Time series analysis helps to
- Apredict the future behaviour of a variable.
- Bunderstand the behaviour of a variable in the past
- ✓all of these.
- Dplan future operations
Answer: C.
View full solution →Question types
Model Paper 5 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 5 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\int e^x\left(\frac{1-x}{1+x^2}\right)^2 d x$ is equal to
- A$-\frac{e^x}{1+x^2}+C$
- B$-\frac{e^x}{\left(1+x^2\right)^2}+C$
- ✓$\frac{e^x}{1+x^2}+C$
- D$\frac{e^x}{\left(1+x^2\right)^2}+C$
Answer: C.
View full solution →For the purpose of t-test of significance, a random sample of size (n) 34 is drawn from a normal population, then the degree of freedom (v) is
- A35
- B$\frac{1}{34}$
- ✓33
- D34
Answer: C.
View full solution →Given that x, y and b are real numbers and x < y, b > 0, then
- A$\frac{x}{b} \geq \frac{y}{b}$
- B$\frac{x}{b} \leq \frac{y}{b}$
- ✓$\frac{x}{b}>\frac{y}{b}$
- D$\frac{x}{b}<\frac{y}{b}$
Answer: C.
View full solution →Feasible region in the set of points which satisfy
- ANon objective functions
- BSome the given constraints
- CThe objective functions
- ✓All of the given constraints
Answer: D.
View full solution →Let $f(x)=2 x^3-15 x^2+36 x+1$
Assertion (A): $f$ is strictly decreasing in [2,3]
Reason (R): $f$ is strictly increasing in $(-\infty, 2] \cup[3,(0)$.
Assertion (A): $f$ is strictly decreasing in [2,3]
Reason (R): $f$ is strictly increasing in $(-\infty, 2] \cup[3,(0)$.
- 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.
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: B.
View full solution →Assertion (A): Scalar matrix $A =\left[a_{i j}\right]=\left\{\begin{array}{ll}k, & i=j \\ 0, & i \neq j\end{array}\right.$, where k is a scalar, is an identity matrix when $k =1$.
Reason (R): Every identity matrix is not a scalar matrix.
Reason (R): Every identity matrix is not a scalar 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.
- ✓A is true but R is false.
- DA is false but R is true.
Answer: C.
View full solution →Solve: $12 x \equiv 44(\bmod 59)$
View full solution →Find the declared rate of return compounded semiannually which is equivalent to $6 \%$ effective rate of return [Use
$
\left.(1.06)^{\frac{1}{2}}=1.0296\right]
$
View full solution →$
\left.(1.06)^{\frac{1}{2}}=1.0296\right]
$
An interviewer gives the following graph on a client's sales in the last 7 years to candidate and said find the CAGR. Given that $\left(\frac{9}{4}\right)^{\frac{1}{7}}=1.1228$.
View full solution →By using property of definite integrals, evaluate $\int_0^2 x \sqrt{2-x} d x$
View full solution →A person has set up a sinking fund so that he can accumulate ₹ 100000 in 10 years for his children's higher education.
How much amount should he deposit every six months if interest is 5% per annum compounded semi-annually?
How much amount should he deposit every six months if interest is 5% per annum compounded semi-annually?
A random sample of 10 boys had the following I.Q's: $70,120,110,101,88,83,95,98,107,100$. Do these data support the assumption of a population mean I.Q. of 100 ? Find a reasonable range in which most of the mean I.Q. values of samples of 10 boys lie. (Given to $(0.05)=2.262)$
View full solution →i. Obtain the three year moving averages for the following series of observations:
ii. Obtain the five year moving average.
iii. Construct also the 4-year centred moving average.
| Year | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 |
| Annual Sales (in 000 ₹) | 3.6 | 4.3 | 4.3 | 3.4 | 4.4 | 5.4 | 3.4 | 2.4 |
iii. Construct also the 4-year centred moving average.
View full solution →
Find the mean, variance and standard deviation of the number of tails in three tosses of a coin.
The demand and supply functions for a commodity are $p = x ^2-6 x +16$ and $p =\frac{1}{3} x^2+\frac{4}{3} x+4$ respectively. Find each of the following assuming $x \leq 5$ :
i. The equilibrium point.
ii. The consumer's surplus at the equilibrium point.
iii. The producer's surplus at the equilibrium point.
View full solution →i. The equilibrium point.
ii. The consumer's surplus at the equilibrium point.
iii. The producer's surplus at the equilibrium point.
The cost of a car purchased 2 years ago, depreciates at the rate of 20 % every year. If its present worth is ₹315600, find:
i. its purchase price
ii. its value after 3 years.
i. its purchase price
ii. its value after 3 years.
Two positive numbers are selected at random (without replacement) from the first five positive integers. Let X denote the larger of the two numbers obtained. Find the mean and the variance of the distribution.
Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Compute the
variance of the number of aces.
variance of the number of aces.
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.
downstream. Find the rate at which the stream is flowing.
If $A=\left[\begin{array}{rrr}1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1\end{array}\right]$, find $A^{-1}$ Using $A^{-1}$ solve the system of linear equations $x-2 y=10,2 x-y-z=8,-2 y+z=7$.
View full solution →
The feasible region for an L.P.P. is shown in the adjoining figure. The line CB is parallel to OA.
i. Find the equation of the line OA.
ii. Find the equation of the line BC.
iii. Find the constraints for the L.P.P
OR
Find the minimum value of the objective function Z = 3x - 4y.
i. Find the equation of the line OA.
ii. Find the equation of the line BC.
iii. Find the constraints for the L.P.P
OR
Find the minimum value of the objective function Z = 3x - 4y.
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.
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.
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