- Team Koncept
- 30 August, 2024

- CA - Foundation (New Syllabus)
- Team Koncept
- 30 August, 2024

CA Foundation Question Paper with Solution June 2024 - MATHS

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1. A less than ogive curve is drawn by plotting

- Less than Cumulative Frequencies on the vertical axis
- More than Cumulative Frequencies on the vertical axis
- Highest frequencies on vertical axis
- Lowest frequencies on vertical axis

**Answer : Choice 'a' is correct as **

In a "less than" ogive curve, the cumulative frequencies are plotted on the vertical axis against the upper class boundaries (or class limits) on the horizontal axis. This type of ogive shows the cumulative total of all data values less than or equal to the upper class boundary.

2. A says “B is my sister’s son”. B says, “C is my father-in-law”. C says, “D is my wife’s brother”. What can be the relationship between A and D?

- Uncle Nephew
- Brother – Sister
- Father Son
- Cousins

**Answer : Choice 'a' is correct as **

Let's analyze the statements:

- A says, "B is my sister's son." This means A is the uncle of B.
- B says, "C is my father-in-law." This means B is married to C's daughter.
- C says, "D is my wife's brother." This means C is D's brother-in-law.

From the statements:

- A is the uncle of B.
- C is the brother-in-law of D.

Therefore, A (uncle of B) and C (brother-in-law of D) are not directly related. However, they could be part of the same extended family through marriage.

The closest relationship between A and D based on the given information would be **cousins** because B (son of A's sister) and D (brother-in-law of C) are cousins to each other.

3. A is B’s sister. C is B’s mother. D is C’s father. E is D’s mother. How is A related to D?

- Grandmother
- Grandfather
- Daughter
- Grand Daughter

**Answer : Choice 'd' is correct as **

Hence, We can say that A is **granddaughter** to D.

4. Two frequency distributions are given to you. To compare them visually, the best diagram to be drawn on the same sheet is

- Pie chart
- Histogram
- Frequency polygon
- Bar chart

**Answer : Choice 'c' is correct as **

A frequency polygon can effectively display the shape and distribution of data across different categories or intervals. By plotting the points and connecting them with straight lines, you can easily compare the patterns and trends of two or more distributions on the same graph. This method allows for a clear comparison while maintaining clarity and visual appeal.

5. If a loan of ₹30,000 is to be paid in 5 annual instalments with interest rate of 14% per annum, then equal annual instalment will be ____________ (Take P (5,0.14) = 3.43308)

- ₹ 7,100
- ₹ 8,100
- ₹ 8,738
- ₹ 8,322

**Answer :**

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6. Assuming that the discount rate of 12 % per annually , how much would you pay to get ₹100 per year, growing at 4 % annually forever?

- ₹ 1,425
- ₹ 1,300
- ₹ 1,250
- ₹ 1,150

**Answer : Choice 'c' is correct as**

To find out how much you should pay initially to receive ₹100 per year, growing at 4% annually forever, we can use the perpetuity formula adjusted for growth:

PV = C/ (r − g)

Where:

- PV is the present value (the amount you should pay initially),
- C is the annual payment (₹100 in this case),
- r is the discount rate (12% per annum, or 0.12),
- g is the growth rate (4% per annum, or 0.04).

Substitute the values into the formula:

PV = (100/ (0.12 − 0.04))

PV = (100/ 0.08)

PV = 1250

Therefore, the present value (the amount you should pay initially) to receive ₹100 per year, growing at 4% annually forever, is ₹1,250.

So, the answer is (c) ₹1,250.

7. Find the future of value of an annuity of ₹5,000 made annually for 6 years at interest rate of 12 % compounded annually, if (1+0.12)* = 1.9738

- ₹ 45,575
- ₹ 39,465
- ₹ 39,465
- ₹ 37,868

**Answer : Choice 'a' is correct as**

To find the future value of an annuity of ₹5,000 made annually for 6 years at an interest rate of 12% compounded annually, we can use the future value of an ordinary annuity formula:

Where:

- P is the annual payment (₹5,000),
- i is the interest rate per period (12% per annum, or 0.12),
- n is the number of periods (6 years).

Given (1+0.12)^{6 }= 1.9738, which is the future value annuity factor for 6 years at 12% interest rate.

Now, calculate the future value:

FV = 5000 × ((1.9738 − 1)/ 0.12)

FV = 5000 × (0.9738/ 0.12)

FV = 5000 × 8.115

FV = 40575

Therefore, the future value of the annuity of ₹ 5,000 made annually for 6 years at 12% interest compounded annually is ₹ 40,575.

