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This mock test of Business Mathematics Mock Test - 1 for CA Foundation helps you for every CA Foundation entrance exam.
This contains 100 Multiple Choice Questions for CA Foundation Business Mathematics Mock Test - 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

In how many ways can we select 5 people from a group of 9 people so that a particular person is never to be included

Solution:

Out of 9 people, one has not to be selected.

Therefore, there are total 8 persons. We have to select 5 among them.

Total number of ways = ^{8}C_{5}

QUESTION: 2

The value of the determination

Solution:

QUESTION: 3

If Rolle's theorem for f(x) = e^{x} (sin x - cos x) is verified on then the value of c is

Solution:

**Correct Answer :- d**

**Explanation : **Thus, all the conditions of Rolle’s theorem are satisfied.

Now, we have to show that, there exists a point c ∈ (π/4 , 5π/4) such that f'(c) = 0.

⇒ e^{x}(sinx – cosx) + e^{x}(cosx + sinx) = 0

⇒ (sinx – cosx) + (cosx + sinx) = 0

⇒ 2sinx = 0 ⇒ sinx = 0

⇒ c = π ∈ (π/4 , 5π/4)

QUESTION: 4

The set of letters in the word ′UNIVERSAL′. Write the set in Roster form .

Solution:

QUESTION: 5

If a,b,c are distinct and the roots of (b-c) x^{2 }+ (c-a) x + (a-b) = 0 are equal ,then a,b,c are in

Solution:

QUESTION: 6

If a series consists only a finite number of terms it is called a ................

Solution:

If a series consists only a finite number of terms it is called a Finite series.

Hence, the answer is finite series.

QUESTION: 7

If α,β,γ are three consecutive integers. If these integers are raised to first, second and third positive powers respectively, and added then they form a perfect square, the square root of which is equal to the sum of these integers. Also, α<β<γ. Then, γ is equals to:

Solution:

QUESTION: 8

Find the missing term(s) :

1 BR, 2 EO,6 HL,15 KI,?

Solution:

QUESTION: 9

Letters of the English alphabet have been formed into groups in a particular order. Find the set of letters that is most appropriate to fill the gap from the sets given in the choice.

CEG : EGC : : LNP : ?

Solution:

CEG is formed by skipping the letters in between them, the second set EGC is formed by simply putting the first letter of CEG at last to form EGC,

Follow the same rule to get the answer. LNP and NPL.

QUESTION: 10

If (x+1)^{2}−(x−1)^{2}=32, find the value of x.

Solution:

QUESTION: 11

If the feasible region for a solution of linear inequations is bounded, it is called as:

Solution:

A bounded feasible region will have both a maximum value and a minimum value for the objective function. It is bounded if it can be enclosed in any shape.

A convex polygon is a simple not self-intersecting closed shape in which no line segment between two points on the boundary ever goes outside the polygon.

Hence, the answer is convex polygon.

QUESTION: 12

In the following question, there are two words to left of the sign ': :' which are connected in some way. The same relationship is shared by one of the four alternative pair of words given below. Find the correct alternative pair.

Cloth : Texture :: ?

Solution:

Quality of cloth is determined by its texture, similarly, quality of wheat is determined by grains.

QUESTION: 13

If the expression has the value ab - cd for all values of a,b,c and d, then the equation

Solution:

QUESTION: 14

Fill up the blank with the most appropriate alphabet given in the choice, in each of the following expression.

E : V : : I : .....

Solution:

The 5th letter from A correspond to 5th from Z and therefore 9th letter 'I' from A would correspond 9th letter 'R' from Z.

QUESTION: 15

In the following question, there are two words to left of the sign ': :' which are connected in some way. The same relationship is shared by one of the four alternative pair of words given below. Find the correct alternative pair.

Volcano : Lava : : ?

Solution:

Volcano causes lava to flow. Faulting or displacement of earth crust causes an earthquake. Both the natural occurrences connected with earth.

QUESTION: 16

For two sets A and B, A∪B=A if and only if

Solution:

QUESTION: 17

Find the derivative of sin(2sin^{−1}x).

