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

(1) Which of the following statement is conjuction?
[A] Ram and Shyam are friends.
[B] Both Ram and Shyam are tall.
[C] Both Ram and Shyam are enemies.
[D] None of the above.
Answer: None of the above.
(2) Which of the following is not a negation of “A natural number is greater than zero”?
[A] A natural number is not greater than zero.
[B] It is false that a natural number is greater than zero.
[C] It is false that a natural number is not greater than zero.
[D] None of the above
Answer: It is false that a natural number is not greater than zero.

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(3) The negation of the statement “The product of 3 and 4 is 9” is
[A] It is false that the product of 3 and 4 is 9.
[B] The product of 3 and 4 is 12.
[C] The product of 3 and 4 is not 12.
[D] It is false that the product of 3 and 4 is not 9.
Answer: It is false that the product of 3 and 4 is 9.
(4) The contrapositive of statement “If Chandigarh is Capital of Punjab, then Chandigarh is in India” is
[A] If Chandigarh is not in India, then Chandigarh is not the Capital of Punjab.
[B] If Chandigarh is in India, then Chandigarh is Capital of Punjab.
[C] If Chandigarh is not Capital of Punjab, then Chandigarh is not Capital of India.
[D] If Chandigarh is Capital of Punjab, then Chandigarh not in India.
Answer: If Chandigarh is not in India, then Chandigarh is not the Capital of Punjab.
(5) The statement “If x2 is not even, then x is not even” is converse of the statement.
[A] If x2 is odd, then x is even.
[B] If x is not even, then x2 is not even.
[C] If x is even, then x2 is even.
[D] If x is odd, then x2 is even.
Answer: If x is not even, then x2 is not even.
(6) The contrapositive of the statement “If p, then q”, is
[A] If q, then p
[B] If p, then ~ q
[C] If ~ q, then ~ p
[D] If ~ p then ~ q
Answer: If ~ q, then ~ p
(7) The converse of the statement “If Sun is not shining, then Sky is filled with clouds” is
[A] If Sky is filled with clouds, then the Sun is not shining.
[B] If Sun is shining, then Sky is filled with clouds.
[C] If Sky is clear, then Sun is shining.
[D] If Sun is not shining, then Sky is not filled with clouds.
Answer: If Sky is filled with clouds, then the Sun is not shining.
(8) The converse of the statement “If x > y, then x + a > y + a” is
[A] If x < y, then x + a < y + a
[B] If x + a > y + a, then x > y
[C] If x < y, then x + a > y + a
[D] If x > y, then x + a < y + a
Answer: If x + a > y + a, then x > y
(9) The contrapositive of the statement “If 7 is greater than 5, then 8 is greater than 6” is
[A] If 8 is greater than 6, then 7 is greater than 5.
[B] If 8 is not greater than 6, then 7 is greater than 5.
[C] If 8 is not greater than 6, then 7 is not greater than 5.
[D] If 8 is greater than 6, then 7 is not greater than 5.
Answer: If 8 is not greater than 6, then 7 is not greater than 5.
(10) The negation of the statement “101 is not a multiple of 3” is
[A] 101 is a multiple of 3.
[B] 101 is a multiple of 2.
[C] 101 is an odd number.
[D] 101 is an even number.
Answer: 101 is a multiple of 3.
(11) The negation of the statement “Rajesh or Rajni lived in Bengaluru” is
[A] Rajesh did not live in Bengaluru or Rajni lives in Bengaluru.
[B] Rajesh live in Bengaluru and Rajni did not live in Bengaluru.
[C] Rajesh did not live in Bengaluru and Rajni did not live in Bengaluru.
[D] Rajesh did not live in Bengaluru or Rajni did not live in Bengaluru.
Answer: Rajesh did not live in Bengaluru and Rajni did not live in Bengaluru.
(12) The negative of the statement “Plants take in CO2 and give out O2” is
[A] Plants do not take in CO2 and do not give out O2.
[B] Plants do not take in CO2 or do not give out O2.
[C] Plants take in CO2 and do not give out O2.
[D] Plants take in CO2 or do not give out O2.
Answer: Plants do not take in CO2 or do not give out O2.
(13) The negation of the statement “72 is divisible by 2 and 3” is
[A] 72 is not divisible by 2 or 72 is not divisible by 3.
[B] 72 is not divisible by 2 and 72 is not divisible by 3.
[C] 72 is divisible by 2 and 72 is not divisible by 3.
[D] 72 is not divisible by 2 and 72 is divisible by 3.
Answer: 72 is not divisible by 2 and 72 is not divisible by 3.
(14) The negation of the statement “7 is greater than 8” is
[A] 7 is equal to 8.
[B] 7 is not greater than 8.
[C] 8 is less than 7.
[D] None of these.
Answer: 7 is not greater than 8.
(15) The negation of the statement “A circle is an ellipse” is
[A] An ellipse is a circle.
[B] An ellipse is not a circle.
[C] A circle is not an ellipse.
[D] A circle is an ellipse.
Answer: A circle is not an ellipse.
(16) The connective in the statement “Earth revolves round the Sun and Moon is a satellite of Earth” is
[A] or
[B] Earth
[C] Sun
[D] and
Answer: and
(17) The connective in the statement ‘2 + 7 > 9 or 2 + 7 < 9’ is
[A] and
[B] or
[C] >
[D] <
Answer: or
(18) Which of the following is not statement?
[A] Smoking is injurious to health.
[B] 2 + 2 = 4.
[C] 2 is only the even prime number.
[D] Come here.
Answer: Come here.
(19) Which of the following is statement?
[A] x is a real number.
[B] Switch of the fan.
[C] 6 is a natural number.
[D] Let me go.
Answer: 6 is a natural number.
(20) Which of the following is the converse of the statement? “If Billu secure good marks, then he will get a bicycle.”
[A] If Billu will not get bicycle, then he will not secure good marks.
[B] If Billu will get a bicycle, then he will secure good marks.
[C] If Billu will get a bicycle, then he will not secure good marks.
[D] If Billu will not get a bicycle, then he will secure good marks.
Answer: If Billu will get a bicycle, then he will secure good marks.

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