Mathematics-III (Differential Calculus) 2025 — MAKAUT · BSC-301 · Mid Sem PYQ with solutions

Q: What is the subject code for Mathematics-III (Differential Calculus)?

BSC-301 is the MAKAUT subject code for Mathematics-III (Differential Calculus).

Q: Which exam is this Mathematics-III (Differential Calculus) question paper from?

The MAKAUT 2025 Mid Sem exam, semester 3. A student shared it, and it was checked before publishing.

Q: Which branches is this Mathematics-III (Differential Calculus) paper for?

It's a common paper for 3 B.Tech branches: Computer Science and Engineering, Computer Science and Engineering (Data Science) and Information Technology. Every branch gets the same questions.

Q: Are there solutions for this paper?

Yes. Every question in the 2025 Mathematics-III (Differential Calculus) paper has a worked answer on this page, grouped like the paper. The first answer is free to read; sign in (it's free) to unlock the rest.

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Maulana Abul Kalam Azad University of Technology

Solutions

30 answers across 3 groups

Try each question first, then open it to check your answer.

Group AVery Short Answer Type Question · answer any 10 · 1 mark eachIWrite one use of Chi square test.Free sampleAnswer: To test the goodness of fit of a theoretical distribution to an observed distribution.IIA random variable is uniformly distributed over the interval 2 and 10. Its variance will be ................IIIIf x+4y+3=0 and 4x+9y+5=0 be the two regression lines then the expectation of y is ____IVFind the mean of 21,32,43,54,65,76,87,98.VIf two fair coins are tossed, then the probability that we get at least one tail is ...........VIIf random variable X has a binomial distribution with parameters 4 and 1/3, then P(X=1) =.....VIITwo variables x and y are related as 3x+4y=5 then correlation co efficient of x and y is ...........VIIIThe first moment about 4 of the set of numbers 2,4,6,8 isIXIf P(A)=0.2, P(B)=0.3 then what is the value of P(AUB) if A and B are independent?XThe probability density function of a random variable is f(x)=k(2x-1) , where 0≤x≤2. Then the value of the parameter k is ......XIWhich probability distribution has the same expected value and variance?XIIA random variable X has a Poisson distribution such that P(1)=P(2). Then the Standard Deviation of X is ......Group BShort Answer Type Question · answer any 3 · 5 marks each2A box contains 2 red & 3 green balls. Two balls are drawn from the box without replacement. a) If the 1st ball is green then what is the probability that the 2nd ball is also green? b) What is the probability that the 2nd ball is Red where the first ball can have any colour?3Find the mean and standard deviation of the following distribution:Class-interval4-66-88-1010-1212-1414-16Frequency13111182105197Show answerHide answer to question 34Find the skewness for the following distribution:x55-5858-6161-6464-6767-70f(x)1217231811Show answerHide answer to question 45Obtain the Rank correlation coefficient from the following two series of observation:X62586845816068485070Y68647550648075405564Show answerHide answer to question 56A population consist of 5 numbers {2, 3, 6, 8, 11}. Consider all possible samples of size two which can be drawn with replacement from this population. Calculate S.E of sample means.Group CLong Answer Type Question · answer any 3 · 15 marks each7(a)In a college there are 900 girl students out of total 2000 students. If a random group of 10 students are taken, then what is the probability that 4 girl students are selected?5 marks7(b)Probability that a target can be hit is 0.2. What is the probability that the target will be hit on 6th shot?5 marks7(c)A biased coin, with 0.6 probability of getting a head, is tossed repeatedly. What is the probability that the 6th head appears on the 15th toss?5 marks8(a)Fit a linear trend equation to the following series on production: Year : 1961. 1962. 1963. 1964. 1965. 1966 Production :. 21. 37. 48. 56. 62. 695 marks8(b)Fit a parabolic curve of second degree to the data given below and estimate the value for 1986 and comment on it: Year : 1973. 1974. 1975. 1976. 1977 Sales( in 1000 Rs.) : 10. 12. 13. 10. 85 marks8(c)The mean life time of a sample of 100 electric bulbs produced by a manufacturing company is estimated to be 1570 hours with a standard deviation of 120 hours. If u be the mean life time of all the bulbs produced by the company, test the hypothesis u=1600 hours against the alternative hypothesis u≠ 1600 hours, using a level of significance 0.05.5 marks9(a)Calculate correlation coefficient between X and Y: X: 155 157 153 151 159 162 158 Y: 118 129 125 124 129 133 1277 marks9(b)Calculate Pearson's coefficient of correlation from the following table using 44 and 26 are are as the origins or X and Y respectively. X: 43 44 46 40 44 42 45 42 38 40 42 57 Y: 29 31 19 18 19 27 27 29 41 30 26 108 marks10(a)Show that the mean of the Binomial distribution with p probability of success and n trials is np.7 marks10(b)Find the mean and variance of a Poisson variate.8 marks11(a)The number of telephone calls arriving on an internal switch board of an office is 90 per hour. Find the probability that at the most 1 to 3 calls in a minute on the board arrive.5 marks11(b)Six dice are thrown together at a time, the process is repeated 729 times. How many times do you expect at least three dice to have 4 to 6?5 marks11(c)Probability distribution of blood types in India is given in the table Types: O A B AB Probability: 0.3712 0.2288 0.3226 0.0774 A random sample of 10 is considered from Indian population. What is the probability that there will be 4 Os, 3 As, 2 Bs and 1 AB blood types, respectively?5 marks

Class-interval	4-6	6-8	8-10	10-12	12-14	14-16
Frequency	13	111	182	105	19	7

x	55-58	58-61	61-64	64-67	67-70
f(x)	12	17	23	18	11

X	62	58	68	45	81	60	68	48	50	70
Y	68	64	75	50	64	80	75	40	55	64

About this paper

The MAKAUT Mathematics-III (Differential Calculus) (BSC-301) 2025 Mid Sem previous year question paper, set in semester 3. Download the verified PDF or read it online, then check your answers against the worked solutions above.