Solution:

**Correct Answer :- a**

**Explanation : **Suppose we want to find the differentiation of a function of x, say f(x). We can write it as: df/dx

Now, if f(x) is itself is not a function of x, but of another function of x, suppose g. That is, we have f[g(x)], we have to use the chain rule of differentiation.

df/dx = df/dg × dg/dx

In the given question, it is clearly observable that

f (x)=sin(x) and g(x)=2sin^{-1}(x)

Thus the answer is as follows:

cos(2sin^{-1}(x)) × 2/(√1−x^{2})

**Correct Answer :- a**

**Explanation : **Suppose we want to find the differentiation of a function of x, say f(x). We can write it as: df/dx

Now, if f(x) is itself is not a function of x, but of another function of x, suppose g. That is, we have f[g(x)], we have to use the chain rule of differentiation.

df/dx = df/dg × dg/dx

In the given question, it is clearly observable that

f (x)=sin(x) and g(x)=2sin^{-1}(x)

Thus the answer is as follows:

cos(2sin^{-1}(x)) × 2/(√1−x^{2})

QUESTION: 18

if then the value of x is

Solution:

QUESTION: 19

Find the approximate maximum transverse speed of a point on the string.

Solution:

**Correct Answer :- c**

**Explanation : **For a standing wave described by y = Asin(kx)sin(ωt)

Speed of a particle is given as v = dy/dt = Aωsin(kx)cos(ωt)

Thus v_{max} = Aω

= 5.6×50

= 280cm/s

QUESTION: 20

Fill in the blank:

if then the pair of linear equations has exactly________ Solution.

Solution:

QUESTION: 21

The exponential form of √(√2×√3) is

Solution:

QUESTION: 22

Consider the equation (1+a+b)^{2} = 3(1+a^{2}+b^{2}), where a, b are real numbers. Then

Solution:

QUESTION: 23

Solution:

QUESTION: 24

In the following question, five pairs of letters are given. Four of them are alike in a certain way while one is different.

Q. Choose the odd one.

Solution:

In other groups, first two letters are consecutive and between second and third there is a gap of one letter.

But in option D all the letters are consecutive.

QUESTION: 25

Find the odd one alternative :

Solution:

Air and Oxygen comes under Atmosphere.

Students are divided in two categories boys and girls.

Dog and Cat comes under the category of Animal.

Man, Worker, Garden are not related category wise.

Hence, option C is different among all.

QUESTION: 26

Pointing towards a boy, Veena said 'He is the son of the only son of my paternal grandfather'. How is that boy related to Veena?

Solution:

Only son of Veena's grandfather is her father. And son of her father is her brother.

Hence, that boy is Veena's brother.

QUESTION: 27

How many zeroes are there in 1×2×3×4...........49×50:

Solution:

QUESTION: 28

What is the sum of the probabilities of all the distinct outcomes within the same sample space ?

Solution:

QUESTION: 29

582 : 194 : : 258 : ?

Solution:

582 ÷ 3 = 194

Similarly, 258 ÷ 3 = 86

Hence answer is option B

QUESTION: 30

Pointing to man on the stage Rita says "He is the brother of the daughter of the wife of my husband" How is the man on the stage related to Rita?

Solution:

Wife of the husband means herself, Brother of her daughter means her son

QUESTION: 31

The equation 3x^{4} − 5x^{3} + 3x^{2} − 4x + 5 = 0 is of the type

Solution:

QUESTION: 32

If probability of getting a red ball from a bag containing blue and red balls is 0.52. then probability of getting a blue ball from the same bag is

Solution:

If probability of getting a red ball from a bag containing blue and red balls =0.52=0.52

The probability of getting a blue ball from the same bag is

=1−0.52

=0.48

QUESTION: 33

Find the compounded ratio of 18 :9, 16 : 13 and 6 : 9

Solution:

QUESTION: 34

In the following question, there are two words to left of the sign ': :' which are connected in some way. The same relationship is shared by one of the four alternative pair of words given below. Find the correct alternative pair.

