The straight line trend is represented by the equation:
- A$y_c=a-b x$
- B$y _{ C }= na -b \Sigma x$
- C$y_c=a+b x$
- D$y _{ C }= na +b \Sigma x$
Question types
Model Paper 2 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 2 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\int(x-1) e^{-x} d x$ is equal to
- A$(x+1) e^{-x}+C$
- B$-x e^{-x}+C$
- C$(x-2) e^{-x}+C$
- D$x^{-x}+C$
If the calculated value of $| t |< t _{ v }(\alpha)$, then the null hypothesis is:
- Aneither accepted nor rejected
- Brejected
- Ccannot be determined
- Daccepted
Region represented by $x \geq 0, y \geq 0$ lies in
- AIV quadrant
- BII quadrant
- CIII quadrant
- DI quadrant
The maximum value of $Z=4 x+2 y$ subjected to the constraints $2 x+3 y \leq 18, x+y \geq 10 ; x, y \geq 0$ is
- Anone of these
- B36
- C40
- D20
Assertion (A): The function $f(x)=(x+2) e ^{- x }$ is increasing in the interval $(-1, \infty)$. Reason (R): A function $f(x)$ is increasing, if $f^{\prime}(x)>0$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C
Assertion (A) is true and Reason (R) is false.
- ✓
Assertion (A) is false and Reason (R) is true.
Answer: D.
View full solution →Assertion (A): The matrix $A=\left[\begin{array}{ccc}3 & -1 & 0 \\ \frac{3}{2} & 3 \sqrt{2} & 1 \\ 4 & 3 & -1\end{array}\right]$ is rectangular matrix of order 3 . Reason (R): If $A =\left[a_{i j}\right]_{m \times 1}$, then A is column matrix.
- 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.
- C) A is true but R is false.
- ✓A is false but R is true.
Answer: D.
View full solution →In what ratio must a person mix two sugar solutions of 30% and 50% concentration respectively so as to get a solution of 45% concentration?
Evaluate the determinant $D=\left|\begin{array}{rrr}2 & 3 & -2 \\ 1 & 2 & 3 \\ -2 & 1 & -3\end{array}\right|$ by expanding it along first column.
View full solution →Find $x , y , z$ and w such that $\left[\begin{array}{cc}x-y & 2 z+w \\ 2 x-y & 2 x+w\end{array}\right]=\left[\begin{array}{cc}5 & 3 \\ 12 & 15\end{array}\right]$
View full solution →Evaluate:
$
\int_0^1 x(1-x)^n d x
$
View full solution →$
\int_0^1 x(1-x)^n d x
$
A banker credits the fixed deposit account of a depositor on a continuous basis. As a result, the effective rate of interest earned by a depositor is $9.43 \%$. Find out the rate of interest that is allowed by the banker. What is the effective rate of interest if it is compounded on quarterly basis?
View full solution →A group of 5 patients treated with medicine A weigh $10,8,12,6,4 kg$. A second group of 7 patients treated with medicine B weigh $14,12,8,10,6,2,11 kg$. Comment on the rejection of hypothesis with $5 \%$ level of significance.
[Given: $t _{(10,0.05)}=1.812$ ]
View full solution →[Given: $t _{(10,0.05)}=1.812$ ]
The profit of a paper hag manufacturing company (in lakhs of rupees) during each month of a year are:
Plot the given data on a graph sheet. Calculate the four monthly moving averages and plot these on the same
graph sheet.
| Month | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
| Profit | 1.2 | 0.8 | 1.4 | 1.6 | 2 | 2.4 | 3.6 | 4.8 | 3.4 | 1.8 | 0.8 | 1.2 |
graph sheet.
If the sum and the product of the mean and variance of Binomial Distribution are 1.8 and 0.8 respectively, find the
probability distribution and the probability of at least one success.
probability distribution and the probability of at least one success.
The random variable $X$ can take only the values $0,1,2,3$. Given that $P(X=0)=P(X=1)=p$ and $P(X=2)=$ $P ( X =3)$ such that $\Sigma p_i x_i^2=2 \Sigma p_i x_i$, find the value of p .
View full solution →Suppose when $x$ units of a commodity are produced, the demand is $p=45-x^2$ rupees per unit, and the marginal cost is MC $=6+\frac{1}{4} x^2$, Assume there is no overhead i.e. $C (0)=0$. Find:
i. the total revenue and the marginal revenue.
ii. the value of $x$ (to the nearest unit) that maximizes profit.
iii. the consumer's surplus at the value of $x$ where profit is maximized (use the exact value of $x$ ).
