The best-fitted trend line is one for which sum of squares of residuals or errors is:
- AMaximum
- ✓Minimum
- CPositive
- DNegative
Answer: B.
View full solution →Question types
Model Paper 1 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 1 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\int \frac{(\log x)^5}{x}$ is equal to
- A$\frac{\log x^6}{6}+C$
- B$\frac{(\log x)^6}{3 x^2}+C$
- ✓$\frac{(\log x)^6}{6}+C$
- D$\frac{\log x^6}{3 x^2}+C$
Answer: C.
View full solution →A simple random sample consists of four observations 1, 3, 5, 7. What is the point estimate of population standard deviation?
- A3.1
- B2.3
- C2.87
- ✓2.58
Answer: D.
View full solution →How many of the following points satisfy the inequality 2x - 3y > - 5?
(1, 1), (-1, 1), (1, -1 ), (-1, - 1), (- 2, 1), (2, -1 ), (-1, 2) and (-2, -1).
(1, 1), (-1, 1), (1, -1 ), (-1, - 1), (- 2, 1), (2, -1 ), (-1, 2) and (-2, -1).
- ✓5
- B3
- C4
- D6
Answer: A.
View full solution →Comer points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let z = 4x + 6y be the objective function. Then, Max. z - Min. z =
- A48
- B42
- ✓60
- D18
Answer: C.
View full solution →Assertion (A): If $x$ is real, then the minimum value of $x^2-8 x+17$ is 1 .
Reason (R): If $f ^{\prime \prime}( x )>0$ at a critical point, then the value of the function at the critical point will be the minimum value of the function.
Reason (R): If $f ^{\prime \prime}( x )>0$ at a critical point, then the value of the function at the critical point will be the minimum value of the function.
- ✓Both 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.
Answer: A.
View full solution →Assertion (A): If $A=\left[\begin{array}{cc}10 & -2 \\ -5 & 1\end{array}\right]$, then $A ^{-1}$ does not exist.
Reason (R): On using elementary column operations $C _2 \rightarrow C _2-2 C _1$ in the following matrix equation $\left[\begin{array}{cc}1 & -3 \\ 2 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}3 & 1 \\ 2 & 4\end{array}\right]$, we have $\left[\begin{array}{cc}1 & -5 \\ 2 & 0\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}3 & -5 \\ 2 & 0\end{array}\right]$.
Reason (R): On using elementary column operations $C _2 \rightarrow C _2-2 C _1$ in the following matrix equation $\left[\begin{array}{cc}1 & -3 \\ 2 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}3 & 1 \\ 2 & 4\end{array}\right]$, we have $\left[\begin{array}{cc}1 & -5 \\ 2 & 0\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}3 & -5 \\ 2 & 0\end{array}\right]$.
- 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.
- CA is true but R is false.
- DA is false but R is true.
Answer: B.
View full solution →Evaluate: $-8 \bmod 5$
View full solution →If the matrix $\left[\begin{array}{ccc}x+4 & x & x \\ x & x+4 & x \\ x & x & x+4\end{array}\right]$ is singular, find x.
View full solution →Using matrix method, solve the following system of equations:
$
\begin{array}{l}
x-2 y+3 z=6 \\
x+4 y+z=12 \\
x-3 y+2 z=1
\end{array}
$
View full solution →$
\begin{array}{l}
x-2 y+3 z=6 \\
x+4 y+z=12 \\
x-3 y+2 z=1
\end{array}
$
Evaluate the definite integral:
$
\int_2^4 \frac{x}{x^2+1} d x
$
View full solution →$
\int_2^4 \frac{x}{x^2+1} d x
$
Rahul purchased an old scooter for ₹ 16000. If the cost of the scooter after 2 years depreciates to ₹14440, find the rate of depreciation.
Find the student's -t for the following variable values in a sample of eight:
-4, -2, -2, 0, 2, 2, 3, 3 taking the mean of the universe to be zero.
-4, -2, -2, 0, 2, 2, 3, 3 taking the mean of the universe to be zero.
Construct 5-year Moving averages from the following data of the number of industrial failure in a country during 2003-2018:
![]()
| Year | No. of Failures | Year | No. of Failure |
| 2003 | 23 | 2011 | 9 |
| 2004 | 26 | 2012 | 13 |
| 2005 | 28 | 2013 | 11 |
| 2006 | 32 | 2014 | 14 |
| 2007 | 20 | 2015 | 12 |
| 2008 | 12 | 2016 | 9 |
| 2009 | 12 | 2017 | 3 |
| 2010 | 10 | 2018 | 1 |
Let X be a discrete random variable whose probability distribution is defined as follows:
$
P(X=x)=\left\{\begin{array}{cl}
k(x+1) & \text { for } x=1,2,3,4 \\
2 k x & \text { for } x=5,6,7 \\
0 & \text { otherwise }
\end{array}\right.
$
where k is a constant
Find:
i. k
ii. E(X)
iii. Standard deviation of X.
