An orderly set of data arranged in accordance with their time of occurrence is called:
- ✓Time Series
- BHarmonic Series
- CGeometric Series
- DArithmetic Series
Answer: A.
View full solution →Question types
Model Paper 10 question types
48 questions across 6 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
48
Questions
6
Question groups
5
Question types
01
MCQ
18 Q→02Assertion (A) & Reason (B) MCQ
2 Q→032 Marks Questions
7 Q→043 Marks Question
8 Q→055 Marks Questions
6 Q→06Case study (4 Marks)
7 Q→Sample Questions
Model Paper 10 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\int x^3 \log x d x$ is equal to
- A$\frac{x^4}{8}\left(\log x-\frac{4}{x^2}\right)+C$
- ✓$\frac{x^4}{16}(4 \log x-1)+C$
- C$\frac{x^4}{16}(4 \log x+1)+C$
- D$\frac{x^4 \log x}{4}+C$
Answer: B.
View full solution →In a school, a random sample of 145 students is taken to check whether a student's average calory intake is 1500 or not. The collected data of average calories intake of sample students is presented in a frequency distribution which is called a
- ✓Sampling distribution
- BParameter
- CPopulation sampling
- DStatistics
Answer: A.
View full solution →If $\frac{1}{2}\left(\frac{3}{5} x+4\right) \geq \frac{1}{3}(x-6), x \in R$, then
- A$x \in(-\infty, 120)$
- ✓$x \in(-\infty, 120]$
- C$x \in[120, \infty)$
- D$x \in(120, \infty)$
Answer: B.
View full solution →The optimal value of the objective function is attained at the points
- ✓given by corner points of the feasible region
- Bgiven by intersection of inequations with xaxis only
- Cgiven by intersection of inequations with yaxis only
- Dgiven by intersection of inequations with the axes only
Answer: A.
View full solution →Assertion (A): If the demand function of a product is $p=200-\frac{x^2}{3}$, then the marginal revenue (MR) of selling 10 units is ₹ 120.
Reason (R): $MR =\frac{d}{d x}( R )$
Reason (R): $MR =\frac{d}{d x}( R )$
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →Let A, B and C are three matrices of same order. Now, consider the following statements
Assertion (A): If A = B, then AC = BC.
Reason (R): If AC = BC, then A = B.
Assertion (A): If A = B, then AC = BC.
Reason (R): If AC = BC, then A = B.
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- ✓A is true but R is false.
- DA is false but R is true.
Answer: C.
View full solution →In what ratio water must be added in milk costing ₹ 60 per litre, so that resulting mixture would be worth ₹ 50 per litre?
Find the effective rate of return which is equivalent to a stated rate of 8% compounded quarterly.[Use $(1.02)^4=1.0824$
View full solution →Mr. Bharti wishes to purchase a flat for ₹ 6000000 with a down payment of ₹ 1000000 and balance in equal monthly payments for 20 years. If bank charges 7.5 % p.a. compounded monthly, calculate the EMI. (Given$\left.(1.00625)^{240}=4.4608\right)$
View full solution →Evaluate the definite integral:
$\int_1^3 \frac{\sqrt[3]{x}}{\sqrt[3]{x}+\sqrt[3]{4-x}} d x$
View full solution →$\int_1^3 \frac{\sqrt[3]{x}}{\sqrt[3]{x}+\sqrt[3]{4-x}} d x$
If money is worth 5% compare the present value of a perpetuity of ₹2,000 payable at the end of each year with that of an ordinary annuity of ₹2,000 per year for 100 years. $\left(\right.$ Given $\left.(1.05)^{-100}=0.0076\right)$
View full solution →Ten individuals are chosen at random from the population and their heights are found to be in inches 63, 63, 64, 65, 66, 69, 69, 70, 70, 71. Discuss the freedom value of Student's -t and 5% level of significance is 2.62.
Consider the following data:
Calculate a suitable moving average and show on a graph against the original data.
| Year: | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 |
| Production: | 137 | 140 | 134 | 137 | 151 | 121 | 124 | 159 | 157 | 169 | 172 | 150 |
An urn contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one with replacement, what is the
probability that
i. all are white?
ii. only 3 are white?
iii. none is white?
iv. at least three are white?
probability that
i. all are white?
ii. only 3 are white?
iii. none is white?
iv. at least three are white?
Four bad eggs are mixed with 10 good ones. If three eggs are drawn one by one with replacement, then find the probability distribution of the number of bad eggs drawn.
A company has approximated the marginal cost and marginal revenue functions for one of its products by MC =$81-16 x+x^2$ and MR = $20 x-2 x^2$ respectively. Determine the profit-maximizing output and the total profit at the optimal output, assuming fixed cost as zero.
View full solution →A firm bought a machinery for ₹ 7,40,000 on 1st April, 2020 and ₹ 60,000 is spent on its installation. Its useful life is estimated to be of 5 years. Its scrap value at the end of 5 years is estimated to be ₹ 40,000. Find the amount of annual depreciation and the rate of depreciation.
The diameter of shafts produced in a factory confirms to normal distribution. 31% of the shafts have a diameter less than 45 mm and 8% have more than 64 mm. Find the mean and standard deviation of the diameter of shafts.
If X denotes the number of heads in a single toss of 4 fair coins, then find
i. $P(X=3)$
ii. $P ( X <2)$
iii. $P ( X \leq 2)$
iv. $P (1< X \leq 3)$.
