If $(2 x+y, y+3)=(7,0)$, then $x$ is
- A-3
- B5
- C0
- D$\frac{7}{2}$
Question types
Model Paper 5 question types
44 questions across 6 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
44
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
7 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.
For the post of 5 teachers, there are 23 applicants. 2 posts are reserved for SC candidates and there are 7 SC candidates among the applicants. In how many ways can the selection be made?
- A3920
- B11760
- C4880
- D5880
The difference between simple interest and compound interest on ₹ 15000 for one yea $8 \%$ per annum calculated half-yearly is:
- A₹ 24
- B₹ 20
- C₹ 22
- D₹ 26
5 boys and 5 girls are sitting in a row randomly. The probability that boys and girls sit alternately is:
- A$\frac{5}{126}$
- B$\frac{3}{126}$
- C$\frac{1}{126}$
- D$\frac{4}{126}$
Two men hit at a target with probabilities $\frac{1}{2}$ and $\frac{1}{3}$, respectively. What is the probability that exactly one of them hits the target?
- A$\frac{1}{6}$
- B$\frac{1}{2}$
- C$\frac{1}{3}$
- D$\frac{2}{3}$
Assertion (A): A sequence is said to definite if it has finite no of terms.
Reason (R): The sequence whose $\mathrm{n}^{\text {th }}$ term if $\frac{2^{n}}{n}$ if $2,2, \frac{8}{3}, 4 \ldots$
Reason (R): The sequence whose $\mathrm{n}^{\text {th }}$ term if $\frac{2^{n}}{n}$ if $2,2, \frac{8}{3}, 4 \ldots$
- 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.
- D$A$ is false but $R$ is true.
Assertion (A): The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3.
Reason (R): The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
Reason (R): The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
- 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.
- DA is false but $R$ is true.
Convert the decimal number to the binary number: 517
Find the derivative of $f(x)=x+\frac{1}{x}$ with respect to $x$.
View full solution →Differentiate the function with respect to $\mathrm{x}: \frac{e^{x} \log x}{x^{2}}$
View full solution →A and B can do a work in 8 days; B and C can do the same work in 12 days; A, B and C together can finish it in 6 days. In how many days A and C together will do the same work?
Write down all possible subsets of $A=(1,\{2,3\})$.
View full solution →Let $A=\{1,2,4,5\}, B=\{2,3,5,6\}, C=\{4,5,6,7\}$ verify the following identity:
$A \cup(B \cap C)=[(A \cup B) \cap(A \cap C)]$
View full solution →$A \cup(B \cap C)=[(A \cup B) \cap(A \cap C)]$
Simplify:
$\frac{1}{1+a^{m-n}+a^{m-p}}+\frac{1}{1+a^{n-m}+a^{n-p}}+\frac{1}{1+a^{p-m}+a^{p-n}}$
View full solution →$\frac{1}{1+a^{m-n}+a^{m-p}}+\frac{1}{1+a^{n-m}+a^{n-p}}+\frac{1}{1+a^{p-m}+a^{p-n}}$
Find the present value of ₹ 25,000 due 10 years hence when the interest of $8 \%$ is compounded:
i. annually
ii. semi-annually
iii. quarterly
iv. continuously
View full solution →i. annually
ii. semi-annually
iii. quarterly
iv. continuously
Find the domain and the range of the given function: $f(x)=\frac{1}{1-x^{2}}$
View full solution →Find the equation of the line passing through the point (-1, 3) and perpendicular to the line 3x - 4y - 16 = 0
Find the equation of a circle whose centre is a point $(1,-2)$ and which passes through the centre of the circle $2 x^{2}$$+2 y^{2}+4 y=5$.
View full solution →Calculate the mean deviation about the mean for the following data:
Income per day | 0 - 100 | 100 - 200 | 200 - 300 | 300 - 400 | 400 - 500 | 500 - 600 | 600 - 700 | 700 - 800 |
Number of persons | 4 | 8 | 9 | 10 | 7 | 5 | 4 | 3 |
Compute the moment coefficient of skewness $\beta_{1}$ for the following distribution:
View full solution →Marks obtained | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
Frequency | 6 | 12 | 22 | 24 | 16 | 12 | 8 |
Suppose $f(x)=\left\{\begin{array}{cc}a+b x, & x<1 \\ 4, & x=1 \\ b-a x, & x>1\end{array}\right.$ and if $\lim _{x \rightarrow 1} \mathrm{f}(\mathrm{x})=\mathrm{f}(1)$, then what are the possible values of a and b ?
