For the given values $15,23,28,36,41,46$, the 3-yearly moving averages are:
- A$22,29,35,41$
- B$24,29,35,41$
- C$24,28,35,41$
- D$22,28,35,41$
Question types
Model Paper 6 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 6 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the supply function for a commodity is $p =\sqrt{9+x}$ and the market price $p _0=4$, then producer's surplus is
- A15
- B3
- C$\frac{10}{3}$
- D10
What is the standard deviation of a sampling distribution called?
- ASimple error
- BSampling error
- CSample error
- DStandard error
If x ≤ 8, then
- A-x ≤ -8
- B-x > -8
- C-x < -8
- D-x ≥ -8
The graph of the inequality 2x + 3y > 6 is
- Ahalf plane that contains the origin
- Bhalf plane that neither contains origin nor the points of the line 2x + 3y = 6
- Cwhole XOY-plane excluding the points on the line 2x + 3y = 6
- Dentire XOY-plane.
Let $a, b \in R$ be such that the function $f$ given by $f(x)=\log |x|+b x^2+a x, x \neq 0$ has extreme values: at $x=-1$ and $x =2$.
Assertion (A): f has local maximum at $x=-1$ and at $x=2$
Reason (R): $a =\frac{1}{2}$ and $b =-\frac{1}{4}$
Assertion (A): f has local maximum at $x=-1$ and at $x=2$
Reason (R): $a =\frac{1}{2}$ and $b =-\frac{1}{4}$
- 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.
- DA is false but R is true.
Assertion (A): If $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4\end{array}\right]$, then $|3 A|=27|A|$
Reason (R): If $A$ is a square matrix of order $n$, then $|k A|=k^n|A|$.
Reason (R): If $A$ is a square matrix of order $n$, then $|k A|=k^n|A|$.
- 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.
- DA is false but R is true.
Prove that: 3500 ≡ 2 (mod 7)
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 (1.00625)240 = 4.4608)
How much money is needed to endure a series of lectures costing ₹2,500 at the beginning of each year indefinitely, if money is worth 5% compounded annually?
By using properties of definite integral, evaluate: $\int_{-1}^1 e^{|x|} d x$
View full solution →Find the present value of a sequence of payments of ₹8,000 made at the end of each 6 months and continuing forever if money is worth 4% compounded semi-annually.
Consider the following hypothesis test:
$H _0: \mu=15$
$
H_{a}: \mu \neq 15
$
A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3.
i. Compute the value of the test statistic.
ii. What is the p-value?
iii. At $\alpha=0.05$, what is your conclusion?
iv. What is the rejection rule using the critical value? What is your conclusion?
View full solution →$H _0: \mu=15$
$
H_{a}: \mu \neq 15
$
A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3.
i. Compute the value of the test statistic.
ii. What is the p-value?
iii. At $\alpha=0.05$, what is your conclusion?
iv. What is the rejection rule using the critical value? What is your conclusion?
Fit the straight line trend to the following series data:
Also, tabulate the trend values.
| Year | 2017 | 2018 | 2019 | 2020 | 2021 |
| Sales of sugar (in thousand kg) | 80 | 90 | 92 | 83 | 94 |
Two biased dice are thrown together. For the first die $P(6)=\frac{1}{2}$, other scores being equally 2 likely while for the second die, $P (1)=\frac{2}{5}$ and other scores are equally likely. Find the probability distribution of 'the number of ones seen'.
View full solution →In a precision bombing attack, there is a 50% chance that any one bomb will strike the target. Two direct hits are required to destroy the target completely. How many bombs must be dropped to give a 99% chance or better, of completely destroying the target?
The marginal cost of production of x units of a commodity is 30 + 2x. It is known that fixed costs are ₹ 120. Find
i. the total cost of producing 100 units
ii. the cost of increasing output from 100 to 200 units.
i. the total cost of producing 100 units
ii. the cost of increasing output from 100 to 200 units.