So, the answer is (a) ₹ 45,575

8. If the interest rate on a loan as 1% per month, the effective annual rate of interest is:

- 12 %
- 12.36 %
- 12.68 %
- 12.84 %

**Answer :**

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9. A random variable has the following probability distribution:

X | 2 | 3 | 5 |

P | K | 2K | 2K |

Find K

- 1/3
- 2/5
- 1/5
- 2/3

**Answer : Choice 'c' is correct as**

To find the value of K in the probability distribution of the random variable X, we need to ensure that the probabilities sum up to 1.

Given:

- X takes values 2,3, and 5.
- The corresponding probabilities are K,2K, and 2K respectively.

The sum of probabilities must equal 1:

K + 2K + 2K = 1

Combine like terms:

5K = 1

Now, solve for K:

K = (1/ 5)

Therefore, the value of K is (1/ 5)

So, the answer is (c) (1/ 5)

10. A number is selected at random from the set {1, 2,…..,99}. The probability that it is divisible by 9 or 11 is ________

- 19/100
- 19/99
- 10/100
- 10/99

**Answer : Choice 'd' is correct as**

To find the probability that a number selected randomly from the set {1,2,…,99} is divisible by 9 or 11, we use the principle of inclusion-exclusion.

First, calculate the number of integers from 1 to 99 that are divisible by 9:

(99/ 9)=11

Next, calculate the number of integers from 1 to 99 that are divisible by 11:

(99/ 11) = 9

Now, calculate the number of integers from 1 to 99 that are divisible by both 9 and 11 (i.e., divisible by their least common multiple, which is 99):

(99/ 99) = 1

Apply the inclusion-exclusion principle to find the total number of integers from 1 to 99 that are divisible by either 9 or 11:

Numbers divisible by 9 or 11 = 11 + 9 – 1 = 19

Now, calculate the probability:

Probability = (Numbers divisible by 9 or 11/ Total numbers from 1 to 99)

= 19/ 99

Therefore, the probability that a number selected randomly from the set {1,2,…,99}is divisible by 9 or 11 is (19/ 99).

So, the answer is (d) (19/ 99)

11. The coefficient of the range of the data: 7, 8, 4, 1, 9, 12, 18, 16, 94, 3, 5, -6 is ______

- 133.6
- 163.3
- 166.3
- 113.6

**Answer :**

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12. Two coins are tossed. Define the events A = {“the first toss is head”}, A_{2}^{ }= {number of heads is 2}; A_{1} = {number of heads is 1}; A_{0} = {number of heads is 0}and A_{3} = {“both outcomes are alike”}. The event A is independent of _________

- A
_{2 } - A
_{3 } - A
_{0} - A
_{1}and A_{0}both

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13. ∫x^{2}√x^{2} + 4 dx =

- 2/9 (4
^{2/4 }– 3^{3/2}) - 2/9 (5
^{2/3 }– 4^{2/3}) - 2/9 (4
^{2/2}– 3^{4/2}) - 2/9 (5
^{2/5}+ 4^{1/5})

**Answer :**

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14. ∫ u(1-u) du = _______

- 1/10x11
- 1/12x11
- 1/10x9
- 1/12x13

**Answer :**

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15. Find dy/dx for x^{2 }y^{2} + y = 0

- dy/dx = 2y
^{2}x/2y^{2}x^{2}+ 1 - dy/dx = -2y
^{2}x/2yx^{2}– 1 - dy/dx -2y
^{2}x/2y^{2}x - dx/dy = 2x’x/2y’x’

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16. Which of the following measure of central tendency will be unaffected if the lowest and highest observation are removed?

- Mean
- Mode
- Median
- Range

**Answer : Choice 'c' is correct as**

The measure of central tendency that will be unaffected if the lowest and highest observations are removed is the **median**.

Here’s why:

**Mean**: The mean is affected by extreme values because it considers all values in the dataset when calculating the average. Removing the lowest and highest values will change the sum and count of the remaining values, thus changing the mean.**Mode**: The mode is the value that appears most frequently in a dataset. Removing the lowest and highest values could potentially change which value appears most frequently, thus changing the mode.**Median**: The median is the middle value in an ordered dataset. If the dataset has an odd number of values, removing the lowest and highest value will still leave the middle value unchanged. If the dataset has an even number of values, removing the lowest and highest value will adjust the dataset so that the two middle values will still represent the median.**Range**: The range is simply the difference between the highest and lowest values in a dataset. Removing these values will definitely change the range.

