NCERT Solutions for class 14 Maths | Chapter 14 - Mathematical Reasoning

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Questions
1 The negation of the statement

“It is raining and weather is cold.” is

A It is not raining and weather is cold.
B It is raining or weather is not cold.
C It is not raining or weather is not cold.
D It is not raining and weather is not cold.

Answer:It is not raining or weather is not cold.
2 Which of the following is a statement?
A Roses are black.
B Mind your own business.
C Be punctual.
D Do not tell lies

Answer:(A) is the correct answer as the sentences in (B), (C) and (D) are neither true nor false. Infect all these sentences are advices.
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3 A sentence is called a mathematically acceptable if it is
A True
B False
C Either true or false
D Neither true nor false

Answer:Either true or false
4 Which of the following is a statement
A x is a real number
B Switch off the fan
C 2 + 2 = 4
D Let me go

Answer:2 + 2 = 4
5 The converse of the statement If a number n is even, then n2 is even is
A If a number n is even, then n2 is even
B If a number n is even, then n2 is not even
C If a number n2 is even, then n is even
D If a number n2 is not even, then n is even

Answer:If a number n2 is even, then n is even
6 If (p or q) is false when
A p is true and q is false
B p is true and q is true
C p is false and q is false
D p is false and q is true

Answer:p is true and q is false
7 p if and only if q is written as
A p => q
B q => p
C p <=> q
D q <=> p

Answer:p <=> q
8 The compound statement with AND is true if all its component statements are
A true
B false
C either true or false
D None of these

Answer:true
9 Which of the following is a compund statement
A Sun is a star
B I am a very strong boy
C There is something wrong in the room
D 7 is both odd and prime number.

Answer:7 is both odd and prime number.
10 If a recipe calls for 2/3 cups of sugar but I only want to make 1/4 of the recipe, how much sugar do I need?
A 2/3
B 1/4
C 1/6
D 1/3

Answer:1/6
11 Which of the following is not a statement
A The product of (-1) and 8 is 8
B All complex number are real number
C Today is windy day
D All of the above

Answer:All of the above
12 If (p or q) is true, then
A p is true and q is false
B p is true and q is true
C p is false and q is true
D All of the above

Answer:All of the above
13 The contrpositive of the statement If you are a citizen of India, then you were born in India is
A If you are not a citizen of India, then you were not born in India
B If you are not a citizen of India, then you were born in India
C If you are a citizen of India, then you were not born in India
D None of these

Answer:If you are not a citizen of India, then you were not born in India
14 Which of the following is a statement
A I will go tomorrow
B She will come today
C 3 is a prime number
D Tomorrow is Friday

Answer:3 is a prime number
15 Which of the following is not a statement
A 8 is less than 6.
B Every set is finite set.
C The sun is a star.
D Mathematics is fun.

Answer:Mathematics is fun.
16 The contrapositive of the statements If you are not a citizen of India, then you were not born in India is
A If you are not a citizen of India, then you were not born in India
B If you are not a citizen of India, then you were born in India
C If you are a citizen of India, then you were not born in India
D If you are a citizen of India, then you were born in India

Answer:If you are a citizen of India, then you were born in India
17 The converse of the statement if a number is divisible by 10, then it is divisible by 5 is
A if a number is not divisible by 5, then it is not divisible by 10
B if a number is divisible by 5, then it is not divisible by 10
C if a number is not divisible by 5, then it is divisible by 10
D if a number is divisible by 5, then it is divisible by 10

Answer:if a number is divisible by 5, then it is divisible by 10
18 The contrapositive of statement p => q is
A q => p
B q => ~p
C ~q => p
D ~q => ~p

Answer:~q => ~p
19 Which of the follwing is not a statement
A Go there
B 2 + 2 = 4
C 2 is the only even prime number.
D Come here

Answer:Come here
20 The contrpositive of the statement If you are a citizen of India, then you were born in India is
A If you are not a citizen of India, then you were not born in India
B If you are not a citizen of India, then you were born in India
C If you are a citizen of India, then you were not born in India
D None of these

Answer:If you are not a citizen of India, then you were not born in India

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