View full solution →i. $P(X=3)$
ii. $P ( X <2)$
iii. $P ( X \leq 2)$
iv. $P (1< X \leq 3)$.
A person can row a boat at 5 km/h in still water. It takes him thrice as long to row upstream as to row downstream. Find the rate at which the stream is flowing.
The sum of three numbers is 6. If we multiply the third number by 2 and add the first number to the result, we get 7. By adding second and third numbers to three times the first number, we get 12. Using matrices find the numbers.
What is the maximum profit earned by the firm?
Read the following text carefully and answer the questions that follow:
A small firm manufacturers gold rings and chains. The total number of rings and chains manufactured per day is almost 24. It takes 1 hour to make ring and 30 minutes to make a chain. The maximum number of hours available per day is 16. If the profit on a ring is ₹ 300 and that on a chain is ₹ 190. Firm is concerned about earning maximum profit on the number of rings (x) and chains (y) that have to be manufactured per day.
i. what is the expression for objective function?
ii. For maximum profit, firm has to make,what should be the number of rings and chains?
iii. What are the Corner points of the feasible region?
A small firm manufacturers gold rings and chains. The total number of rings and chains manufactured per day is almost 24. It takes 1 hour to make ring and 30 minutes to make a chain. The maximum number of hours available per day is 16. If the profit on a ring is ₹ 300 and that on a chain is ₹ 190. Firm is concerned about earning maximum profit on the number of rings (x) and chains (y) that have to be manufactured per day.
i. what is the expression for objective function?
ii. For maximum profit, firm has to make,what should be the number of rings and chains?
iii. What are the Corner points of the feasible region?
Aeroplane is an important invention for three reasons. It shortens travel time, is more comfortable and facilitates the transport of heavy cargo.
An aeroplane can carry a maximum of 200 passengers.
A profit of ₹400 is made on each executive class ticket and a profit of ₹300 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However at least 4 times as many passenger prefer to travel by economy class than by executive class.
Based on above information answer the following questions.
i. If x tickets of executive class and y tickets of economy class be sold, then write the constraint.
ii. Write the correct pair of constraints.
iii. If profit earned by airlines is represented by Z, then write the constraint.
iv. Airlines are interested to maximise the profit. For this what are the value of x and y i.e.r number of executive class ticket and economy class ticket to be sold?
v. What is the maximum profit earned by airlines?
An aeroplane can carry a maximum of 200 passengers.
A profit of ₹400 is made on each executive class ticket and a profit of ₹300 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However at least 4 times as many passenger prefer to travel by economy class than by executive class.
Based on above information answer the following questions.
i. If x tickets of executive class and y tickets of economy class be sold, then write the constraint.
ii. Write the correct pair of constraints.
iii. If profit earned by airlines is represented by Z, then write the constraint.
iv. Airlines are interested to maximise the profit. For this what are the value of x and y i.e.r number of executive class ticket and economy class ticket to be sold?
v. What is the maximum profit earned by airlines?
What amount is received at the end of every 6 months forever, if ₹ 72000 kept in a bank earns 8% per annum compounded half yearly?
Read the text carefully and answer the questions:
Understanding Perpetuity
An annuity is a stream of cash flows. A perpetuity is a type of annuity that lasts forever, into perpetuity. The stream of cash flows continues for an infinite amount of time. In finance, a person uses the perpetuity calculation in valuation methodologies to find the present value of a company's cash flows when discounted back at a certain rate.
An example of a financial instrument with perpetual cash flows was the British-issued bonds known as consols, which the Bank of England phased out in 2015. By purchasing a consol from the British government, the bondholder was entitled to receive annual interest payments forever.
Perpetuity Present Value Formula
The formula to calculate the present value of perpetuity or security with perpetual cash flows is as follows:
$PV =\frac{C}{(1+r)^1}+\frac{C}{(1+r)^2}+\frac{C}{(1+r)^3} \cdots=\frac{C}{r}$
where:
PV present value
C = cash flow
r = discount rate
(a) Find the present value of a perpetuity of ₹ 900 payable at the end of each year, if money is worth 5% per annum.
(b) Find the present value of a perpetuity of ₹ 500 payable at the end of each quarter, if money is worth 8% per annum.
(c) Find the present value of a perpetuity of ₹ 300 payable at the beginning of every 6 months, if money is worth 6% per annum.
View full solution →Understanding Perpetuity
An annuity is a stream of cash flows. A perpetuity is a type of annuity that lasts forever, into perpetuity. The stream of cash flows continues for an infinite amount of time. In finance, a person uses the perpetuity calculation in valuation methodologies to find the present value of a company's cash flows when discounted back at a certain rate.
An example of a financial instrument with perpetual cash flows was the British-issued bonds known as consols, which the Bank of England phased out in 2015. By purchasing a consol from the British government, the bondholder was entitled to receive annual interest payments forever.
Perpetuity Present Value Formula
The formula to calculate the present value of perpetuity or security with perpetual cash flows is as follows:
$PV =\frac{C}{(1+r)^1}+\frac{C}{(1+r)^2}+\frac{C}{(1+r)^3} \cdots=\frac{C}{r}$
where:
PV present value
C = cash flow
r = discount rate
(a) Find the present value of a perpetuity of ₹ 900 payable at the end of each year, if money is worth 5% per annum.
(b) Find the present value of a perpetuity of ₹ 500 payable at the end of each quarter, if money is worth 8% per annum.
(c) Find the present value of a perpetuity of ₹ 300 payable at the beginning of every 6 months, if money is worth 6% per annum.
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