Sample QuestionsModel Paper 3 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For predicting the straight line trend in the sales of scooters (in thousands) on the basis of 6 consecutive years data, the company makes use of 4-year moving averages method. If the sales of scooters for respective years are $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}$, e and f respectively, then which of the following average will not be computed?
- A
$\frac{a+c+d+e}{4}$
- B
$\frac{c+d+e+f}{4}$
- C
$\frac{b+c+d+e}{4}$
- D
$\frac{a+b+c+d}{4}$
View full solution →$\int \mathrm{e}^{\mathrm{x}}\left\{\mathrm{f}(\mathrm{x})+\mathrm{f}^{\prime}(\mathrm{x})\right\} \mathrm{dx}=$
- A
$2 e^{x} f(x)+C$
- B
$e^{x}-f(x)+C$
- C
$e^{x} f(x)+C$
- D
$e^{x}+f(x)+C$
View full solution →For testing the significance of difference between the means of two independent samples, the degree of freedom (v) is taken as:
- A
$n_{1}-n_{2}+2$
- B
$n_{1}-n_{2}-2$
- C
$n_{1}+n_{2}-1$
- D
$n_{1}+n_{2}-2$
View full solution →The corner points of the feasible region determined by the following system of linear inequalities:
$2 \mathrm{x}+\mathrm{y} \leq 10, \mathrm{x}+3 \mathrm{y} \leq 15, \mathrm{x}, \mathrm{y} \geq 0$ are $(0,0),(5,0),(3,4)$ and $(0,5)$.
Let $\mathrm{Z}=\mathrm{px}+\mathrm{qy}$, where $\mathrm{p}, \mathrm{q}>0$.
Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both $(3,4)$ and $(0,5)$ is
- A
$p=3 q$
- B
$q=3 p$
- C
$p=q$
- D
$p=2 q$
View full solution →If the objective function for an L.P.P. is $Z=3 x-4 y$ and the comer points for the bounded feasible region are (0,$0),(5,0),(6,5),(6,8),(4,10)$ and $(0,8)$, then the maximum of $Z$ occurs at
- A
$(5,0)$
- B
$(4,10)$
- C
$(6,5)$
- D
$(6,8)$
View full solution →Assertion (A): The rate of change of area of a circle with respect to its radius r when $\mathrm{r}=6 \mathrm{~cm}$ is $12 \pi \mathrm{~cm}^{2} / \mathrm{cm}$.
Reason (R): Rate of change of area of a circle with respect to its radius r is $\frac{d A}{d r}$, where A is the area of the circle.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of A.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of A.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
View full solution →Assertion (A): If $\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right]$, then $\mathrm{A}+\mathrm{B}=\left[\begin{array}{ll}3 & 7 \\ 1 & 7\end{array}\right]$.
Reason (R): Two different matrices can be added only if they are of same order.
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of A.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of A.
- C
$A$ is true but $R$ is false.
- D
A is false but $R$ is true.
View full solution →Evaluate: $(9+23) \bmod 12$
View full solution →If the cash equivalent of the perpetuity of ₹$ 1,200$ payable at the end of each quarter is ₹$ 96,000$, find the rate of interest convertible quarterly.
View full solution →An asset costs ₹$ 4,50,000$ with an estimated useful life of 5 years and a scrap value of ₹$ 1,00,000$. Using linear depreciation method, find the annual depreciation of the asset and construct a yearly depreciation schedule.
View full solution →Evaluate: $\int_{1}^{2}\left(4 x^{3}-5 x^{2}+6 x+9\right) d x$
View full solution →The effective annual rate of interest corresponding to normal rate of $6 \%$ p.a. payable half yearly is ____________.
View full solution →Ten cartons are taken at random from an automatic filling machine. The mean net weight of the cartons is 11.8 kg and the standard deviation 0.15 kg. Does the sample mean differ significantly from the intended weight of 12 kg? [Given that for d.f. $=9, \mathrm{t}_{0.05}=2.26$]
View full solution →From the following time series obtain trent value by 3 yearly moving averages.
| Year | Sales ( in ₹ 000) | Year | Sales ( in ₹ 000) |
| 2008 | 8 | 2013 | 12 |
| 2009 | 12 | 2014 | 16 |
| 2010 | 10 | 2015 | 17 |
| 2011 | 13 | 2016 | 14 |
| 2012 | 15 | 2017 | 17 |
Let X denote the no of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form where K is some unknown constant
$P(\chi=x)= \begin{cases}0.1, & \text { if } x=0 \\ k x, & \text { if } x=1, \text { or } 2 \\ K(5-x), & \text { if } x=3 \text { or } 4 \\ 0, & \text { otherwise }\end{cases}$
i. Find the value of $K$.
ii. What is the probability that you study at least two hours? Exactly two hours. At most two hours.