Q. Soldier : Regiment : : ?

Solution:

Soldiers form part of a Regiment as coil forms a part of motor. This is part and whole relationship.

QUESTION: 35

The differential equation of all non-horizontal lines in a plane is

Solution:

QUESTION: 36

The probability of an event is

Solution:

The probability that an event will occur is expressed as a number between 0 and 1

QUESTION: 37

The sets E= {All even numbers } and O ={All odd numbers} are

Solution:

The sets E and F have no elements in common, so are disjoint sets.

QUESTION: 38

S_{n}= 1^{3} + 2^{3 }+.....+ n^{3} and Tn = 1 + 2 +.....+ n, then

Solution:

QUESTION: 39

A man bought goods worth Rs. 6000 and sold half of them at a gain of 10%. At what gain percent must he sell the remainder so as to get a gain of 25% on the whole ?

Solution:

QUESTION: 40

Find the value of x−y^{x−y} when x=2 and y=−2.

Solution:

= 2 + 2^{2+2}

= 2 + 2^{4}

= 2 + 16

= 18

QUESTION: 41

Historical notations used and reasons for their discontinuation are

Solution:

Historical notations are used and discontinued because the box notation is difficult for printers to reproduce

The other reason is small vertical bar above a variable , confusion with the differentiation symbol therefore correct option is C.

QUESTION: 42

Complete the second pair of given analogous pair based on the pattern followed by the first pair:

Bank : River : : Coast : ?

Solution:

Note that the word 'bank' denotes the land besides the river. (Bank has two meanings, one is the place where we safekeep our money, and other means the land besides the river).

Hence, bank is the land beside a river and coast is the land beside a sea.

QUESTION: 43

Find the missing term(s) :

P3C, R5F, T8I, V12L, ?

Solution:

In the following series first letter is moved two steps forward,second number is moved 2,3,4,5 step forward,and third letter is moved and third letter is moved three steps forward to form the next term of the series

Following the series the next term will be X17O

QUESTION: 44

Wax is to Wave as Zenith is to-

Solution:

Wave is antonym of wax .

Similarly, antonym of Zenith is Nadir.

Hence, answer is option D

QUESTION: 45

Ratio of 200 ml to 2 litre is____

Solution:

QUESTION: 46

A,B and C together earn Rs.300 per day, while A and C together earn Rs.188 and B and C together earn Rs.152 The daily earning of C is :

Solution:

QUESTION: 47

If A+B=2C and C+D=2A, then

Solution:

QUESTION: 48

LETTER : WORD :: ?

Solution:

Letter is composed of words similarly books are made up of pages

QUESTION: 49

In the question, there are four options. Three in these options, are alike in certain manner. Only one number does not fit in. Find the one which doesn't fit.

Solution:

Only in 9309, the digit 9 is repeated whereas in other numbers no digits are repeated.

Hence, 9309 is different amongst all.

QUESTION: 50

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train is 120 metres, in how much time (in seconds) will they cross each other if travelling in opposite direction?

Solution:

QUESTION: 51

The number of A in Tp such that the trace of A is not divisible by pp but det(A) is divisible by p is?

[Note: The trace of a matrix is the sum of its diagonal entries.]

Solution:

QUESTION: 52

Solution:

QUESTION: 53

What is the value of [2−3(2−3)^{−1}]^{−1} ?

Solution:

QUESTION: 54

Solution:

QUESTION: 55

Name the game, which is played by the slim player but cannot be played by the fat player?

Solution:

Player number 10 plays Cricket, Kabaddi and Kho-Kho.

The fat player plays Cricket and Kabaddi.

So, the fat player can't play Kho-Kho which is played by slim player.

Hence, option C is correct.

QUESTION: 56

Squint is to Eye as Squeeze is to-

Solution:

To constrict eyes we squint.

Similarly, to constrict hands we squeeze.

Hence, answer is option D.

QUESTION: 57

The transpose of a rectangular matrix is a

Solution:

The transpose of a rectangular matrix is a rectangular matrix.