View full solution →A die has two faces with number 1, three faces each with number 2 and one face with number 3 . If die is ruled once, find (i) P (3) (ii) $\mathrm{P}(1$ or 2$)$ (iii) $\mathrm{P}(2)$
View full solution →
Read the text carefully and answer the questions:
A mobile number is having 10 digits. It is not just a group of numbers strung out at random. All mobile numbers have 3 things in common, a 2-digit Access code (AC), a 3-digit provider code (PC), and a 5 digit subscriber code (SC). AC code and PC code are fixed, then
(a) How many mobile number are possible if number start with 98073 and no other digit can repeat.
(b) How many AC code are possible if both digit in AC code are different and must be greater than 6.
(c) How may mobile number are possible if AC and PC code are fixed and digits can repeat
(d) How many mobile numbers are possible with AC code 98 and PC code 123 and digit used in AC and PC code will not be used in SC code.
A mobile number is having 10 digits. It is not just a group of numbers strung out at random. All mobile numbers have 3 things in common, a 2-digit Access code (AC), a 3-digit provider code (PC), and a 5 digit subscriber code (SC). AC code and PC code are fixed, then
(a) How many mobile number are possible if number start with 98073 and no other digit can repeat.
(b) How many AC code are possible if both digit in AC code are different and must be greater than 6.
(c) How may mobile number are possible if AC and PC code are fixed and digits can repeat
(d) How many mobile numbers are possible with AC code 98 and PC code 123 and digit used in AC and PC code will not be used in SC code.
Read the text carefully and answer the questions:
In class of Statistics, teacher was discussing the concept of Measures of Correlation, in which he was discussing about Karl Pearson's Coefficient of Correlation. During his class, he discussed the following few points on this: This is the best method for finding correlation between two variables provided the relationship between the two variables is linear. This method is also known as product moment correlation coefficient. Pearson's correlation coefficient may be defined as the ratio of covariance between the two variables to the product of the standard deviations of the two variables.
If the two variables are denoted by x and y and of the corresponding bivariates data are $\left(\mathrm{x}_{\mathrm{i}}, \mathrm{y}_{\mathrm{i}}\right)$ for $\mathrm{i}=1,2,3, \ldots$, n , then the coefficent of correlation between x and y due to Karl Pearson, is given by:
$r=r_{x y}$
or, $\mathrm{r}_{\mathrm{xy}}=\frac{\operatorname{Cov}(x, y)}{\sqrt{\operatorname{Var} x} \cdot \sqrt{\operatorname{Var} y}}$
$=\frac{\operatorname{Cov}(x, y)}{\sigma_{x} \cdot \sigma_{y}}$
where,
$\operatorname{cov}(\mathrm{X}, \mathrm{y})=\frac{\Sigma(x-\bar{x})(y-\bar{y})}{N}$
$=\frac{\Sigma x y}{N}-\bar{x} \cdot \bar{y}$
$\sigma_{x}=\sqrt{\frac{\Sigma(x-\bar{x})^{2}}{N}}=\sqrt{\frac{\Sigma x^{2}}{N}-x^{-2}}$
$\sigma_{y}=\sqrt{\frac{\Sigma(y-\bar{y})^{2}}{N}}=\sqrt{\frac{\Sigma y^{2}}{N}-y^{-2}}$
If $\mathrm{x}-\bar{x}-\bar{y}$ are small fractions, we use
$\mathrm{r}=\frac{\Sigma(x-\bar{x})(y-\bar{y})}{\sqrt{\Sigma(x-\bar{x})^{2}} \sqrt{\Sigma(y-\bar{y})^{2}}}$
If $x, y$ are small numbers, we use
$r=\frac{\Sigma x y-\frac{1}{N} \Sigma x \Sigma y}{\sqrt{\Sigma x^{2}-\frac{1}{N}(\Sigma x)^{2}} \sqrt{\Sigma y^{2}-\frac{1}{N}(\Sigma y)^{2}}}$
If $x, y$ are large numbers, we use assumed mean $A$ and $B$ and $u=x-A, v=y-B$
$\mathrm{r}=\frac{\Sigma u v-\frac{1}{N} \Sigma u \Sigma v}{\sqrt{\Sigma u^{2}-\frac{1}{N}(\Sigma u)^{2}} \sqrt{\Sigma v^{2}-\frac{1}{N}(\Sigma v)^{2}}}$
For example:
Find Karl Pearson's coefficient of correlation between X and Y for the following:
Following problem was given to students on the same concept:
(a) What is the value $\Sigma x y$ in this data?