Therefore, the measure of central tendency that remains unaffected when the lowest and highest observations are removed is the **median**.

17. Which sampling is based on the discretion of the sampler?

- Systematic
- Multi-stage
- Stratified
- Purposive

**Answer : Choice 'd' is correct as**

Purposive sampling, also known as judgmental or selective sampling, involves the selection of sample members based on the researcher's judgment or discretion. In this method, the researcher intentionally selects individuals, groups, or items that they believe will best serve the research purpose or objectives. It is not based on randomization or predefined selection criteria but rather on the researcher's subjective choice.

In contrast:

**Systematic sampling**involves selecting every kkk-th element from a list or population after a random start.**Multi-stage sampling**involves using a combination of different sampling methods in stages.**Stratified sampling**involves dividing the population into homogeneous subgroups (strata) and then sampling from each subgroup.

Therefore, the correct answer to the question is (d) Purposive.

18. Which of the following is not a type of sampling?

- Probability
- Non- Probability
- Stand-alone
- Mixed

**Answer : Choice 'c' is correct as**

**Probability sampling**(a) involves random selection where each member of the population has a known and nonzero chance of being selected.**Non-probability sampling**(b) involves non-random selection where the probability of selection cannot be accurately determined.**Mixed sampling**(d) refers to a combination of probability and non-probability sampling methods.

However, **stand-alone** sampling (c) is not a recognized type of sampling method in the typical categorization used in research and statistics. It seems to be a term that does not fit into the conventional classification of sampling methods.

Therefore, the correct answer is (c) Stand-alone.

19. An ogive is used to represent:

- The frequency of each data point
- The number of data points falling below a specific value
- The proportion of data points falling below a specific value
- The relationship between two variables

**Answer : Choice 'c' is correct as**

- An ogive plots cumulative frequencies (or cumulative relative frequencies) against the upper class boundaries or midpoints of the intervals.
- It shows how many data points fall below a certain value or within a certain range relative to the total number of data points.
- It helps visualize the cumulative distribution of the data.

Therefore, the correct answer is (c) The proportion of data points falling below a specific value.

24. Ram borrowed ₹5,000 at 12.5 % per annum compound interest. The money was repaid after 3 years. The total interest paid by him approximately is ______ , if (1 + 0.125)^{2} = 1.4238

- ₹ 2,119
- ₹ 2,220
- ₹ 2,000
- ₹ 2,500

**Answer :**

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25. A person invests in a fund that pays 4% per annum for four years. The future value of current ₹4,000 would be ₹__________ (Use, if needed, (1.04)^{4} = 1.1698, 1/(1.04)^{4} = 0.08548, (1.04)^{5} = 1.2160 and 1/(1.04)^{5} = 0.8219)

- ₹ 3,419
- ₹ 4,679
- ₹ 4,866
- ₹ 3,287

**Answer : Choice 'b' is correct as**

To calculate the future value of an investment of ₹4,000 at an interest rate of 4% per annum compounded annually for four years, we use the future value formula for compound interest:

FV = PV × (1+r)^{n} Where:

- PV is the present value (₹4,000),
- r is the annual interest rate (4% or 0.04 as a decimal),
- n is the number of years (4),
- FV is the future value.

Given (1.04)^{4 }= 1.1698, we can calculate the future value:

FV = 4000 × 1.1698

Rounding to the nearest rupee, the future value of the investment is approximately ₹ 4,679.

Therefore, the correct answer is (b) ₹4,679.

26. What is the present value of ₹ 5,000 to be obtained after six years if the interest rate is 5% per annum? (Use the following if needed 1/1.05^{6} = 0.74621, 0.71068, 0.67686, 0.64462, for n = 6, 7, 8 and 9 respectively.)

- ₹3,731
- ₹ 3,553
- ₹ 3,384
- ₹ 3,223

**Answer : **

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27. Find the effective rate of interest if an amount of ₹ 40,000 deposited in a bank for 1 year at the rate of 10% compounded semi-annually

- 10.20%
- 10.05%
- 10.25%
- 10.10%

**Answer : **

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28. For the first 20 natural numbers, the standard deviation is _

- 5.77
- 7.75
- 5.64
- 6.54

**Answer : **

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29. If Mean Deviation about Arithmetic Mean is 1.78 and Arithmetic Mean is 3.50 then coefficient of Mean Deviation about Arithmetic Mean is

- 50.85
- 44.33
- 52.65
- 51.85

**Answer : **

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30. If Mean of a data set is 22 and Median is 22.33 then Mode is

- 21
- 21.34
- 22.99
- 21.54

**Answer : **

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31. If Arithmetic Mean and coefficient of variation of y are 5 and 20 respectively, the variance of 12-3y

- 9
- 81
- 3
- 100

**Answer : Choice 'a' is correct as**

To find the variance of 12 − 3y, given the arithmetic mean and coefficient of variation (CV) of y, we proceed as follows:

Given:

- Arithmetic Mean of y = =5
- Coefficient of Variation of y = CVy = 20% = 0.20

Coefficient of Variation (CV) is defined as (Standard Deviation/ Mean).

**1. Calculate the Standard Deviation (σ _{y}) of y**

CVy = (σ_{y}/y)

σ_{y} = CV_{y × yˉ }= 0.20 × 5 = 1

**2. Calculate the variance of 12 − 3y:**

First, find the variance of −3y:

Var(−3y) = (−3)^{2 }⋅ Var(y) = 9 ⋅ σ^{2}y = 9 ⋅ 1^{2} = 9

Since 12 is a constant (and its variance is 0), the variance of 12−3y is:

Var(12 − 3y) = Var(−3y) = 9

Therefore, the variance of 12−3y is 9.

32. A histogram and a pie chart represent the same data On Monthly expenses of a household Which statement is most likely true?

- The Histogram only shows the frequency of each expense category, while the pie chart shows the proportion of each category
- Both the histogram and pie chart shows the frequency of each expense category
- Both the histogram and pie chart shows the proportion of each expense category
- Pie charts are always better than histograms for representing expenses

**Answer : Choice 'c' is correct as**

- A
**histogram**displays the distribution of data by grouping continuous or discrete data into bins or intervals, showing the frequency (or sometimes density) of data points within each interval. In the context of monthly expenses, a histogram would show the proportion of total expenses accounted for by each expense category or interval. - A
**pie chart**represents data in a circular graph divided into slices to illustrate numerical proportion. Each slice of the pie chart represents the proportion (percentage) of total expenses attributed to a specific expense category.

In summary:

- The
**histogram**would display proportions through the area or height of bars representing different expense categories. - The
**pie chart**would display proportions through the angles of slices representing different expense categories.

Therefore, (c) Both the histogram and pie chart show the proportion of each expense category is the most accurate statement regarding their representation of monthly household expenses.

33. Which of the following measure of central tendency depends on the position of the observation?

- Mean
- Median
- Mode
- Harmonic Mean

**Answer : **

( Avaiable only to our paid subscribers )

34. The following set of data cannot be presented in a table

- The heights of students described in centimetres
- The weights of candidates expressed in kilograms
- The amount of rainfall opined as “medium”, “average”, “heavy", etc.
- The number of bills per day cleared by an auditor in a month

**Answer : Choice 'c' is correct as**

- Heights of students (a) and weights of candidates (b) can be presented in a table with columns indicating the measurement in centimeters and kilograms, respectively.
- The number of bills per day cleared by an auditor (d) can also be presented in a table with columns for each day of the month and the corresponding number of bills cleared.

However, (c) presents qualitative data that categorizes rainfall into descriptive terms ("medium", "average", "heavy", etc.). While these categories can be represented in a summary format or through descriptive statistics, they do not represent numerical or discrete data that can be straightforwardly presented in a traditional table format.

Therefore, the correct answer is (c) The amount of rainfall opined as "medium", "average", "heavy", etc.

35. According to the empirical rule, if the data form a "bell-shaped “distribution, then the maximum and minimum frequencies occur at __________ and _______ respectively.

- Middle, left end
- Middle, right end
- End, middle
- Middle, ends

**Answer : Choice 'd' is correct as**

In a bell-shaped distribution, which is symmetric around the mean:

- The maximum frequency occurs at the middle (mean) of the distribution because this is where the data are most concentrated.
- The minimum frequencies occur at the ends (tails) of the distribution, farthest from the mean, where the data are least concentrated.

Therefore, the correct answer is (d) Middle, ends.

47. The Mean of a set of 20 observations on 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:

- 17.6
- 18.0
- 5.7
- 24.6

**Answer : Choice 'c' is correct as**

To solve this problem, let's denote the sum of the original 20 observations as SSS, and let xxx be the new observation.

Given:

- Mean of the original 20 observations = 18.3
- Mean of the 21 observations (including xxx) = 18.3 - 0.6 = 17.7

The equation representing the mean of the 21 observations is: (S + x)/ 21 = 17.7

From this equation, solve for S + x:

S + x = 17.7 × 21

S + x = 371.7

Now, substitute the mean of the original 20 observations to find S:

(S/ 20) =18.3

S = 18.3×20

S = 366

Now, substitute S into the equation S + x = 371.7:

366 + x = 371.7

x = 371.7 – 366

x = 5.7

Therefore, the new observation xxx is 5.75.75.7.

So, the correct answer is (c) 5.7.

48. Consider the data sets :X={-6,2,-2,6}, Y={4,8,2,6}, Z={103,100,102,101}. Let S_{x}, S_{y} and S_{z }be the standard deviations of the sets X, Y and Z respectively. We have the relations

- S
_{x}< S_{y}< S_{z} - S
_{x}< S_{y}< S_{x} - S
_{x}< S_{x }< S - S
_{x}< S_{2}< S_{r}

**Answer : **

( Avaiable only to our paid subscribers )

49. If in a data set, 25 percent of values are smaller than 30 and one fourth of values are larger than 70, then the coefficient of quartile deviation is ______ %

- 40
- 30
- 70
- 50

**Answer : ****Choice 'b' is correct as**

To find the coefficient of quartile deviation, we need to calculate the first quartile (Q1) and the third quartile (Q3) based on the given information.

Given:

- 25% of values are smaller than 30.
- One fourth (25%) of values are larger than 70.

**Step-by-Step Calculation:**

**Finding Q1 (First Quartile):**- 25% of values are smaller than 30, implying Q1 is 30.
**Finding Q3 (Third Quartile):**- One fourth (25%) of values are larger than 70, implying Q3 is 70.

**Formula for Quartile Deviation and Coefficient of Quartile Deviation:**

- Quartile Deviation (QD) = Q3 - Q1
- Coefficient of Quartile Deviation = (QD/ Q1) × 100%

**Calculation:**

- Q1 = 30
- Q3 = 70

Therefore,

- Quartile Deviation (QD) = Q3 - Q1 = 70 - 30 = 40
- Coefficient of Quartile Deviation = (40/ 30) × 100% = (4/ 3) × 100% = (400/ 3)% ≈ 133.33%

However, the options provided are in percentages (40%, 30%, 70%, 50%), so we should consider the closest match after calculating.

From the options provided, the coefficient of quartile deviation closest to our calculated value (approximately 133.33%) is:

(b) 30%

Therefore, the correct answer is (b) 30%.

50. If there are two groups containing 40 and 30 observations and have arithmetic means as 50 and 60 then the combined arithmetic mean is

- 55.48
- 56.35
- 54.28
- 50.28

**Answer : Choice 'c' is correct as**

To find the combined arithmetic mean of two groups with given means and observations, we use the formula for the combined mean:

Combined Mean = (n_{1}⋅Mean_{1} + n_{2}⋅Mean_{2})/ n_{1 }+ n_{2}

Given:

- Group 1: n
_{1}= 40, Mean1 = 50 - Group 2: n
_{2}= 30, Mean2 = 60

Calculate the combined mean:

Combined Mean = (40⋅50 + 30⋅60)/ (40+30)

Combined Mean = (2000 + 1800) / 70

Combined Mean = (3800/ 70)

Combined Mean=54.2857

Rounding to two decimal places, the combined arithmetic mean is approximately 54.29.

Therefore, the closest option provided is (c) 54.28.

51. If the arithmetic mean of two numbers is 10 and the geometric mean is 6, then the difference in the numbers is

- 12
- 14
- 16
- 8

**Answer :**

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52. In an arithmetic progression, the seventh term is x, and (x+7)^{ab} term is zero. Then x^{ab} term is

- 6
- 7
- 8
- 10

**Answer : Choice 'b' is correct as**

In an arithmetic progression (AP), the n-th term Tn is given by:

Tn=a+(n−1)d

a is the first term,

d is the common difference.

Given:

The seventh term T_{7} is x, so a+6d=x.

The (x+7)-th term T_{x+7} is zero, so a+(x+6)d=0.

Solving these equations, we find x=−1 and d=1.

Now, we need to find xab, which represents x×a×b:

Since x=−1, the answer is −1×a×b.

The correct answer is 7

53. If the second and eight terms of an arithmetic progression (AP) are equal to constant a, then the sum of first n terms of this AP is equal to

- na
- a/n
- 2n + n(a - 1)
- n + a(n - 1)

**Answer :**

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54. The 3^{rd} term of arithmetic progression is 7 and Seventh term is 2 more than thrice of third term. The common difference is

- 4
- 3
- 5
- 6

**Answer :**

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55. The range of the coefficient of correlation is

- between-1 and 1
- between-1 and 1 including 1
- between-1 and 1 including-1
- between-1 and 1 including-1, 1

**Answer :**

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56. A company produces 5 defective items out of 300 items. The probability distribution follows a:

- Binomial distribution
- Normal distribution
- Poisson distribution
- Standard normal distribution

**Answer : Choice 'a' is correct as**

The situation described involves counting the number of defective items (successes) out of a fixed number of items (trials) with a constant probability of a defect for each item. This setup is characteristic of a binomial distribution.

So, the correct answer is: **Binomial distribution**

57. The mean of Poisson distribution is 4. The probability of two-successes in

- 8/e
^{4} - 4/e
^{4} - 16/e
^{4} - 8/e
^{2}

**Answer : Choice 'a' is correct as**

To find the probability of getting exactly 2 successes in a Poisson distribution with a mean (λ) of 4, we use the formula:

P(X=k)= λ^{k}e−^{λ} / k!

Where:

λ=4

k=2

Substituting the values, we get:

P(X=2)= 4^{2}e^{−}^{4}/2! = 16e^{−}^{4}/2 = 8e^{−}^{4}/1 = 8/e^{4}

Thus, the correct answer is: **8/e4**

58. If the regression lines are 3x - 4y + 8 = 0 and 4x - 3y = 1 then the correlation coefficient between x and y is

- 3/4
- 3/8
- 4/8
- 1/4

**Answer : Choice 'a' is correct as**

Given the regression lines:

1.3x−4y+8=0

2.4x−3y=1

We find the slopes of these lines:

1.Rearrange 3x−4y+8=0 to get y=3/4x+2, so the slope m_{1}=3/4.

2.Rearrange 4x-3y=1 to get y=4/3x−1/3 so the slope m_{2}=4/3.

The correlation coefficient r is given by:

r=±√(m1⋅m2)

Calculate:

r=±√(3/4⋅4/3) =±√1 = ±1

Given the options, the closest is: **3/4**

59. A car starts from a point, runs 20 kms towards north, turns right and runs 35 kms, turns right again and runs. Which is the direction now it is facing?

- North
- South
- East
- West

**Answer : Choice 'b' is correct as**

1.The car starts by going 20 km north.

2.It then turns right (90 degrees clockwise) and runs 35 km eastward.

3.After the second right turn (another 90 degrees clockwise), the car is now facing south.

Therefore, the answer is B. South.

60. Shyam walks 12 m south from his house, turns left and walks 20 m, again turns left and walks 45 m. then turns right and walks 10 m to reach coffee shop. In which direction is coffee shop from his house?"

- South West
- East
- North East
- North

**Answer : Choice 'c' is correct as**

Shyam's movements:

1.Starts 12 m south.

2.Turns left and walks 20 m east.

3.Turns left again and walks 45 m north.

4.Turns right and walks 10 m east.

5.Combining these directions:

He starts south, then turns left (east), left again (north), and finally right (east).

Therefore, the coffee shop is located in the North East direction from Shyam's house.

61. If Shyam Sees the rising sun behind the tower and setting sun behind the Railway station from his house. What is the direction of tower from the Railway station?

- South
- North
- West
- East

**Answer : **

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62. Five players named as A, B, C, D, and E are sitting on a bench, facing south, and are waiting to be interviewed by a selector. The person C is an immediate neighbor of both A and B. The person A is the fourth person from right end; If E is to the right of B. then where is E sitting?

- Fifth from right end
- Fourth from right end
- Fifth from left end
- Second from right end

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63. The equation x^{3} - 3x^{2} - 4x + 12 = 0 has three real roots. They are

- -2, 2, 1
- -2, -2, 3
- 2, -2, -3
- -2, 2, -3

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64. If α and β are roots of the equation ax^{2} + bx + c = 0 then the equation whose routs 1/ α and 1/ β is

- cx
^{2}- bx + a = 0 - cx
^{2}+ bx + a = 0 - x
^{2}+ bx + a = 0 - x
^{2}+ bx - a = 0

**Answer : Choice 'b' is correct as**

α and β as roots of ax^{2}+bx+c=0, by Vieta's formulas:

α+β= −a/b

αβ=c/a

To find the equation with roots 1/ α and 1/ β ,substitute x=1/ α and x = 1/β into ax2+bx+c=0:

a(1x) ^{2} + b(1/x) + c = 0

Simplify and rearrange to get:

cx^{2}+bx+a=0

Therefore, the equation with roots 1/ α and 1/ β is cx^{2} + bx + a = 0

65. If a and are roots of the equation x ^ 2 - 8x + 12 = 0 then 1/ α - 1/ β = ____

- 2/3
- 2/4
- 3/4
- 4/5

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66. The roots of the equation x^{2} – 7x + 10 = 0 are:

- 2 and 5
- -2 and -5
- 2 and -5
- -2and 5

**Answer : Choice 'b' is correct as**

To find the roots of the quadratic equation x^{2}−7x+10=0:

1.Factorize the quadratic equation into two binomials:

x^{2}−7x+10 =(x−2)(x−5)

- Set each factor equal to zero to find the roots:

x−2=0⇒x=2

x−5=0⇒x=5

Therefore, the roots of the equation x^{2}−7x+10=0 are x=2 and x=5.

67. Which index number formula satisfies both the time reversal and factor reversal tests?

- Fisher's Ideal index
- Laspeyres' index
- Paasche's index
- Marshall-Edgeworth index

**Answer : Choice 'a' is correct as**

The index number formula that satisfies both the time reversal and factor reversal tests is Fisher's Ideal index.

Fisher's Ideal index is designed to satisfy both tests:

Time reversal test: Reversing the base and comparison periods should yield the same index value.

Factor reversal test: Reversing the weights or quantities should yield the reciprocal index value.

Therefore, the correct answer is: Fisher's Ideal index

68. What of the followings is not a test of adequacy in the context of index numbers?

- Unit Test
- Square Test
- Circular Test
- Factor Reversal Test

**Answer : Choice 'b' is correct as**

The test of adequacy in the context of index numbers refers to various statistical tests used to evaluate the quality and reliability of an index number formula. Let's break down the options:

1. Unit Test: This test checks if the index number is dimensionless (i.e., unit-free) and consistent in its unit of measurement.

2. Square Test: This test checks if the index number formula is well-behaved under the squaring of price relatives, ensuring consistency and reliability.

3. Circular Test: This test checks if the index number is consistent when comparing multiple sets of prices or quantities in a cyclical or circular manner.

4. Factor Reversal Test: This test checks if reversing the weights or quantities used in the index calculation results in the reciprocal index value, ensuring the index formula's reliability.

Among these options, the term "Square Test" does not correspond to a recognized test of adequacy in index number theory or practice. The correct answer is: B. Square Test

69. If the prices of all commodities in the base year are twice the values of the respective commodities in the current year, then the Fisher's ideal index number is equal to:

- 200
- 50
- 400
- 25

**Answer :**

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70. Which index number formula does not satisfy the time reversal test?

- Fisher's Ideal index and Laspeyre's Index
- Laspeyres' index and Paasche's Index
- Paasche's Index and Fisher's Ideal Index
- Laspeyres index, Fisher's Ideal Index and Paasche's Index

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71. A user wants to create a password using 4 lowercase letters (a-2) and 3 uppercase letters (A-Z). No letter can be repented in any form. In how many ways can the password be created if the password must start with an uppercase letter?

- 26 × 25 × 24 × 23 × 22 × 5 × 21
- 26 × 25 × 24 ×23 × 22 × 2 × 21
- 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21
- 6 × 26 × 25 × 24 × 23 × 22 × 21

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72. In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together

- 14,400
- 14,000
- 14,425
- 12,400

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73. In how many ways the letters of the word "STADIUM" be arranged in such a say that the vowels all occur together?

- 7!/ 3!
- 5! 4!
- 5! 3!
- 7! 3!

**Answer :**

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74. How many ways can 5 different trophies can be arranged on a shelf if one particular trophy must always be in the middle?

- 24
- 120
- 48
- 144

**Answer :**

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82. If log _{a }b = 3 and log _{b }c = 2 then log _{a} c is:

- 5
- 6
- 9
- 1

**Answer :**

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83. If and 2^{x} = 4^{y} = 8^{z} and 1/(2x) + 1/(4y) + 1/(6z) = 24/7 then the value of z is:

- 7/16
- 7/32
- 7/48
- 7/64

**Answer :**

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84. A fraction becomes 1, when 3 are added to the numerator and 1 is added to the denominator. But when the numerator and denominator are decreased by 2 and 1, respectively, it becomes 1/2. The denominator of the fraction is:

- 5
- 6
- 7
- 8

**Answer :**

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85. If the four numbers 1/4, 1/6 1/10 and 1/x are proportional, then what is the value of x?