QUESTION: 58

If for a matrix A, A^{3}=I, then A^{−1} is equal to-

Solution:

QUESTION: 59

A set of annual numerical data, comparable over the years, is given for the last 12 years.

Consider the following statements:

1. The data is best represented by a broken line graph, each corner (turning point) representing the data of one year.

2. Such a graph depicts the chronological change and also enables one to make a short-term forecast.

Q. Which of the above statements is/are correct?

Solution:

The first statement is true as we can easily track the ups and downs of datat form 1 year to the next.

Statement 2 is false as the graph would require some kind of mathematical model to predict the short-term forecast and would not be helpful on its own.

QUESTION: 60

Choose the Venn diagram which best illustrates the three given classes.

Citizens, Educated, Men

Solution:

QUESTION: 61

What is the mode from the following table ?

Solution:

Mode is the value which has the highest frequency.

In the given table, 23 has the highest frequency 15 i.e., 23 marks were obtained to many people than other marks.

Therefore 23 is the mode.

QUESTION: 62

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. What is the excluded number?

Solution:

QUESTION: 63

Pankaj records the measurement of resistance and current to find the potential across A and B. Estimate the resistance for a current of 7.5 amps.

Solution:

QUESTION: 64

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

Solution:

QUESTION: 65

Which of the two days did they export more bottles of pickles?

Solution:

From the pictograph, they export 8 bottles on Monday, 5 on Tuesday, 3 on Wednesday, 8 on Thursday and 6 on Friday.

So, Monday and Thursday are the two days when they export more bottles of pickles.

QUESTION: 66

Construction of a cumulative frequency table is useful in determining the

Solution:

A cumulative frequency table helps to determine the median of the series.

QUESTION: 67

The age-specific death rates for a town are given in the following table:

The curve drawl between ages and specific death rates will be

Solution:

QUESTION: 68

The year in which the most number of TV sets have been sold is

Solution:

From the table,we can say the answer.

Ans is 2008.

QUESTION: 69

Which one of the following is not central tendency ?

Solution:

Mean deviation is deviation from the mean. It is not the central tendency.

QUESTION: 70

Which one of the following is not correct ?

Solution:

Answer:- C) Statistical laws are exact.

Reason:-

The statistical laws are based on probability. Using probability we can only estimate the answer, it will not be accurate.

So statistical laws are not exact.

QUESTION: 71

The measure of dispersion is

Solution:

Measures of dispersion include:

1)Sample standard deviation

2)Interquartile range (IQR) or Interdecile range

3)Range

4)Mean difference

5)Median absolute deviation (MAD)

6)Average absolute deviation (or simply called average deviation)

7)Distance standard deviation

QUESTION: 72

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 680. Then which one of the following gives possible values of a and b ?

Solution:

QUESTION: 73

_______ are sets of mathematical equations that are used to analyze what is happening in the world around us.

Solution:

Statistics are sets of mathematical equations that are used to analyze what is happening in the world around us.

QUESTION: 74

Represent the following data using histogram, hence find the mode.

Solution:

QUESTION: 75

Before 3000 BC, the ______ used small clay tablets to record tabulations of agricultural yields and of commodities bartered or sold.

Solution:

QUESTION: 76

At the beginning of the 20^{th }century, who developed the methods for decision making based on small set of data?

Solution:

At the beginning of the 20th century, William S Gosset has developed the methods for decision making based on small set of data.he has developed t-distribution theory.

QUESTION: 77

A grouped frequency distribution table with classes of equal sizes using 63 — 72 (72 included) as

one of the class is constructed for the following data:

30,32,45,54,74,78,108,112,66, 76,88,

40,14, 20,15,35,44,66,75,84,95,96,

102,110,88,74,112,14,34,44

The number of classes in the distribution will be:

Solution:

The given frequency is vary from 14 to 112.

So the class intervals are:

13-22, 23-32, 33-42, 43-52, 53-62, 63-72, 73-82, 83-92, 93-102, 103-112.

Number of class interval = 10.

