Which of the following is not an example of a time series model?
- ACross-sectional
- BMoving average
- CExponential smoothing
- ✓Naive approach
Answer: D.
View full solution →Question types
Model Paper 8 question types
45 questions across 6 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
45
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)
4 Q→Sample Questions
Model Paper 8 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\int \frac{x^3}{x+1} d x$ is equal to
- A$x-\frac{x^2}{2}-\frac{x^3}{3}-\log |1+ x |+ C$
- B$x+\frac{x^2}{2}-\frac{x^3}{3}-\log |1- x |+ C$
- ✓$x-\frac{x^2}{2}+\frac{x^3}{3}-\log |1+ x |+ C$
- D$x+\frac{x^2}{2}+\frac{x^3}{3}-\log |1- x |+ C$
Answer: C.
View full solution →Inferential statistics is a process that involves all of the following except
- Atest a hypothesis
- Banalyse relationships
- ✓estimating a statistic
- Destimating a parameter
Answer: C.
View full solution →If x is a negative integer, then the solution set of -12x > 30 is
- A{-2, -1}
- B{-2, -1, 0, 1, 2 ...}
- C{..., -5, -4, -3, -2}
- ✓{..., -5, -4, -3}
Answer: D.
View full solution →In an L.P.P. if the objective function Z = ax + by has same maximum value on two corner points of the feasible region, then the number of points at which the maximum value of Z occurs is
- A$0$
- Bfinite
- ✓infinite
- D2
Answer: C.
View full solution →The function $f$ be given by $f(x)=2 x^3-6 x^2+6 x+5$.
Assertion (A): x = 1 is not a point of local maxima.
Reason (R): x = 1 is not a point of local minima.
Assertion (A): x = 1 is not a point of local maxima.
Reason (R): x = 1 is not a point of local minima.
- ABoth A and R are true and R is the correct explanation of A.
- ✓Both A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: B.
View full solution →Assertion (A): If A, B and C are the matrices of order 3 x 1, 2 x m and 3 x n respectively, then (CA + BA) is defined, if n = 3 and m = 3.
Reason (R): Multiplication of two matrices A and B i.e. AB is defined if number of columns of A = number of rows of B.
Reason (R): Multiplication of two matrices A and B i.e. AB is defined if number of columns of A = number of rows of 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.
- CA is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →How many kg of sugar costing ₹ 45 per kg must be mixed with 30 kg sugar costing ₹ 35 per kg so that there may be a gain of 12% by selling the mixture at ₹ 47.04 per kg?
A machine being used by a company is estimated to have a life of 15 years. At that time a new machine would cost ₹ $75000$ and the scrap of the old machine would yield ₹ $9600$ only. A sinking fund is created for replacing the machine at the end of its life. What sum should be retained by the company at the end of every year to accumulate at $6\%$ per annum?
View full solution →Amrita bought a car worth ₹ $12,50,000$ and makes a down payment of ₹ $3,00,000.$ The balance amount is to be paid in 4 years by equal monthly instalments at an interest rate of $15\%$ p.a. Find the EMI that Amrita has to pay for the car. $\left\{\right.$Given $\left.\left.(1.0125)^{-48}=0.5508565\right)\right\}$
View full solution →Evaluate the definite integral:
$\int_2^e\left(\frac{1}{\log x}-\frac{1}{(\log x)^2}\right) d x$
View full solution →$\int_2^e\left(\frac{1}{\log x}-\frac{1}{(\log x)^2}\right) d x$
Find the effective rate of return equivalent to a nominal rate of $6\%$ per annum compounded
i. quarterly
ii. continuously.$\left(\right.$Given $(1.015)^4=1.06136$ and $\left.e ^{0.06}=1.06183\right)$
View full solution →i. quarterly
ii. continuously.$\left(\right.$Given $(1.015)^4=1.06136$ and $\left.e ^{0.06}=1.06183\right)$
The I.Q.'s (intelligence quotients) of 16 students from one area of a city showed a mean of 107 with a standard deviation of 10 while the I.Q.'s of 14 students from another area of the city showed a mean of 112 with a standard deviation of 8. Is there a significant difference between the I.Q.’s of the two groups at
i. $1\%$
ii. $5\%$ level of significance?
View full solution →i. $1\%$
ii. $5\%$ level of significance?
The average number, in lakhs, of working days lost in strikes during each year of the period 2001-2010 was
Calculate the three-yearly moving averages and draw the moving averages graph.
| 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
| 1.5 | 1.8 | 1.9 | 2.2 | 2.6 | 3.7 | 2.2 | 6.4 | 3.6 | 5.4 |
If X is a normal variate with mean 30 and S.D. 5. Find:
i. $P (26 \leq X \leq 40)$
ii. $P(X \geq 45)$
iii. $P (| X -30|>5)$
View full solution →i. $P (26 \leq X \leq 40)$
ii. $P(X \geq 45)$
iii. $P (| X -30|>5)$
In a normal distribution $31\%$ of the articles are under 45 and $8\%$ are over $64.$ Calculate the mean and standard deviation of the distribution.
