Class 11th Applied Mathematics - Mathematical Reasoning Case Study Questions and Answers 2022 - 2023
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Mathematical Reasoning Case Study Questions With Answer Key
11th Standard CBSE
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Reg.No. :
Applied Mathematics
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In a class of few students, teacher give students fewcode and ask them questions related to those codes. Codes are: # $ @: Dust is harmful; @!%: harmful object kill; #*%: Dust can kill; 123: DOG; 59: For; 547: Lungs.
On the basis of this information, teacher ask following questions:
(i) What is the code for Dust in this language ?(a) # (b) $ (c) ! (d) @ (ii) What is the code for kill in this code language ?
(a) # (b) % (c) ! (d) @ (iii) What is the code for Dust kill DOG?
(a) # @ 123 (b) # % 123 (c) $ % 123 (d) # $ 123 (iv) What is the code for "Dust is harmful For Lungs"
(a) # $ @ 59 547 (b) # $ 59 @ 547 (c) # $ ! 59 547 (d) # ! @ 59 547 (v) What is code for "Dust kill" ?
(a) %$ (b) ! % (c) # % (d) ! $ -
Teacher asked students about family relationship questions. Teacher states that "In a house there are six members A, B, C, D, E and F. They are related to each other in some manner".
On the basis of this information answer the following questions.
(i) A is B’s sister. C is B’s mother. D is C’s father. E is D’s mother. Then, how is A related to D?(a) Grand father (b) Grand daughter (c) Grand mother (d) Daughter (ii) A and B are a married couple, A being the male member. D is the only son of C, who is the brother of A. E is the sister of D. B is the daughter-in-law of F, whose husband has died. How is E related to C.
(a) Sister (b) daughter (c) Cousin (d) Mother (iii) All the six members of a family A, B, C, D, E and F are travelling together. B is the son of C but C is not the mother of B. A and C are a married couple. E is the brother of C. D is the daughter of A. F is the brother of B. Who is the mother of B ?
(a) D (b) F (c) B (d) A (iv) Pointing to a photograph, A tells E, "I am the only daughter of this lady and her son is your maternal uncle." How is the A related to E’s father.
(a) Sister-in-law (b) Wife (c) sister (d) mother (v) A girl introduced a boy as the son of the daughter of the father of her uncle. The boy is girl’s
(a) Brother (b) Son (c) Uncle (d) Son-in-law -
Kuldeep, Pravesh, Manjeet, and Saurabh's group of friends went for a picnic. When they reached the picnic spot the whether was clear and Sun was shining. After one hour they saw weather was suddenly changed and it was totally cloudy.
On the basis of this information answer the following questions:
(i) It will rain today. This type of statement is called(a) simple statement (b) compound statement (c) negative statements (d) none of these (ii) Which of the following is mathematically acceptable statement ?
(a) It will rain today (b) Where is Ramesh? (c) Delhi is capital of India (d) Who are you (iii) Saurabh states that " If it rains, then metro services will stop".This type of statement is called
(a) simple statement (b) compound statement (c) open statement (d) none of these (iv) Kuldeep states "It will rain today ". The negation of this statement is
(a) Will it rain today? (b) It may rain today (c) Perhaps it may rain today (d) It will not rain today (v) If Pravesh gives a statement A: "It will not rain today" which is true and if Manjeet gives a statement B: "I am the prime minister of India" which is false. What will be the resultant of the statement A ∧ B?
(a) False (b) True (c) Data Insufficient -
Ashish, Tarun, Arshad and Varun went to attend republic day parade. They saw Air force planes showing stunts in the sky.