(b) What is the value $\Sigma x^{2}$?
(c) What is the value of $\Sigma y^{2}$?
OR
What is the value of Karl Pearson's Coefficient of Correlation between x and y?
View full solution →In class of Statistics, teacher was discussing the concept of Measures of Correlation, in which he was discussing about Karl Pearson's Coefficient of Correlation. During his class, he discussed the following few points on this: This is the best method for finding correlation between two variables provided the relationship between the two variables is linear. This method is also known as product moment correlation coefficient. Pearson's correlation coefficient may be defined as the ratio of covariance between the two variables to the product of the standard deviations of the two variables.
If the two variables are denoted by x and y and of the corresponding bivariates data are $\left(\mathrm{x}_{\mathrm{i}}, \mathrm{y}_{\mathrm{i}}\right)$ for $\mathrm{i}=1,2,3, \ldots$, n , then the coefficent of correlation between x and y due to Karl Pearson, is given by:
$r=r_{x y}$
or, $\mathrm{r}_{\mathrm{xy}}=\frac{\operatorname{Cov}(x, y)}{\sqrt{\operatorname{Var} x} \cdot \sqrt{\operatorname{Var} y}}$
$=\frac{\operatorname{Cov}(x, y)}{\sigma_{x} \cdot \sigma_{y}}$
where,
$\operatorname{cov}(\mathrm{X}, \mathrm{y})=\frac{\Sigma(x-\bar{x})(y-\bar{y})}{N}$
$=\frac{\Sigma x y}{N}-\bar{x} \cdot \bar{y}$
$\sigma_{x}=\sqrt{\frac{\Sigma(x-\bar{x})^{2}}{N}}=\sqrt{\frac{\Sigma x^{2}}{N}-x^{-2}}$
$\sigma_{y}=\sqrt{\frac{\Sigma(y-\bar{y})^{2}}{N}}=\sqrt{\frac{\Sigma y^{2}}{N}-y^{-2}}$
If $\mathrm{x}-\bar{x}-\bar{y}$ are small fractions, we use
$\mathrm{r}=\frac{\Sigma(x-\bar{x})(y-\bar{y})}{\sqrt{\Sigma(x-\bar{x})^{2}} \sqrt{\Sigma(y-\bar{y})^{2}}}$
If $x, y$ are small numbers, we use
$r=\frac{\Sigma x y-\frac{1}{N} \Sigma x \Sigma y}{\sqrt{\Sigma x^{2}-\frac{1}{N}(\Sigma x)^{2}} \sqrt{\Sigma y^{2}-\frac{1}{N}(\Sigma y)^{2}}}$
If $x, y$ are large numbers, we use assumed mean $A$ and $B$ and $u=x-A, v=y-B$
$\mathrm{r}=\frac{\Sigma u v-\frac{1}{N} \Sigma u \Sigma v}{\sqrt{\Sigma u^{2}-\frac{1}{N}(\Sigma u)^{2}} \sqrt{\Sigma v^{2}-\frac{1}{N}(\Sigma v)^{2}}}$
For example:
Find Karl Pearson's coefficient of correlation between X and Y for the following:
| x | 5 | 4 | 3 | 2 | 1 |
| y | 4 | 2 | 10 | 8 | 6 |
Following problem was given to students on the same concept:
(a) What is the value $\Sigma x y$ in this data?
(b) What is the value $\Sigma x^{2}$?
(c) What is the value of $\Sigma y^{2}$?
OR
What is the value of Karl Pearson's Coefficient of Correlation between x and y?
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