View full solution →A bag contains 8 red and 5 white balls. Two successive draws of all 3 balls are made at random from the bag without replacements. Find the probability that the first draw yields 3 white balls and second draw yields 3 red balls.
If the marginal revenue function for output x is given by $\mathrm{MR}=\frac{6}{(x+2)^{2}}+5$, find the total revenue function and the demand function.
View full solution →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. Find
i. the equated monthly installment
ii. the principal outstanding at the beginning of 40th month.
iii. the interest paid in $40^{\text {th }}$ payment.
$
\text { [Given } \left.(1.01)^{96}=2.5993,(1.01)^{57}=1.7633\right]
$
View full solution →Let X denote the number of hours a person watches television during a randomly selected day. The probability that X can take the values $\mathrm{x}_{\mathrm{i}}$ has the following form, where k is some unknown constant.
$\mathrm{P}\left(\mathrm{X}=\mathrm{x}_{\mathrm{i}}\right)= \begin{cases}0.2, & \text { if } x_{i}=0 \\ k x_{i}, & \text { if } x_{i}=1 \text { or } 2 \\ k\left(5-x_{i}\right), & \text { if } x_{i}=3 \\ 0, & \text { otherwise }\end{cases}$
a. Find the value of $k$.
b. What is the probability that the person watches two hours of television on a selected day?
c. What is the probability that the person watches at least two hours of television on a selected day?
d. What is the probability that the person watches at most two hours of television on a selected day?
e. Calculate mathematical expectation.
f. Find the variance and standard deviation of random variable X.
View full solution →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.
Solve the system of inequations graphically: $2 x+y \geq 8, x+2 y \geq 8, x+y \leq 6$
View full solution →A small manufacturer has employed 5 skilled men and 10 semi-skilled men and makes an article in two qualities deluxe model and an ordinary model. The making of a deluxe model requires 2 hrs. work by a skilled man and 2 hrs. work by a semi-skilled man. The ordinary model requires 1 hr by a skilled man and 3 hrs. by a semi-skilled man. By union rules no man may work more than 8 hrs per day. The manufacturers clear profit on deluxe model is ₹15 and on an ordinary model is ₹10. How many of each type should be made in order to maximize his total daily profit.
Express the following matrices as the sum of symmetric and skew-symmetric matrices: $\left[\begin{array}{lll}3 & 2 & 5 \\ 4 & 1 & 3 \\ 0 & 6 & 7\end{array}\right]$
View full solution →An automobile company uses three types of steel $\mathrm{S}_{1}, \mathrm{~S}_{2}$ and $\mathrm{S}_{3}$ for producing three types of cars $\mathrm{C}_{1}, \mathrm{C}_{2}$ and $\mathrm{C}_{3}$.
Steel requirements (in tons) for each type of cars are given below:| | Cars |
| steel | $\mathrm{C}_{1}$ | $\mathrm{C}_{2}$ | $\mathrm{C}_{3}$ |
| $\mathrm{~S}_{1}$ | 2 | 3 | 4 |
| $\mathrm{~S}_{2}$ | 1 | 1 | 2 |
| $\mathrm{~S}_{3}$ | 3 | 2 | 1 |
Using Cramer's rule, find the number of cars of each type which can be produced using 29, 13 and 16 tonnes of steel of three types respectively. View full solution →Read the text carefully and answer the questions:
A sinking fund contains money set aside or saved to pay off a debt or bond. A company that issues debt will need to pay that debt off in the future, and the sinking fund helps to soften the hardship of a large outlay of revenue. A sinking fund allows companies that have floated debt in the form of bonds gradually save money and avoid a large lump-sum payment at maturity.
Example
- Cost of Machine: ₹2,00,000/-
- Effective Life: 7 Years
- Scrap Value: ₹30,000/-
- Sinking Fund Earning Rate: 5%
- The Expected Cost of New Machine: ₹3,00,000/-
(a) What is the money required for a new machine after 7 years?
(b) What is the value of $\mathrm{A}, \mathrm{i}$ and n here?
(c) What formula will you use to get the requisite amount?
or
What amount should the company put into a sinking fund earning 5% per annum to replace the machine after its useful life?
View full solution →View full solution →