Class 12 CBSE Specimen Paper 2022 - Term 2
Class 12 CBSE Applied Maths aims to develop an understanding of basic
mathematical and statistical tools and their
applications in the field of commerce (business/ finance/economics) and social
sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and
Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index
Numbers and Time-based data , Financial Mathematics , Linear Programming.
SECTION β A
Q1. The marginal revenue function for a commodity is given by ππ
= 9 + 2π₯ β
6π₯2
Find the demand function.
OR
The marginal cost of producing π₯ pairs of tennis shoes is given by
MC=50+ 300/x+1
If the fixed cost is βΉ2000, find the total cost function
Solution :
Q2. Find the present value of perpetuity of βΉ600 at end of each quarter if money is worth 8% compounded quarterly
Solution :
Q3. What effective rate is equivalent to a nominal rate of 8% per annum compounded
quarterly?
OR
Find the present value of an annuity of βΉ1000 payable at the end of each year
for 5 years if money is worth 6%compounded annually.
[Use (1.06)-5 = 0.7473]
Solution :
Q4. A sampling distribution of the sample means π is formed from a population with mean weight π = 60ππ and standard deviation π = 9ππ. What is the expected value and standard deviation of π , if sample size is 36?
Solution :
Q5. Find the trend values using 3 yearly moving average for the loans sanctioned to farmers by a particular branch of a bank in a village
Solution :
Q6. The feasible region of the LPP
Min π = 3π₯ + 2π¦
subject to constraints
2π₯ + π¦ β₯ 6, π₯ β π¦ β₯ 0, π₯ β₯ 0, π¦ β₯ 0 is given below:
Determine the optimal solution. Justify your answer
Solution :
SECTION β B
Q7. The supply function for a commodity is given by π = π₯2 + 4π₯ + 3, where π₯ is the quantity supplied at the price π. Find the producers surplus when the price of the commodity is βΉ48
Solution :
Q8. The following table shows the quarterly sales (in βΉcrore) of a real estate
company.
Compute the trend by quarterly moving averages.
OR
Fit a straight line trend by the method of least squares and estimate the trend
for the year 2023.
Solution :
Q9. A machine produces washers of thickness 0.50 mm. To determine whether the
machine is in proper working order, a sample of 10 washers is chosen for which
the mean thickness is 0.53mm and the standard deviation is 0.03 mm. Test the
hypothesis at 5% level of significance that the machine is working in proper order.
[πΊππ£ππ ππππ‘ππππ π£πππ’π,π‘0.025 = 2.262 ππ‘ π(π. π)=9 ]
Solution :
Q10. A person invested βΉ15000 in a mutual fund and the value of investment at the
time of redemption was βΉ25000. If CAGR for this investment is 8.88%, Calculate
the time period for which the amount was invested?
[πΊππ£ππ log(1.667) = 0.2219 & log(1.089) = 0.037]
Solution :
SECTION β C
Q11. S & D chemicals produces two products, an alkaline solution and a base oil
that
are sold as raw material to companies manufacturing soaps and detergents. On
the basis of current inventory levels and estimated demand for the coming month,
S & Dβs management has decided that combined production of alkaline solution
and base oil must be at least 3500 gallons. S & D chemicals are also committed
to supply 1250 gallons of alkaline solution to one of its major customer. The
alkaline solution and base oil requires respectively 2 hours and 1 hour of
processing time per gallon. The total processing time available for the coming
month is 6000 hours. The production cost is βΉ200 per gallon for the alkaline
solution and βΉ300 per gallon for base oil.
Formulate the above as a L.P.P and solve it by graphical method to help S & D
chemicals determine the minimum production cost.
Solution :
Q12. A machine costing βΉ50,000 is to be replaced at the end of 10 years, when it
will
have a salvage value of βΉ5000. In order to provide money at that time for a
machine costing the same amount, a sinking fund is set up. If equal payments
are placed in the fund at the end of each quarter and the fund earns 8%
compounded quarterly, then what should each payment be?
[πΊππ£ππ (1.02)40 = 2.208 ]
Solution :
Q13. TA couple wishes to purchase a house for βΉ15,00,000 with a down payment of
βΉ4,00,000. If they can amortize the balance at an interest rate 9% per annum
compounded monthly for 10 years, find the monthly installment (EMI). Also find
the total interest paid. [πΊππ£ππ (1.0075)-120 = 0.4079 ]
OR
A βΉ2000, 8% bond is redeemable at the end of 10 years at βΉ105. Find the
purchase price to yield 10% effective rate. [πΊππ£ππ(1.1)-10 = 0.3855]
Solution :
Q14. CASE STUDY
General anesthesia is used for major operations to cure the patients and conduct
pain free surgeries. Propofol is a commonly used anesthetic injected for major
operations such as knee replacement or open heart surgery. It also acts as a
sedative and an analgesic.
A patient is rushed to operation theatre for a 2-hour cardiac surgery. A person is
anesthetized when its blood stream contains at least 3 mg of propofol per kg of
body weight. The rate of change of propofol(π₯), in the body is proportional to the
quantity of propofol present at that time. Based on the above information. Answer
the following questions:
a. Show that propofol given intravenously is eliminated exponentially from
the patientsβ blood stream
b. What dose of propofol should be injected to induce unconsciousness in a
50 Kg adult for a two hours operation?
(Given (2)1/5 = 1.1487 & assume half-life of propofol = 5 hours )
Solution :
