CMA Foundation Business Mathematics and Statistics Important Question | Dec 25

1. 9 and 15
2. 10 and 16
3. 15 and 25
4. 12 and 20 

Solution:

Question 2. 

1. 24,000
2. 18,000
3. 20,000
4. 30,000

Solution:

Question 8. 

An enterprise produced 500 units in the 2nd year of its existence and 800 units in its 6th year. If production follows an Arithmetic Progression (AP), what was the production in the 1st year? 

1. 425
2. 450
3. 475
4. 490

The sum of three numbers in G.P. is 70. If the two extremes are multiplied each by 4 and the mean by 5, the products are in AP. The numbers are

1. 12, 18, 40
2. 10, 20, 40
3. 40,20,10
4. None of These

"For the given series: 66, 71, 76, 81, 86, 91, 96 …. 666, 671, 676. With ‘n’ terms in the series, what will be the value of ‘d’ ?"

1. -5
2. 15
3. -3
4. 5

If ₹1,000 is deposited at the end of each year for a period of 5 years at an interest rate 10% p.a., then the Future Value Interest Factor for Annuity (Regular) is

1. 5.610
2. 6.501
3. 6.105
4. 5.160

The distance between two terminal metro stations A & B is 300 km. A metro rail takes 1.50 hours to cover the distance. Calculate the total time worked by the driver (in terms of days) in a week, if 6 trips from Station A to Station B takes place in a day?

1. 3.50 days
2. 5.25 days
3. 2.50 days
4. 4.25 days

A takes 4 hours to cover a distance 80 km and B takes 5 hours to cover the same distance. How much distance would A cover more than B in 15 hours?

1. 40 km
2. 60 km
3. 55 km
4. 45 km

A town has a total population of 50,000. Out of it 28,000 read the newspaper X and 23,000 read Y while 4,000 read both the papers. The number of persons not reading X and Y both is

1. 2,000
2. 3,000
3. 2,500
4. none of these

In a class of 100 students, 45 students read Physics, 52 students read Chemistry and 15 students read both the subjects. Find the number of students who study neither Physics nor Chemistry

1. 18
2. 10
3. 28
4. 22

If log4(t−1) + 1 = 2 × log₄t, find the value of t.

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

Find the value of x if logₓ 3 + logₓ 9 + logₓ 729 = 9.

1. 2
2. 3
3. 4
4. 6

Every two persons shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is

1. 11
2. 12
3. 13
4. 14

In how many ways 6 customers stand in a queue for depositing cash in bank? 

1. 680 ways
2. 480 ways
3. 600 ways
4. 720 ways

Find the square of the difference of the roots of 115 + 5(x² −12x) = 0

1. 24
2. 48
3. 26
4. 52

The difference between the roots of the equation x² - 7x - 9 = 0 is

1. 7
2. 9
3. √85
4. 2√85

If f(x) = (1/3)x³ − (1/2)x² − 2x, then find the points where f(x) has maximum and minimum values.

1. maximum, x = 1, minimum, x = −2
2. maximum, x = −1, minimum, x = −2
3. maximum, x = 1, minimum, x = 2
4. maximum, x = −1, minimum, x = 2

A manufacturer has a monthly fixed cost of ₹ 1, 00,000 and a production cost of ₹ 50 per unit produced. The product is sold at ₹ 75. Find the cost function and the number of products be sold by the manufacturer to have break even. 

1. 25x + 50,000; 2000
2. 50x + 1,00,000; 4000
3. 5x + 1,00,000; 3000
4. 2.5x + 10,000; 5000

Given (dy/dx) is calculated as

1. t
2. –1/t
3. 1/t
4. none of these

Given: C(x) = 9x + 350 and P = 14. Find the condition of getting break-even point

1. 5x - 350 = 0
2. 7x - 350 = 0
3. -14x - 350 = 0
4. None of these

Find the values of x for which the given function has maximum and minimum points

f(x) = (^x³⁄₃₎ - 9x² + 81x + 70

1. Maximum, x = 9; Minimum, x = 9
2. Minimum, x = 3; Maximum, x = 5
3. No curvature
4. None of the above

The entire upper part of a table is known as

1. Caption
2. Stub
3. Box head
4. Body.

1. Continuous distribution
2. Discrete distribution
3. Cumulative frequency distribution
4. None of the above  

Hidden trend, if any, in the data can be noticed in

The frequency distribution of a continuous variable is known as

1. Grouped frequency distribution
2. Simple frequency distribution
3. (a) or (b)
4. (a) and (b).

Two variables x and y are given by y= 2x – 3. If the median of x is 20, what is the median of y?

