Let $n(A)=m$, and $n(B)=n$. Then the total number of possible relations that can be defined from $A$ to $B$ is
- ✓$2^{\mathrm{mn}}$
- B$m^{n}-1$
- C$n^{m}-1$
- D$\mathrm{m}^{\mathrm{n}}$
Answer: A.
View full solution →Question types
Model Paper 10 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 10 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Out of 5 men and 2 women, a committee of 3 persons is to be formed so as to include at least one woman. The number of ways in which it can be done is
- ✓25
- B35
- C45
- D10
Answer: A.
View full solution →The amount at the compound interest which is calculated yearly on a certain sum of money is ₹ 1250 is one year and ₹ 1375 in two years. The rate of interest per annum is:
- A$9 \%$
- ✓$10 \%$
- C$8 \%$
- D$11 \%$
Answer: B.
View full solution →A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is
- A$\frac{45}{196}$
- ✓$\frac{15}{56}$
- C$\frac{15}{29}$
- D$\frac{135}{392}$
Answer: B.
View full solution →A man is known to speak truth in 3 out of 4 times. He throws a dice and reports that it is a six. Then the probability that it is actually a six is
- A$\frac{4}{9}$
- B$\frac{2}{7}$
- C$\frac{1}{6}$
- ✓$\frac{3}{8}$
Answer: D.
View full solution →Assertion (A): In an AP., the sum of 4th term from the beginning and sum of 4th term from the end is equal to sum of 7th term from the beginning and 7th term from the end.
Reason (R): Sum of first n terms of a AP., $\mathrm{S}_{\mathrm{n}} \frac{n}{2}(a+l)$, where $\mathrm{a}=$ first term, $\mathrm{l}=$ last term.
Reason (R): Sum of first n terms of a AP., $\mathrm{S}_{\mathrm{n}} \frac{n}{2}(a+l)$, where $\mathrm{a}=$ first term, $\mathrm{l}=$ last term.
- 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.
- DA is false but $R$ is true.
Answer: B.
View full solution →Consider the following data
Assertion (A): The variance of the data is 45.8.
Reason (R): The standard deviation of the data is 6.77.
| $x_{i}$ | 4 | 8 | 11 | 17 | 20 | 24 | 32 |
| $f_{i}$ | 3 | 5 | 9 | 5 | 4 | 3 | 1 |
Reason (R): The standard deviation of the data is 6.77.
- 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.
- DA is false but $R$ is true.
Answer: B.
View full solution →Convert the decimal number 394 to the binary number.
If $\mathrm{y}=\sqrt{x}+\frac{1}{\sqrt{x}}$, prove that $2 \mathrm{x} \frac{d y}{d x}+\mathrm{y}=2 \sqrt{x}$
View full solution →Differentiate the function with respect to $\mathrm{x}: \frac{1}{\sqrt{a^{2}-x^{2}}}$
View full solution →I travelled a certain distance at a speed of $40 \mathrm{~km} / \mathrm{h}$ and the remaining distance at $60 \mathrm{~km} / \mathrm{h}$. The total distance of 240 km was covered in 5 hours. Find the distance covered at the speed of $40 \mathrm{~km} / \mathrm{h}$.
View full solution →There are 210 members in a club. 100 of them drink tea and 65 drink tea but not coffee, each member drinks tea or coffee. Find how many drink coffee? How many drink coffee but not tea?
If $A=\{1,2,3,4,5\}, B=\{2,3,4\}$ and $C=\{2,4,5\}$; state whether the following statements are true or false.
i. $\mathrm{A} \subset \mathrm{B}$
ii. $\mathrm{A} \subset \mathrm{C}$
iii. $B \subset A$
iv. $\mathrm{B} \subset\mathrm{C}$
v. $\mathrm{C} \subset \mathrm{A}$
vi. $C \subset B$
vii. $B=C$
viii. $\phi \subset \mathrm{B}$
ix. $\mathrm{A} \leftrightarrow \mathrm{B}$
x. $B \leftrightarrow C$
xi. $A \leftrightarrow C$
View full solution →i. $\mathrm{A} \subset \mathrm{B}$
ii. $\mathrm{A} \subset \mathrm{C}$
iii. $B \subset A$
iv. $\mathrm{B} \subset\mathrm{C}$
v. $\mathrm{C} \subset \mathrm{A}$
vi. $C \subset B$
vii. $B=C$
viii. $\phi \subset \mathrm{B}$
ix. $\mathrm{A} \leftrightarrow \mathrm{B}$
x. $B \leftrightarrow C$
xi. $A \leftrightarrow C$
In a factory the production of scooters rose to 46,305 from 40,000 in 3 years. Find the annual rate of growth of the product of scooters.
Divide ₹ 15,500 into two parts such that if one part be lent out at $15 \%$ per annum and the other at $24 \%$ per annum, the total annual income is ₹ 3,000 .
