CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

Mathematics

Case study questions on Relations & Functions, Matrices, Determinants, Applications of Derivatives, Applications of Integral, Differential equations, Vector Algebra, three dimensional Geometry and Probability etc.

RELATIONS & FUNCTIONS

A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in general election held in 2019. A relation ‘R’ is defined on I as follows:

R = {(𝑉1, 𝑉2) 𝑉1, 𝑉2 𝐼 and both use their voting right in general election – 2019}

Q1) Two neighbors X and Y I. X exercised his voting right while Y did not cast her vote in general election – 2019. Which of the following is true?

a) (X, Y) R

b) (Y, X) R

c) (X, X) R

d) (X, Y) R

2. Mr.’𝑋’ and his wife ‘𝑊’both exercised their voting right in general election -2019, Which of the following is true?

a) both (X, W) and (W, X) R

b)  (X, W) R but (W, X) R

c)  both (X, W) and (W, X) R

d)  (W, X) R but (X, W) R

Q3) Three friends F1, F2 and F3 exercised their voting right in general election-2019, then which of the following is true?

a) (F1, F2 ) R, (F2, F3) R and (F1,F3) R

b) (F1, F2 ) R, (F2,F3) R and (F1,F3) R

c) (F1, F2 ) R, (F2,F2) R but (F3,F3) R

d) (F1, F2 ) R, (F2,F3) R and (F1,F3) R

4. The above defined relation R is ______

a) Symmetric and transitive but not reflexive

b) Universal relation

c) Equivalence relation

d) Reflexive but not symmetric and transitive

5. Mr. Shyam exercised his voting right in General Election – 2019, then Mr. Shyam is related to which of the following?

a) All those eligible voters who cast their votes

b) Family members of Mr. Shyam

c) All citizens of India

d) Eligible voters of India

 Q No. Option Answer 1 d (X, Y) ∉R 2 a both (X, W) and (W, X) ∈ R 3 a (F1, F2 ) ∈R, (F2, F3) ∈ R and (F1, F3) ∈ R 4 c Equivalence relation 5 a All those eligible voters who cast their votes

RELATIONS & FUNCTIONS

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes

A = {S, D}, B = {1,2,3,4,5,6}

Q1. Let 𝑅 𝐵𝐵 be defined by R = {(𝑥, 𝑦): 𝑦 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 𝑥 } is

a) Reflexive and transitive but not symmetric

b) Reflexive and symmetric and not transitive

c) Not reflexive but symmetric and transitive

d) Equivalence

2. Raji wants to know the number of functions from A to B. How many number of functions are possible?

a) 6 2

b) 2 6

c) 6!

d) 2 12

3. Let R be a relation on B defined by R = {(1,2), (2,2), (1,3), (3,4), (3,1), (4,3), (5,5)}. Then R is

a) Symmetric

b) Reflexive

c) Transitive

d) None of these three

4. Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?

a) 6 2

b) 2 6

c) 6!

d) 2 12

5. Let 𝑅: 𝐵𝐵 be defined by R={(1,1),(1,2), (2,2), (3,3), (4,4), (5,5),(6,6)}, then R is

a) Symmetric

b) Reflexive and Transitive

c) Transitive and symmetric

d) Equivalence

 Q No. Option Answer 1 a Reflexive and transitive but not symmetric 2 a 62 3 d None of these three 4 d 212 5 b Reflexive and Transitive

MATRICES

A manufacture produces three stationery products Pencil, Eraser and Sharpener which he sells in two markets. Annual sales are indicated below

 Market Products in numbers Pencil Eraser Sharpener A 10000 2000 18000 B 6000 20000 8000

If the unit Sale price of Pencil, Eraser and Sharpener are Rs. 2.50, Rs. 1.50 and Rs. 1.00 respectively, and unit cost of the above three commodities are Rs. 2.00, Rs. 1.00 and Rs. 0.50 respectively, then,

Based on the above information answer the following:

1) Total revenue of market A

a) Rs. 64,000

b) Rs. 60,400

c) Rs. 46,000

d) Rs. 40600

2) Total revenue of market B

a) Rs. 35,000

b) Rs. 53,000

c) Rs. 50,300

d) Rs. 30,500

3) Cost incurred in market A

a) Rs. 13,000

b) Rs.30,100

c) Rs. 10,300

d) Rs. 31,000

4) Profit in market A and B respectively are

a) (Rs. 15,000, Rs. 17,000)

b) (Rs. 17,000, Rs. 15,000)

c) (Rs. 51,000, Rs. 71,000)

d) ( Rs. 10,000, Rs. 20,000)

5) Gross profit in both market

a) Rs.23,000

b) Rs. 20,300

c) Rs. 32,000

d) Rs. 30,200

 Q No. Option Answer 1 c Rs. 46,000 2 b Rs. 53,000 3 d Rs.31,000 4 a Rs.15, 000, Rs.17, 000 5 c Rs. 32,000

MATRICES

CASE STUDY 2:

Amit, Biraj and Chirag were given the task of creating a square matrix of order 2. Below are the matrices created by them. A, B , C are the matrices created by Amit, Biraj and Chirag respectively.

