: c. 4

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Question 3.

Seema is the daughter-in-law of Sudhir and sister-in-law of Ramesh. Mohan is the son of Sudhir and only brother of Ramesh. Find the relation between Seema and Mohan.

  1. Sister-in-law
  2. Aunt
  3. Cousin
  4. Wife

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CA Foundation Quantitative Aptitude Important Question - 5

Statistics

Chapter 1: Statistical Representation of Data

Question 1.

The number of observation falling within a class is called

  1. Density
  2. Frequency
  3. Both
  4. None

Answer: b. Frequency

Description: The figure corresponding to a particular class, signifying the number of times or how frequently a particular class occurs, is known as the frequency of that class. Thus, the number of Indians, as found from the given data, signifies the frequency of the Indians. So, frequency distribution is a statistical table that distributes the total frequency to a number of classes.

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Question 2.

“Cumulative Frequency“ only refers to the

  1. Less-than type
  2. More-than type
  3. Both 
  4. None

Answer: c. Both

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Question 3.

For the overlapping classes 0 - 10, 10 - 20, 20 - 30 etc. the class mark of the class 0 - 10 is

  1. 5
  2. 0
  3. 10
  4. None

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Question 4.

There were 200 employees in an office in which 150 were married. Total male employees were 160 out of which 120 were married. What was the female unmarried employees?

  1. 30
  2. 10
  3. 40
  4. 50

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 2: Sampling

Question 1.

According to Neyman’s allocation, in stratified sampling

  1. Sample size is proportional to the population size
  2. Sample size is proportional to the sample SD
  3. Sample size is proportional to the sample variance
  4. Population size is proportional to the sample variance.

Answer: a. Sample size is proportional to the population size

Description: Neyman's allocation approach to stratified sampling allocates sample sizes based on variability and population size, aiming to maximize sampling resources for strata with higher variability or larger populations, minimizing estimator variance.

Question 2.

If a random sample of size two is taken without replacement from a population containing the units a,b,c and d then the possible samples are

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

Answer: d. (a, b), (a, c), (a, d), (b, c), (b, d), (c,d)

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Question 3.

Which of the following is not a type of sampling?  

  1. Probability
  2. Non-probability
  3. stand-alone
  4. mixed

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 3: Measures of Central Tendency and DIspersion

Question 1.

The algebraic sum of deviations of observations from their A.M is

  1. 2
  2. -1
  3. 1
  4. 0

Answer: d. 0

Description: 

The algebraic sum of deviations of observations from their AM is indeed zero.

                \Rightarrow \overline x = AM

    & {x_n}  are n observation then the deviations of observations form AM are 

 {x_1} - \overline x

 {x_2} - \overline x

 {x_3} - \overline x

 . 

 .

 {x_n} - \overline x

 their algebraic sum is given as

 {x_1} - \overline x + {x_2} - \overline x + {x_3} - \overline x ..........{x_n} - \overline x

  = {x_1} + {x_2} + ..........{x_n} - n \times \overline x

 (as there are n number of \overline x  terms)

  = n\overline x - n\overline x  

 (as \bar x = \frac{{\sum {xi} }}{n} = \frac{{{x_1} + {x_2} + .......... + {x_n}}}{n}

          \Rightarrow {x_1} + {x_2} + ..........{x_n} = n\bar x)

 = 0

Question 2.

1st percentile is less than 2nd percentile

  1. True 
  2. False 
  3. Both 
  4. None 

Answer: a. True 

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Question 3.

In measuring dispersion, it is necessary to know the amount of _____& the degree of __________.

  1. variation, variation
  2. variation, median
  3. median, variation
  4. None

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Question 4. 

If the Standard Deviation of 10 observations is 4 and if each item is divided by – 2 then Standard Deviation of new series is

  1. 2
  2. -2
  3. 4
  4. none of these

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 4: Probability

Question 1. 

The following table gives the distribution of wages of 100 workers –

Wages(in ₹) 120-140 140-160 160-180 180-200 200-220 220-240 240-260
No. of workers 9 20 0 10 8 35 18

The probability that his wages are under ₹160 is

  1. 9/100
  2. 20/100
  3. 29/100
  4. none

Answer: 29/100

Description:  P(wage < 140) = (No. of workers with wages <140)/ Total no. of workers 

                        = 9/100.

Question 2.