View full solution →Suppose that the demand function for a certain commodity is $p=20-4 x^2$ and the marginal cost is $\text{MC} = 2x + 6,$ where x is the number of units produced. Find the consumer’s surplus at the sales level $x _0$ where profit is maximized.
View full solution →How much amount has to be deposited at the end of each year for 4 years at 6% p.a compounded annually so as to get a sum of ₹ 80,000. [Use $\left.(1.06)^4=1.262\right]$
View full solution →Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Find the probability distribution of the number of aces drawn. Also find the mean and standard deviation of the distribution.
A die is tossed twice. Success is defined as getting an odd number on a random toss. Find the mean and variance of the number of successes.
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.
Following equations are consistent? If consistent, solve the:
$x + y - 2z = 4$
$x - 2y + z = -2$
$5x - 5y + z = -2$
View full solution →$x + y - 2z = 4$
$x - 2y + z = -2$
$5x - 5y + z = -2$
A company started airlines business and for running business it bought aeroplanes. Now an aeroplane can carry maximum of 200 passengers. A profit of ₹ 400 is made on each first-class ticket and a profit of ₹300 is made on each second class ticket. The airline reserves at least 20 seats for first class. However, at least four times as many passengers prefer to travel by second class than by first class. Company wants to make maximum profit by selling tickets of first-class (x) and second class (y).
i. To get maximum profit how many first-class tickets should be sold?
ii. What is the difference between the maximum profit and minimum profit value?
iii. Write any two corner points of feasible region.
OR
What will be the minimum profit value?
i. To get maximum profit how many first-class tickets should be sold?
ii. What is the difference between the maximum profit and minimum profit value?
iii. Write any two corner points of feasible region.
OR
What will be the minimum profit value?
A factory manufactures tennis rackets and cricket bats. A tennis racket takes $1 \frac{1}{2}$ hours of machine time and 3 hours of craftsmanship in its making; while a cricket bat takes 3 hours of machine time and 1 hour of craftsmanship. In a day, the factory has availability of not more than 42 hours of machine time and 24 hours of craftsmanship. Profit on a racket and on a bat are ₹ 20 and ₹ 10 respectively.
i. If x and y are the numbers of bats and rackets manufactured by the factory, then write the expression of total profit.
ii. Write the constraint that relates the number of craftsmanship hours.
iii. Determine the maximum profit (in ₹) earned by the factory.
OR
How many bats and rackets respectively, are to be manufactured to earn maximum profit?
View full solution →i. If x and y are the numbers of bats and rackets manufactured by the factory, then write the expression of total profit.
ii. Write the constraint that relates the number of craftsmanship hours.
iii. Determine the maximum profit (in ₹) earned by the factory.
OR
How many bats and rackets respectively, are to be manufactured to earn maximum profit?
Flexible payment arrangements, in which the borrower might pay higher sums of his or her choosing, are not the same as EMIs. Borrowers on EMI programmes are usually only allowed to make one set payment per month. Borrowers profit from an EMI since they know exactly how much money they will have to pay towards their loan each month, making personal financial planning easier. Lenders benefit from the loan interest, as it provides a consistent and predictable stream of income.
Example:
A loan of ₹400000 at the interest rate of 6.75% p.a. compounded monthly is to be amortized by equal payments at the end of each month for 10 years.
$\left(\right.$Given $\left.(1.005625)^{120}=1.9603,(1.005625)^{60}-1.4001\right)$
(a) Find the size of each monthly payment.
(b) Find the principal outstanding at the beginning of 61st month.
(c) Find the interest paid in 61st payment.
OR
Find the principal contained in 61st payment.
View full solution →Example:
A loan of ₹400000 at the interest rate of 6.75% p.a. compounded monthly is to be amortized by equal payments at the end of each month for 10 years.
$\left(\right.$Given $\left.(1.005625)^{120}=1.9603,(1.005625)^{60}-1.4001\right)$
(a) Find the size of each monthly payment.
(b) Find the principal outstanding at the beginning of 61st month.
(c) Find the interest paid in 61st payment.
OR
Find the principal contained in 61st payment.
The sum of the length of hypotenuse and a side of a right-angled triangle is given by AC + BC = 10
(a) Base BC =?
(b) If S be the area of the triangle, then find the value of $\frac{d S}{d c}$ ?
(c) What is the values of c when $\frac{d S}{d c}$=0?
Find the value of $\frac{d^2 S}{d c^2}$ at $C =\frac{10 \sqrt{3}}{3}$ ?
View full solution →(a) Base BC =?
(b) If S be the area of the triangle, then find the value of $\frac{d S}{d c}$ ?
(c) What is the values of c when $\frac{d S}{d c}$=0?
Find the value of $\frac{d^2 S}{d c^2}$ at $C =\frac{10 \sqrt{3}}{3}$ ?
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