View full solution →Find the domain and range of $f(x)=|2 x-3|-3$.
View full solution →A line passes through $P(1,2)$ such that its intercept between the axes is bisected at $P$. Find the equation of line.
View full solution →Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum: $x^{2}=6 y$
View full solution →The following table gives the number of finished articles turned out per day by different number of workers in a factory. Find the standard deviation of the daily output of finished articles.
| Number of articles: | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| No. of workers: | 3 | 7 | 11 | 14 | 18 | 17 | 13 | 8 | 5 | 4 |
While calculating the mean and variance of 10 readings, a student wrongly uses the reading 52 for the correct reading 25 . He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and variance.
For what value of $\lambda$ is the function defined by $f(x)=\left\{\begin{array}{cl}\lambda\left(x^{2}-2 x\right), & \text { if } x \leq 0 \\ 4 x+1, & \text { if } x>0\end{array}\right.$ continuous at $\mathrm{x}=0$?
View full solution →In a bolt factory, three machines, A, B, C, manufacture $25 \%, 35 \%$ and $40 \%$ of the total production respectively. Of their respective outputs, $5 \%, 4 \%$ and $2 \%$ are defective. A bolt is drawn at random from the total product and it is found to be defective. Find the probability that it was manufactured by the machine C.
View full solution →Read the text carefully and answer the questions:
Two friends Pankaj and Pooja were playing cards. There were 52 cards in a deck.
(a) In how many ways Sunil can select all four cards from same suit?
(b) In how many ways Anita can select four cards from different suit?
(c) In how many ways Sunil can select all face cards?
(d) In how many ways Anita can select two cards of same colour?
Two friends Pankaj and Pooja were playing cards. There were 52 cards in a deck.
(a) In how many ways Sunil can select all four cards from same suit?
(b) In how many ways Anita can select four cards from different suit?
(c) In how many ways Sunil can select all face cards?
(d) In how many ways Anita can select two cards of same colour?
Read the text carefully and answer the questions:
The purpose of the student council is to give students an opportunity to develop leadership by organizing and carrying out school activities and service projects. Create an environment where every student can voice out their concern or need. Raju, Ravi Joseph, Sangeeta, Priya, Meena and Aman are members of student's council. There is a photo session in a school these 7 students are to be seated in a row for photo session.
(a) Find the total number of arrangements so that Raju and Ravi are at extreme positions?
(b) Find the number of arrangements so that Joseph is sitting in the middle.
(c) Find the number of arrangements so that three girls are together.
(d) Find the number of arrangements so that Aman and Ravi are not together?
The purpose of the student council is to give students an opportunity to develop leadership by organizing and carrying out school activities and service projects. Create an environment where every student can voice out their concern or need. Raju, Ravi Joseph, Sangeeta, Priya, Meena and Aman are members of student's council. There is a photo session in a school these 7 students are to be seated in a row for photo session.
(a) Find the total number of arrangements so that Raju and Ravi are at extreme positions?
(b) Find the number of arrangements so that Joseph is sitting in the middle.
(c) Find the number of arrangements so that three girls are together.
(d) Find the number of arrangements so that Aman and Ravi are not together?
Read the text carefully and answer the questions:
In this age of competitions rank plays an important role. Let us try to answer some questions related to percentile rank with respect to the given data of marks of 10 students $13,52,42,22,44,105,45,88,90,76$.
(a) If score is 90 , then find the percentile rank?
(b) If score is 52 then find the percentile rank?
(c) If score is 105 then find the percentile rank?
OR
If percentile rank is 60 then find the score?
View full solution →In this age of competitions rank plays an important role. Let us try to answer some questions related to percentile rank with respect to the given data of marks of 10 students $13,52,42,22,44,105,45,88,90,76$.
(a) If score is 90 , then find the percentile rank?
(b) If score is 52 then find the percentile rank?
(c) If score is 105 then find the percentile rank?
OR
If percentile rank is 60 then find the score?
Read the text carefully and answer the questions:
A triangular park has two of its vertices as $B(-4,1)$ and $C(2,11)$. The third vertex $A$ is a point dividing the line joining the points $(3,1)$ and $(6,4)$ in the ratio $2: 1$.
(a) Find the coordinates of third vertex A.
(b) Find the equation of line passing through A and parallel to BC.
(c) Find the equation of the line passing through A and perpendicular to BC .
OR
Find the area of triangular field ABC .
View full solution →A triangular park has two of its vertices as $B(-4,1)$ and $C(2,11)$. The third vertex $A$ is a point dividing the line joining the points $(3,1)$ and $(6,4)$ in the ratio $2: 1$.
(a) Find the coordinates of third vertex A.
(b) Find the equation of line passing through A and parallel to BC.
(c) Find the equation of the line passing through A and perpendicular to BC .
OR
Find the area of triangular field ABC .
Generate a Model Paper 10 paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.