A = $\left [ \begin{matrix}1 & 2 \\-1 & 3 \\\end{matrix} \right ]$ ,   B = $\left [ \begin{matrix}4 & 0 \\1 & 5 \\\end{matrix} \right ]$,  C = $\left [ \begin{matrix}2 & 0 \\1 & -2 \\\end{matrix} \right ]$

If a = 4 and b = −2, based on the above information answer the following:

1. Sum of the matrices A, B and C , A+(𝐵 + 𝐶) is

a) $\left [ \begin{matrix}1 & 6 \\2 & 7 \\\end{matrix} \right ]$

b) $\left [ \begin{matrix}6 & 1 \\7 & 2 \\\end{matrix} \right ]$

c) $\left [ \begin{matrix}7 & 2 \\1 & 6 \\\end{matrix} \right ]$

d) $\left [ \begin{matrix}2 & 1 \\7 & 6 \\\end{matrix} \right ]$

2. (𝐴 𝑇 ) 𝑇 is equal to

a) $\left [ \begin{matrix}1 & 2 \\-1 & 3 \\\end{matrix} \right ]$

b) $\left [ \begin{matrix}2 & 1 \\3 & -1 \\\end{matrix} \right ]$

c) $\left [ \begin{matrix}1 & -1 \\2 & 3 \\\end{matrix} \right ]$

d) $\left [ \begin{matrix}2 & 3 \\-1 & 1 \\\end{matrix} \right ]$

3. (𝑏𝐴) 𝑇 is equal to

a) $\left [ \begin{matrix}-2 & -4 \\2 & -6 \\\end{matrix} \right ]$

b) $\left [ \begin{matrix}-2 & 2 \\-4 & -6 \\\end{matrix} \right ]$

c) $\left [ \begin{matrix}-2 & 2 \\-6 & -4 \\\end{matrix} \right ]$

d) $\left [ \begin{matrix}-6 & -2 \\2 & 4 \\\end{matrix} \right ]$

4. AC−𝐵𝐶 is equal to

a) $\left [ \begin{matrix}-4 & -6 \\-4 & 4 \\\end{matrix} \right ]$

b) $\left [ \begin{matrix}-4 & -4 \\4 & -6 \\\end{matrix} \right ]$

c) $\left [ \begin{matrix}-4 & -4 \\-6 & 4 \\\end{matrix} \right ]$

d) $\left [ \begin{matrix}-6 & 4 \\-4 & -4 \\\end{matrix} \right ]$

5. (𝑎 + 𝑏)𝐵 is equal to

a) $\left [ \begin{matrix}0 & 8 \\10 & 2 \\\end{matrix} \right ]$

b) $\left [ \begin{matrix}2 & 10 \\8 & 0 \\\end{matrix} \right ]$

c) $\left [ \begin{matrix}8 & 0 \\2 & 10 \\\end{matrix} \right ]$

d) $\left [ \begin{matrix}2 & 0 \\8 & 10 \\\end{matrix} \right ]$

 Q No. Option Answer 1 c $\left [ \begin{matrix}7 & 2 \\1 & 6 \\\end{matrix} \right ]$ 2 a $\left [ \begin{matrix}1 & 2 \\-1 & 3 \\\end{matrix} \right ]$ 3 b $\left [ \begin{matrix}-2 & 2 \\-4 & -6 \\\end{matrix} \right ]$ 4 c $\left [ \begin{matrix}-4 & -4 \\-6 & 4 \\\end{matrix} \right ]$ 5 c $\left [ \begin{matrix}8 & 0 \\2 & 10 \\\end{matrix} \right ]$

Case study based questions

Chapter - 6 Class XII

Application of Derivatives

In the PDF given below there are six case study based questions with detailed explanation of the solutions.

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Case study based questions

Chapter -13 Class XII

Probability

The reliability of a COVID PCR test is specified as follows:

Of people having COVID, 90% of the test detects the disease but 10% goes undetected.

Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/her as COVID positive.

Based on the above information, answer the following

1) What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually having COVID?

a) 0.001

b) 0.1

c) 0.8

d) 0.9

2) What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually not having COVID’?

a) 0.01

b) 0.99

c) 0.1

d) 0.001

3) What is the probability that the ‘person is actually not having COVID?

a) 0.998

b) 0.999

c) 0.001

d) 0.111

4) What is the probability that the ‘person is actually having COVID given that ‘he is tested as COVID positive’?

a) 0.83

b) 0.0803

c) 0.083

d) 0.089

5) What is the probability that the ‘person selected will be diagnosed as COVID positive’?

a) 0.1089

b) 0.01089

c) 0.0189

d) 0.189

 Q No. Option Answer 1 d 0.9 2 a 0.01 3 b 0.999 4 c 0.083 5 b 0.01089

In the PDF given below there are eight case study based questions with detailed explanation of the solutions.

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