View full solution →i. the total revenue and the marginal revenue.
ii. the value of $x$ (to the nearest unit) that maximizes profit.
iii. the consumer's surplus at the value of $x$ where profit is maximized (use the exact value of $x$ ).
It is known that, if the interest is compounded continuously, the principal changes at the rate equal to the product of the rate of bank interest per annum and the principal.
a. If the interest is compounded continuously at 5% p.a., in how many years will ₹ 100 double?
b. At what interest rate will ₹ 100 double itself in 10 years?
[Given: loge 2 = 0.6931]
a. If the interest is compounded continuously at 5% p.a., in how many years will ₹ 100 double?
b. At what interest rate will ₹ 100 double itself in 10 years?
[Given: loge 2 = 0.6931]
A fair coin is tossed four times, and a person win ₹ 1 for each head and lose ₹ 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.
A die is tossed twice. A success is getting an odd number on a random toss. Find the variance of the number of successes.
A company manufactures cassettes and its cost and revenue functions for a week are $C =300+\frac{3}{2} x$ and $R =2 x$ respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?
View full solution →A box manufacturer makes large and small boxes from a large piece of cardboard. The large boxes require 4 sq. metre per box while the small boxes require 3 sq. metre per box. The manufacturer is required to make at least three large boxes and at least twice as many small boxes as large boxes. If 60 sq. metre of carboard is in stock, and if the profits on the large and small boxes are ₹3 and ₹2 per box, how many of each should be made in order to maximize the total profit?
A total amount of ₹7000 is deposited in three different savings bank accounts with annual interest rates of 5%, 8%and $8 \frac{1}{2} \%$ respectively. The total annual interest from these three accounts s is ₹550. Equal amounts have been deposited in the 5% and 8% savings accounts. Find the amount deposited in each of the three accounts, with the help of matrices.
View full solution →The sales figures for two-car dealers during January showed that dealer A sold 5 Luxury, 3 premium and 4 standard cars, while dealer B sold 7 luxury, 2 premium and 3 standard cars. Total sales over 2-month period of January - February revealed that dealer A sold 8 luxury, 7 premium and 6 standard cars. In the same 2-month period, dealer B sold 10 luxury, 5 premium and 7 standard cars. Write 2 X 3 matrices summarizing sales data for January and the 2-month period for each dealer. Hence, find the sales in February for each year
Loans are an integral part of our lives today. We take loans for a specific purpose - for buying a home, or a car,or sending kids abroad for education - loans help us achieve some significant life goals. That said, when we talk about loans, the word “EMI", eventually crops up because the amount we borrow has to be returned to the lender
with interest.
Suppose a person borrows ₹1 lakh for one year at the fixed rate of 9.5 percent per annum with a monthly rest. In this case, the EMI for the borrower for 12 months works out to approximately ₹8,768.
Example:
In year 2000, Mr. Tanwar took a home loan of ₹3000000 from State Bank of India at 7.5% p.a. compounded monthly for 20 years.
(a) Find the equated monthly installment paid by Mr. Tanwar.
(b) Find interest paid by Mr. Tanwar in 150th payment.
(c) Find Principal paid by Mr. Tanwar in 150th payment
OR
Find principal outstanding at the beginning of 193th month.
with interest.
Suppose a person borrows ₹1 lakh for one year at the fixed rate of 9.5 percent per annum with a monthly rest. In this case, the EMI for the borrower for 12 months works out to approximately ₹8,768.
Example:
In year 2000, Mr. Tanwar took a home loan of ₹3000000 from State Bank of India at 7.5% p.a. compounded monthly for 20 years.
(a) Find the equated monthly installment paid by Mr. Tanwar.
(b) Find interest paid by Mr. Tanwar in 150th payment.
(c) Find Principal paid by Mr. Tanwar in 150th payment
OR
Find principal outstanding at the beginning of 193th month.
The front gate of a building is in the shape of a trapezium as shown below. Its three sides other than base are 10m each. The height of the gate is h meter. On the basis of this information and figure given below answer the following questions:
OR
At the value of $x$ where $\frac{d A}{d x}=0$, area of trapezium is maximum then what is the maximum area of trapezium?
View full solution →OR
At the value of $x$ where $\frac{d A}{d x}=0$, area of trapezium is maximum then what is the maximum area of trapezium?
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