Anil plans to send his daughter for higher studies abroad after 10 years. He expects the cost of the studies to be ₹ 2,00,000. How much must he set aside at the end of each quarter for 10 years to accumulate this amount, if money is worth 6% compounded quarterly? [Given: (1.015)40 = 1.8140]
A die is thrown 5 times. Find the probability that an odd number will turn up
i. exactly 3 times
ii. atleast 4 times
iii. maximum 3 times
i. exactly 3 times
ii. atleast 4 times
iii. maximum 3 times
The probability that Rohit will hit a shooting target is $\frac{2}{3}$. While preparing for an international shooting competition. Rohit aims to achieve the probability of hitting the target atleast once to be 0.99 . What is the minimum number of chances must he shoot to attain this probability?
View full solution →In a 1000-metre race, A, B and C get Gold, Silver and Bronze medals respectively. If A beats B by 100 metres and B beats C by 100 metres, then by how many metres does A beat C?
Find $A^{-1}$, where $A=\left[\begin{array}{rrr}1 & 2 & -3 \\ 2 & 3 & 2 \\ 3 & -3 & -4\end{array}\right]$. Hence solve the system of equations: $x+2 y-3 z=-4,2 x+3 y+2 z=2,3 x-$ $3 y-4 z=11$
View full solution →A bakery in an establishment produces and sells flour-based food baked in an oven such as bread, cakes, pastries, etc. Ujjwal cake store makes two types of cake. First kind of cake requires 200g of flour and 25 g of fat and 2nd type of cake requires 100g of flour and 50 g of fat.
Based on above information answer the following questions.
i. If the bakery make x cakes of first type and y cakes of 2nd type and it can use maximum 5 kg flour, then write the constraint.
ii. If Bakery can use maximum 1 kg fat, then write the constraint.
iii. Represent total number of cakes made by bakery which is represented by Z.
iv. What is the maximum number of total cakes which can be made by bakery, assuming that there is no shortage of ingredients used in making the cakes?
v. What are number of first and second type of cakes?
Based on above information answer the following questions.
i. If the bakery make x cakes of first type and y cakes of 2nd type and it can use maximum 5 kg flour, then write the constraint.
ii. If Bakery can use maximum 1 kg fat, then write the constraint.
iii. Represent total number of cakes made by bakery which is represented by Z.
iv. What is the maximum number of total cakes which can be made by bakery, assuming that there is no shortage of ingredients used in making the cakes?
v. What are number of first and second type of cakes?
Read the text carefully and answer the questions:
EMI or equated monthly installment, as the name suggests, is one part of the equally divided monthly outgoes to clear off an outstanding loan within a stipulated time frame. The EMI is dependent on multiple factors, such as:
• Principal borrowed
• Rate of interest
• Tenure of the loan
• Monthly/annual resting period
For a fixed interest rate loan, the EMI remains fixed for the entire tenure of the loan, provided there is no default or part-payment in between. The EMI is used to pay off both the principal and interest components of an outstanding loan.
Example:
A person amortizes a loan of ₹1500000 for renovation of his house by 8 years mortgage at the rate of 12% p.a. compounded monthly.
$\left(\right.$ Given $\left.(1.01)^{96}=2.5993,(1.01)^{57}=1.7633\right)$
(a) Find the equated monthly installment.
(b) Find the principal outstanding at the beginning of 40th month.
(c) Find the interest paid in 40th payment.
OR
Find the principal contained in 40th payment.
View full solution →EMI or equated monthly installment, as the name suggests, is one part of the equally divided monthly outgoes to clear off an outstanding loan within a stipulated time frame. The EMI is dependent on multiple factors, such as:
• Principal borrowed
• Rate of interest
• Tenure of the loan
• Monthly/annual resting period
For a fixed interest rate loan, the EMI remains fixed for the entire tenure of the loan, provided there is no default or part-payment in between. The EMI is used to pay off both the principal and interest components of an outstanding loan.
Example:
A person amortizes a loan of ₹1500000 for renovation of his house by 8 years mortgage at the rate of 12% p.a. compounded monthly.
$\left(\right.$ Given $\left.(1.01)^{96}=2.5993,(1.01)^{57}=1.7633\right)$
(a) Find the equated monthly installment.
(b) Find the principal outstanding at the beginning of 40th month.
(c) Find the interest paid in 40th payment.
OR
Find the principal contained in 40th payment.
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