In a single throw with two dice, the probability of getting a sum of six on the two dice is

  1. 1/9
  2. 5/36
  3. 5/9
  4. none

Answer: b. 5/36

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Question 3.

In a class 40 % students read Mathematics, 25 % Biology and 15 % both Mathematics and Biology. One student is selected at random. The probability that he reads Mathematics if it is known that he reads Biology is

  1. 2/5
  2. 3/5
  3. 4/5
  4. none

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Question 4.

The value of P(S) were S is the sample space is

  1. -1
  2. 1
  3. 0
  4. none

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 5: Theorectical Distributions

Question 1.

When p = 0.5, the binomial distribution is

  1. asymmetrical
  2. symmetrical
  3. Both
  4. None

Answer: b. symmetrical

Description:It will assume symmetry when p=0.5

Question 2.

When the number of trials is large and probability of success is small then we use the distribution

  1. Normal
  2. Poisson
  3. Binomial
  4. None

Answer: b. Poisson

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Question 3.

In Normal distribution, the probability has the maximum value at the

  1. mode 
  2. mean
  3. median
  4. all

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 6: Correlation and Regression

Question 1.

In Method of Concurrent Deviations, only the directions of change (Positive direction /Negative direction) in the variables are taken into account for calculation of

  1. coefficient of S.D
  2. coefficient of regression.
  3. coefficient of correlation
  4. none

Answer: c. coefficient of correlation

Description: 

Coefficient of concurrent deviations is a simple method of finding correlation when we are not series about the magnitude of the two variables.

This method involves in attaching a positive sign for a x-value. If this value is more than the previous value, and assigning a negative value if this value is less than the precious value.

This is done for the y series as well.

The determination in x-value and the corresponding y value is known to the concurrent, if both the deviations have the same sign.

Donating the number of concurrent deviation by c and total number of deviations as m, the coefficient of concurrent deviations is given by 

{r_c} = \pm \sqrt {\frac{{2c - m}}{m}}

Question 2.

Which is true?

  1. {b_{yx}} = r\frac{{{\sigma _x}}}{{{\sigma _y}}}

  2. {b_{yx}} = r\frac{{{\sigma _y}}}{{{\sigma _x}}}

  3. {b_{yx}} = r\frac{{{\sigma _{xy}}}}{{{\sigma _x}}}

  4. {b_{yx}} = r\frac{{{\sigma _{yy}}}}{{{\sigma _x}}}

Answer: b. {b_{yx}} = r\frac{{{\sigma _y}}}{{{\sigma _x}}}

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Question 3.

In linear equations, Y = a + bx and X= a + b y ‘a‘ is the

  1. intercept of the line
  2. slope 
  3. both
  4. none

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Question 4.

For a positive and perfectly correlated random varaiables , one of the regression coefficeint is 1.3 and the standard devation of X is 2, the variance of Y is

  1. 2.37
  2. 6.76
  3. 6.56
  4. 3.16

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CA Foundation Quantitative Aptitude Important Question - 5

Chapter 7: Index Number

Question 1.

With the base year 1960 the C. L. I. in 1972 stood at 250. x was getting a monthly Salary of ₹ 500 in 1960 and ₹ 750 in 1972. In 1972 to maintain his standard of living in 1960 x has to receive as extra allowances of

  1. ₹ 600/-
  2. ₹ 500/-
  3. ₹ 300/-
  4. none of these

Answer: b. ₹ 500/-

Description: 

Given, 

salar{y_{1960}} = 500 = {s_{1960}} 

   CP{I_{1960}} = 100 = CP{I_{1960}} 

 salar{y_{1972}} = 750 = {s_{1972}} 

    CP{I_{1972}} = 250 = CP{I_{1972}} 

According to the given information, if x wants to maintain his standard of living, then salar{y_{1972}} = \frac{{{s_{1960}}}}{{CP{I_{1960}}}} \times CP{I_{1972}}

                                                                                                                                               = \frac{{500}}{{100}} \times 250

                                                                                                                                              = 1,250Rs.

\therefore The difference in the salary to be paid as an extra allowance = 1,250 – 750

                                                                                              = ₹ 500.

Question 2.

The circular test is satisfied by

  1. Fisher’s index number.
  2. Paasche’s index number.
  3. Laspeyre’s index number.
  4. none of these

Answer: d. none of these

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Question 3.

The price level of a country in a certain year has increased 25% over the base period. The index number is

  1. 25
  2. 125
  3. 225
  4. 2500

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