View full solution →$
P(X=x)=\left\{\begin{array}{cl}
k(x+1) & \text { for } x=1,2,3,4 \\
2 k x & \text { for } x=5,6,7 \\
0 & \text { otherwise }
\end{array}\right.
$
where k is a constant
Find:
i. k
ii. E(X)
iii. Standard deviation of X.
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is What is the probability that he will win a prize $\frac{1}{100}$.
i. at least once
ii. exactly once
iii. at least twice?
View full solution →i. at least once
ii. exactly once
iii. at least twice?
The demand function for a commodity is p = 20 e-x/10. Find the consumer's surplus at equilibrium price p = 2. (Given log10 e = 0.4343)
A start-up company invested ₹ 3,00,000 in shares for 5 years. The value of this investment was ₹ 3,50,000 at the end of second year, ₹ 3,80,000 at the end of third year and on maturity, the final value stood at ₹ 4,50,000. Calculate the Compound Annual Growth Rate (CAGR) on the investment. [Given that $\left.(1.5)^{\frac{1}{5}}=1.084\right]$
View full solution →Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Compute the variance of the number of aces.
A class XII has 20 students whose marks (out of 30) are 14, 17, 25, 14, 21, 17, 17, 19, 18, 26, 18, 17, 17, 26, 19, 21, 21, 25, 14 and 19. If random variable X denotes the marks of a selected student given that the probability of each student to be selected is equally likely.
a. Prepare the probability distribution of the random variable X.
b. Find mean, variance and standard deviation of X.
a. Prepare the probability distribution of the random variable X.
b. Find mean, variance and standard deviation of X.
Solve the following system of inequalities graphically:
3y - 2x < 4, x + 3y > 3 and x + y ≤ 5.
3y - 2x < 4, x + 3y > 3 and x + y ≤ 5.
Solve the following LPP graphically:
$
\text { Minimize } Z=3 x+5 y
$
Subject to
$
\begin{array}{l}
-2 x+y \leq 4 \\
x+y \geq 3 \\
x-2 y \leq 2 \\
x, y \geq 0
\end{array}
$
View full solution →$
\text { Minimize } Z=3 x+5 y
$
Subject to
$
\begin{array}{l}
-2 x+y \leq 4 \\
x+y \geq 3 \\
x-2 y \leq 2 \\
x, y \geq 0
\end{array}
$
In an engineering workshop there are 10 machines for drilling, 8 machines for turning and 7 machines for grinding. Three types of brackets are made. Type I brackets require 0 minutes for drilling, 5 minutes for turning and 4 minutes for grinding. The corresponding times for type II and III brackets are 3, 3, 2 and 3, 2, 2, minutes respectively. How many brackets of each type should be produced per hour so that all the machines remain fully occupied during an hour? Solve by using matrix method.
A shopkeeper has 3 varieties of pens A, B and C. Meenu purchased 1 pen of each variety for a total of ₹ 21. Jean purchased 4 pens of A variety, 3 pens of B variety and 2 pens of C variety for ₹ 60. While Shikha purchased 6 pens of A variety, 2 pens of B variety and 3 pens of C variety for ₹ 70. Using matrix method find the cost of each pen.
Read the text carefully and answer the questions:
The nominal rate of return shows the yield of an investment over time without accounting for negative elements such as inflation or taxes. By calculating the nominal rate of return, you can compare the performance of your assets easily, regardless of the inflation rate or differing spans of time for each investment. By obtaining a bird’s-eye view of how your assets are growing, you can make more prudent investment decisions in the future.
(a) A man invests a sum of money in ₹100 shares paying $15 \%$ dividend quoted at $20 \%$ premium. If his annual dividend is ₹540, calculate the rate of return on his investment.
(b) Mr. Satya holds 1500, ₹100 shares of a company paying $15 \%$ dividend annually quoted at $30 \%$ premium. Calculate rate of return on his investment.
(c) ₹100 shares of a company are sold at a discount of ₹20 . If the return on the investment is $15 \%$, find the rate of dividend declared.
OR
A company declared a dividend of $14 \%$. Find the market value of ₹50 shares, if the return on the investment was $10 \%$.
View full solution →The nominal rate of return shows the yield of an investment over time without accounting for negative elements such as inflation or taxes. By calculating the nominal rate of return, you can compare the performance of your assets easily, regardless of the inflation rate or differing spans of time for each investment. By obtaining a bird’s-eye view of how your assets are growing, you can make more prudent investment decisions in the future.
(a) A man invests a sum of money in ₹100 shares paying $15 \%$ dividend quoted at $20 \%$ premium. If his annual dividend is ₹540, calculate the rate of return on his investment.
(b) Mr. Satya holds 1500, ₹100 shares of a company paying $15 \%$ dividend annually quoted at $30 \%$ premium. Calculate rate of return on his investment.
(c) ₹100 shares of a company are sold at a discount of ₹20 . If the return on the investment is $15 \%$, find the rate of dividend declared.
OR
A company declared a dividend of $14 \%$. Find the market value of ₹50 shares, if the return on the investment was $10 \%$.
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