QUESTION: 78

The coefficient of quartile deviation is calculated by the formula :

Solution:

QUESTION: 79

Marks scored by 10 students in an examination are listed in the table

Q. What is the range of marks for given marks distribution ?

Solution:

From the given table, we have

Lowest marks for given distribution =33

Highest marks =49

Therefore, range of marks = 49−33=16

QUESTION: 80

**Assertion **

If lines of regressions are 8x - 10y + 66 = 0 & 40x - 18y - 214 = 0, then

**Reason **

Regression lines pass through Where are mean.

Solution:

QUESTION: 81

______ are used for bar chart where the data represent continuous rather than discrete categories.

Solution:

QUESTION: 82

Coefficient of correlation between the observations ( 1, 6 ) , ( 2 , 5 ) , ( 3 , 4) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) is

Solution:

QUESTION: 83

There are 500 students in a class in which there are 100 boys. 50 boys like Mathematics and 100 girls dislike Mathematics. Tabulate the given data and calculate the number of girls who like the subject Mathematics.

Solution:

QUESTION: 84

The one which is the measure of the central tendency is

Solution:

The mean (often called the average) is most likely the measure of central tendency but there are others, such as the median and the mode are also measure of central tendency.

QUESTION: 85

In the year 1602, who used the word "statist" in his drama Hamlet?

Solution:

William Shakespeare used the word statist in his drama Hamlet 1602.

QUESTION: 86

Statistics is the branch of mathematics that deals with the collection, organization, analysis, and interpretation of numerical ____.

Solution:

Statistics is the branch of mathematics that deals with the collection, organization, analysis, and interpretation of numerical data.

QUESTION: 87

A cumulative frequency graph, also known as an

Solution:

An ogive, sometimes called a cumulative frequency polygon, is a type of frequency polygon that shows cumulative frequencies.

In other words, the cumulative percents are added on the graph from left to right.

QUESTION: 88

Following table gives frequency distribution of milk (in litres) given per week by so cows.

Find average (mean) amount of milk given by a cow by 'shift of origin method'.

Solution:

QUESTION: 89

Which frequency curve is correct for the following histogram ?

Solution:

Frequency curve can also be drawn with the help of histogram by joining their mid points of rectangle.

QUESTION: 90

Solution:

QUESTION: 91

Upper limit of class interval 75−85 is

Solution:

Upper value is called upper limit

75 - lower limit, 85 - upper limit.

QUESTION: 92

Data classification is the process of organizing data into categories for its _____.

Solution:

Data classification is the process of organizing the data into categories for its division. The types of data are qualitative and quantitative data.

QUESTION: 93

Since the population size is always larger than the sample size, then the sample statistic -

Solution:

Sample statistic will depend upon the sample chosen.

It can be less than, greater than, equal to population parameter.

It can assume the value of zero.

QUESTION: 94

The following table gives the height of trees:

Q. Draw both ogives for the data above. Hence, obtain the median of the data.

Solution:

QUESTION: 95

Which of the following is not a measure of central location?

Solution:

Mean, median and mode give us the knowledge about the central value.

But the Variance will give us the deviations from the central tendencies.

QUESTION: 96

For a certain frequency distribution, the values of Mean and Mode are 54.6 and 54 respectively. Find the value of median.

Solution:

QUESTION: 97

Calculate Pearson's coefficient of correlation between the values of X and Y.

Solution:

QUESTION: 98

Tally marks are used find

Solution:

Tally marks are used for counting. They represent frequency.

QUESTION: 99

In the Merits of observation method:

Q. Subject bias is ________ if the observation is done correctly.

Solution:

If the subject bias is eliminated then there is no confusion of how the subjects act in the experiment.

Therefore, if the observation is done correctly then it becomes the merit of the method.

Hence, the answer is eliminated.

QUESTION: 100

Which of the following is/are not the methods of collection of primary data.

Solution:

There are various methods for the collection of primary data mainly in surveys and descriptive researches.

The observation, interview and questionnaire methods, we collect the primary data.

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