1. 20
2. 40
3. 37
4. 35

Solution:

A person walks 8 km at 4km an hour, 6km at 3km an hour and 4km at 2km an hour.  Average speed per hour is _________________.

1. 0.33
2. 2
3. 3
4. 5

Solution:

The sum of the deviations of a certain number of observations measured from 4 is 72 and the sum of the deviations of the observations from 7 is -3. Mean of the observations is: 

1. 6.88
2. 25
3. 3.63
4. Cannot be ascertained with given data;

Solution:

The appropriate measure of dispersion for open – end classification is

1. Standard deviation
2. Mean deviation
3. Quartile deviation
4. All these measures

Solution:

The quartiles of a variable are 45, 52 and 65 respectively. Its quartile deviation is

1. 10
2. 20
3. 25
4. 8.30

Solution:

Frequencies are also called weights

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

Solution:

The number of observations smaller than _____________is the same as the number larger than it

1. median
2. mode
3. mean
4. none

Solution:

Consider the following results N = 12, Σdx = 0, Σdy = 4, Σdx² = 1344, Σdy² = 215, Σdxdy = – 4360 Appropriate regression coefficient is

1. -0.821
2. 1
3. 5.67
4. -3.244 

Solution:

If R = 0.8, ∑D² = 33, find N 

1. 10
2. 11
3. 12
4. 13

Solution:

Find the Spearman’s rank correlation coefficient from the given data:

Σd1² = 70, n = 6

1. -1
2. 1
3. 0.32
4. -0.68

Solution:

In a bivariate regression analysis comprising of series X & Y, if Σ(x − x̄)² = Σ(y − ȳ)² then :

1. b_XY = b_YX
2. b_XY > b_YX
3. b_XY < b_YX
4. Correlation co - eficient = 1 

Solution:

It is the most suitable average when it is desired to give greater weight to smaller observations and less weight to larger ones. It is

1. AM
2. HM
3. GM
4. Median

Solution:

Bivariate Data are the data collected for

1. Two variables irrespective of time
2. More than two variables
3. Two variables at the same point of time
4. Two variables at different points of time.

Solution:

Product moment correlation coefficient is considered for

1. Finding the nature of correlation
2. Finding the amount of correlation
3. Both (A) and (B)
4. Either (A) and (B).

Solution:

Addition rule for mutually exclusive events A & B is :

1. P(A or B) = P(A) +P(B)
2. P(A or B) = P(A+B)
3. P(A or B) = P(A) +P(B)-P(AB)
4. P(A or B) = P(A+B - AB)

Solution:

For an event Odds in favour are “five to two” This means that: 

1. In a total of seven trials the event will occur five times
2. In a total of seven trials the event will occur two times
3. In a total of five trials the event will occur two times
4. In a total of seven trials the event will not occur five times

Solution:

An ordinary die is tossed twice and the difference between the number of spots turned up is noted. What is the probability that the difference between the numbers rolled is 3?

1. 1/6
2. 1/36
3. 1/9
4. 1/18

Solution:

If P(A ∩ B) = 0 and P(A ∪ B) = 1, then events A and B are

1. mutually exclusive but not exhaustive
2. neither mutually exclusive nor exhaustive
3. not mutually exclusive but exhaustive
4. mutually exclusive and exhaustive.

Solution:

A bag contains 10 red and 10 green balls. A ball is drawn from it. The probability that it will be green is :

1. 1/10
2. 1/3
3. 1/2
4. None of these

Solution:

If two unbiased coins are tossed once, the probability of getting both the heads is?

1. 0.25
2. 0.50
3. 0.75
4. 1

Solution:

Probability theory is often referred to as

1. Science of prediction
2. Science of uncertainty
3. Science of chance
4. Science of decision making

Solution:

If Fisher’s and Laspeyres’ price index numbers are respectively 129 and 132.5, the Paasche’s price index number is

1. 126.4
2. 124.7
3. 122.8
4. 125.6

Solution:

“Rain has affected very badly the wheat crop” is an example of

1. secular trend
2. cyclical movement
3. seasonal movement
4. irregular movement

Solution:

If ΣPnQn = 500, ΣP0Q0= 100, ΣPnQ0= 300, ΣP0Qn= 200, find the Fisher’s quantity index number for the “nth “year with base year:

1. 54.77
2. 183.33
3. 273.86
4. 182.57

Solution:

A series of numerical figures which show the relative position is called

1. index number
2. relative number
3. absolute number
4. none

Solution:

__________ is a point of reference in comparing various data describing individual behavior.

1. Sample
2. Base period
3. Estimation
4. none

Solution: