CA Foundation Question Paper with Solution June 2024 (2024)

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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

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:

Numbersdivisibleby9or11 = 11 + 9 – 1 = 19

Now, calculate the probability:

Probability = (Numbersdivisibleby9or11/ Totalnumbersfrom1to99)

= 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”}, A₂= {number of heads is 2}; A₁ = {number of heads is 1}; A₀ = {number of heads is 0}and A₃ = {“both outcomes are alike”}. The event A is independent of _________

A₂
A₃
A₀
A₁ and A₀ both

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13. ∫x²√x² + 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 = _______

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15.Find dy/dx for x²y² + y = 0

dy/dx = 2y²x/2y²x² + 1
dy/dx = -2y²x/2yx² – 1
dy/dx -2y²x/2y²x
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 hom*ogeneous 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 1/1.05⁶ = 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

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 (StandardDeviation/ 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 ⋅ σ²y = 9 ⋅ 1² = 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 :

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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_zbe 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 < S₂ < S_r

Answer :

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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 ______ %

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:

CombinedMean = (n₁⋅Mean₁ + n₂⋅Mean₂)/ n₁+ n₂

Given:

Group 1: n₁ = 40, Mean1 = 50
Group 2: n₂ = 30, Mean2 = 60

Calculate the combined mean:

CombinedMean = (40⋅50 + 30⋅60)/ (40+30)

CombinedMean = (2000 + 1800) / 70

CombinedMean = (3800/ 70)

CombinedMean=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

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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

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 T₇ 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

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/e⁴
4/e⁴
16/e⁴
8/e²

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^ke−^λ / k!

Where:

λ=4

k=2

Substituting the values, we get:

P(X=2)= 4²e⁻⁴/2! = 16e⁻⁴/2 = 8e⁻⁴/1 = 8/e⁴

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

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 m₁=3/4.

2.Rearrange 4x-3y=1 to get y=4/3x−1/3 so the slope m₂=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

Answer :

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63. The equation x³ - 3x² - 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 ax² + bx + c = 0 then the equation whose routs 1/ α and 1/ β is

cx² - bx + a = 0
cx² + bx + a = 0
x² + bx + a = 0
x² + bx - a = 0

Answer : Choice 'b' is correct as

α and β as roots of ax²+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:

cx²+bx+a=0

Therefore, the equation with roots 1/ α and 1/ β is cx² + bx + a = 0

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

Answer :

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66. The roots of the equation x² – 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 x²−7x+10=0:

1.Factorize the quadratic equation into two binomials:

x²−7x+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 x²−7x+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:

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

Answer :

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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!

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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?

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82. If log _ab = 3 and log _bc = 2 then log _a c is:

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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

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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:

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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

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

3x² - 1
3x² + 1
x² - 3
x² + 3

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87. The = ________

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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?

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

0
1
-1
2

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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%

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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?

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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

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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%

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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

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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

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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

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

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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 :