- 14
- 15
- 10
- 1/12

**Answer :**

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86. If f(x) = (x - 1) × (x + 1) then dy/ dx =

- 3x
^{2}- 1 - 3x
^{2}+ 1 - x
^{2}- 3 - x
^{2}+ 3

**Answer :**

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87. The = ________

- 0
- 1
- 2
- 0.5

**Answer :**

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88. Consider the following relations on A = {1, 2, 3} R = {(1, 1), (1, 2)(1, 3)(3, 3)} T = {(1, 1), (1, 2)(2, 2), (2, 3)} and empty set Which one of these forms an equivalence relation?

- R
- S
- T
- φ

**Answer :**

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89. If f(x) = (x + 1)^{x + 1} then find f'(0)

- 0
- 1
- -1
- 2

**Answer :**

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90. You bought a painting 10 years ago as an investment. You originally paid 85,000 for it. If you sold it for ₹ 4,84,050, what was your annual return on investment?

- 47%
- 4.75%
- 19%
- 12.8%

**Answer :**

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91. What is the present value of an investment that pays ₹ 400 at the end of three years and ₹ 500 at the end of 6 years?

- 320
- 335
- 340
- 280

**Answer :**

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92. At 8% compounded annually, how long will it take ₹ 750 to double?

- 6.5 years
- 48 months
- 9 years
- 12 years

**Answer :**

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93. You are considering two investments. Investment A yields 10% compounded quarterly. Investment B yields r% compounded semi-annually. Both investments have equal annual yields. Find r.

- 19.875%
- 10%
- 10.38%
- 10.125%

**Answer :**

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94. From a bag containing 4 red, 5 blue and 6 white caps, two caps are drawn without replacement. What is the probability that the caps are of different colours?

- 74/ 105
- 37/ 105
- 94/ 105
- 31/ 105

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95. A question in statistics is given to three students A, B, and C. Their chances of solving the question are 1/3, 1/5 and 1/7 respectively. The probability that the question would be solved is

- 19/35
- 16/35
- 1/105
- 104/105

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96. A company produces two types of products. A and B. The probability of a defective product in type A is 0.05 and in type B is 0.03. If the company produces 60% type A and 10% type B. what is the probability of a randomly selected product being defective?

- 0.042
- 0.03
- 0.048
- 0.052

**Answer :**

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97. In a certain code TEACHER is written as VGCEJGT, How is CHILDREN written in that code.

- EJKNEGTP
- EGKNFITP
- EJKNFGTO
- EJKNFTGP

**Answer :**

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98. If a function is given by f(x) = e^{3x}, what is the derivative of the function?

- 3e
^{3x} - e
^{3x} - 3xe
^{3x} - 3e
^{3x }+ 3

**Answer :**

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99. Find the missing value in the series: 51, 52, 60, 87, 151, _____________, 492.

- 195
- 276
- 317
- 420

**Answer :**

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100. In a certain code INACTIVE is written as VITCANIE, How is COMPUTER written in the same code

- PMOCRETU
- ETUPMOCR
- UTEPMOOR
- MOCPETUR

**Answer :**

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Ruchika Saboo
An All India Ranker (AIR 7 - CA Finals, AIR 43 - CA Inter), she is one of those teachers who just loved studying as a student. Aims to bring the same drive in her students.

Ruchika Ma'am has been a meritorious student throughout her student life. She is one of those who did not study from exam point of view or out of fear but because of the fact that she JUST LOVED STUDYING. When she says - love what you study, it has a deeper meaning.

She believes - "When you study, you get wise, you obtain knowledge. A knowledge that helps you in real life, in solving problems, finding opportunities. Implement what you study". She has a huge affinity for the Law Subject in particular and always encourages student to - "STUDY FROM THE BARE ACT, MAKE YOUR OWN INTERPRETATIONS". A rare practice that you will find in her video lectures as well.

She specializes in theory subjects - Law and Auditing.

Yashvardhan Saboo
A Story teller, passionate for simplifying complexities, techie. Perfectionist by heart, he is the founder of - Konceptca.

Yash Sir (As students call him fondly) is not a teacher per se. He is a story teller who specializes in simplifying things, connecting the dots and building a story behind everything he teaches. A firm believer of Real Teaching, according to him - "Real Teaching is not teaching standard methods but giving the power to students to develop his own methods".

He cleared his CA Finals in May 2011 and has been into teaching since. He started teaching CA, CS, 11th, 12th, B.Com, M.Com students in an offline mode until 2016 when Konceptca was launched. One of the pioneers in Online Education, he believes in providing a learning experience which is NEAT, SMOOTH and AFFORDABLE.

He specializes in practical subjects – Accounting, Costing, Taxation, Financial Management. With over 12 years of teaching experience (Online as well as Offline), he SURELY KNOWS IT ALL.