On the basis of this information answer the following questions:
(i) Ashish states that "Planes may meet with accident". This statement is a mathematically acceptable statement.(a) True (b) False (c) none of these (ii) Mathematical symbol for the word "or" is
(a) ∨ (b) ∧ (c) ∪ (d) ∩ (iii) There exists fighter planes, whose speeds are more than 1000 km/hr. Such statements in which phrases like there exists come are called
(a) Quantifiers (b) Verbs (c) Noun (d) Adjective (iv) Tarun states that "if the speed of all the planes are not same, then they won't be able to fly parallel". This sentence is called
(a) Simple statement (b) Open statement (c) Compound Statement (d) None of these (v) Planes are flying at equidistant from each other, they are forming a parallelogram in the sky. The components of this compound statement are
(a) p: Planes are flying at equidistant from each other.
q: They are forming a parallelogram in the sky.(b) p: Planes are flying at equal distances.
q: They are forming a parallelogram.(c) p: Planes are at equidistant.
q: They are forming a quadrilateral called parallelogram.(d) p: Planes flying in the air forming a parallelogram.
q: Planes are at equal distance. -
Statement I: "There exists a number which is not natural". In this statement. "There exists" is a quantifier.
Statement II: In Mathematics, we come across many mathematical statements containing phrases "There exists" or "For all" or "For every". These phrases are called quantifiers.
Codes:
(a) Both I and II are true and II is a correct explanation for I.
(b) Both I and II are true, but II is not correct explanation for I.
(c) I is true, but II is false.
(d) I is false, but II is true. -
Statement I: It is raining today and we can't go outside. It is a compound statement.
Statement II: If any two simple statements combined by the word ’and’, then it form a compound statement.
Codes:
(a) Both I and II are true and II is a correct explanation for I.
(b) Both I and II are true, but II is not correct explanation for I.
(c) I is true, but II is false.
(d) I is false, but II is true.
Case Study
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Answers
Mathematical Reasoning Case Study Questions With Answer Key Answer Keys
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(i) (a): #
Dust is harmful: # $ @
Dust can kill : # * %
So, common code is the code for 'Dust' i.e., #
(ii) (b): %
Harmful object kill% @ ! %
Dust can kill% # * %
Thus, common code is the code for 'kill' i.e ., %
(iii) (b): # % 123
Code for 'Dust': #
Code for 'Kill' %
Code for 'DOG': 123
(iv) (a): # $ @ 59 547
Dust is harmful% # $ @
harmful object kill: @ ! %
So, code for 'harmful: @ and code for 'is': $; code for 'For': 59; code for Lungs:123
(v) (c): # %
Code for Dust: #
Code for kill: % -
(i) (b): Grand daughter
A is the sister of B and B is the daughter of C. So, A is the daughter of C. Also, D is the father of C. So, A is the granddaughter of D.
(ii) (b): Daughter
A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died that means F is the mother of A.
(iii) (d): A
B is the son of C but C is not the mother of B means C is the father of B. A is married to C means A is the mother of B. F is brother of B means F is son of A and C. D is daughter of A means D is daughter of A and C. Therefore, A is the mother of B.
(iv) (b): Wife
Clearly, the A’s brother is E’s maternal uncle. So, A is E’s mother or his father ’s wife.
(v) (a): Brother
Daughter of uncle’s father— Uncle’s sister— Mother; Mother ’s son— Brother -
(i) (a): simple statement
(ii) (c): Delhi is capital of India
(iii) (b): compound statement
Here, the statement is formed by combining two simple statements therefore it is compound statement.
(iv) (d): It will not rain today
(v) (a): False.
The resultant of A ∧ B = false. -
(i) (a): False
This statement is not mathematically acceptable statement.
(ii) (a): ∨
(iii) (a):Quantifiers
Statements containing phrases "There exists" or "For all" or "For every" is called quantifiers Such statements are called a quantifier.
(iv) (c): Compound Statement
Since the two sentences are connected with if and then, therefore this sentence is compound sentence.
(v) (a): p: Planes are flying at equidistant from each other.
q: They are forming a parallelogram in the sky.
The components of this compound statement are p: Planes are flying at equidistant from each other. q: They are forming a parallelogram in the sky. -
(a) Statement I and Statement II both are true, Statement II is the correct explanation of statement I.
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(a) Both statements are true and Statement II is correct explanation of Statement I.
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