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Frequently asked questions

5 questions

What is the subject code for Mathematics-III (Differential Calculus)?

BSC-301 is the MAKAUT subject code for Mathematics-III (Differential Calculus).

Which exam is this Mathematics-III (Differential Calculus) question paper from?

The MAKAUT 2025 Mid Sem exam, semester 3. A student shared it, and it was checked before publishing.

Which branches is this Mathematics-III (Differential Calculus) paper for?

It's a common paper for 3 B.Tech branches: Computer Science and Engineering, Computer Science and Engineering (Data Science) and Information Technology. Every branch gets the same questions.

Where can I find more BSC-301 question papers?

On the Mathematics-III (Differential Calculus) subject page, which collects every year's papers along with notes and the syllabus.

Are there solutions for this paper?

Yes. Every question has a worked answer on this page, grouped like the paper. The first answer is free to read; sign in (it's free) to unlock the rest.

Solutions

Group AVery Short Answer Type Question · answer any 10 · 1 mark each

Write one use of Chi square test.

A random variable is uniformly distributed over the interval 2 and 10. Its variance will be ................

If x+4y+3=0 and 4x+9y+5=0 be the two regression lines then the expectation of y is ____

Find the mean of 21,32,43,54,65,76,87,98.

If two fair coins are tossed, then the probability that we get at least one tail is ...........

If random variable X has a binomial distribution with parameters 4 and 1/3, then P(X=1) =.....

Two variables x and y are related as 3x+4y=5 then correlation co efficient of x and y is ...........

The first moment about 4 of the set of numbers 2,4,6,8 is

If P(A)=0.2, P(B)=0.3 then what is the value of P(AUB) if A and B are independent?

The probability density function of a random variable is f(x)=k(2x-1) , where 0≤x≤2. Then the value of the parameter k is ......

Which probability distribution has the same expected value and variance?

A random variable X has a Poisson distribution such that P(1)=P(2). Then the Standard Deviation of X is ......

Group BShort Answer Type Question · answer any 3 · 5 marks each

A box contains 2 red & 3 green balls. Two balls are drawn from the box without replacement. a) If the 1st ball is green then what is the probability that the 2nd ball is also green? b) What is the probability that the 2nd ball is Red where the first ball can have any colour?

Find the mean and standard deviation of the following distribution:

Find the skewness for the following distribution:

Obtain the Rank correlation coefficient from the following two series of observation:

A population consist of 5 numbers {2, 3, 6, 8, 11}. Consider all possible samples of size two which can be drawn with replacement from this population. Calculate S.E of sample means.

Group CLong Answer Type Question · answer any 3 · 15 marks each

In a college there are 900 girl students out of total 2000 students. If a random group of 10 students are taken, then what is the probability that 4 girl students are selected?

Probability that a target can be hit is 0.2. What is the probability that the target will be hit on 6th shot?

A biased coin, with 0.6 probability of getting a head, is tossed repeatedly. What is the probability that the 6th head appears on the 15th toss?

Fit a linear trend equation to the following series on production: Year : 1961. 1962. 1963. 1964. 1965. 1966 Production :. 21. 37. 48. 56. 62. 69

Fit a parabolic curve of second degree to the data given below and estimate the value for 1986 and comment on it: Year : 1973. 1974. 1975. 1976. 1977 Sales( in 1000 Rs.) : 10. 12. 13. 10. 8

Calculate correlation coefficient between X and Y: X: 155 157 153 151 159 162 158 Y: 118 129 125 124 129 133 127

Calculate Pearson's coefficient of correlation from the following table using 44 and 26 are are as the origins or X and Y respectively. X: 43 44 46 40 44 42 45 42 38 40 42 57 Y: 29 31 19 18 19 27 27 29 41 30 26 10

Show that the mean of the Binomial distribution with p probability of success and n trials is np.

Find the mean and variance of a Poisson variate.

The number of telephone calls arriving on an internal switch board of an office is 90 per hour. Find the probability that at the most 1 to 3 calls in a minute on the board arrive.

Six dice are thrown together at a time, the process is repeated 729 times. How many times do you expect at least three dice to have 4 to 6?

Probability distribution of blood types in India is given in the table Types: O A B AB Probability: 0.3712 0.2288 0.3226 0.0774 A random sample of 10 is considered from Indian population. What is the probability that there will be 4 Os, 3 As, 2 Bs and 1 AB blood types, respectively?

About this paper

Why solve Mathematics-III (Differential Calculus) PYQs?

Frequently asked questions

What is the subject code for Mathematics-III (Differential Calculus)?

Which exam is this Mathematics-III (Differential Calculus) question paper from?

Which branches is this Mathematics-III (Differential Calculus) paper for?

Where can I find more BSC-301 question papers?

Are there solutions for this paper?

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