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NCERT Exemplar · Class 11 Mathematics Mathematical Reasoning

37 questions · 37 still being checked

This chapter is from the older syllabus and is not in the current NCERT textbook, so you may skip it.

EXERCISE 14.3 31–37 (part 4 of 4)

  1. Choose the correct answer out of the four options given against each of the Exercises $\displaystyle 17$ to $\displaystyle 36$ (M.C.Q.).

    Exercise 31

    The statement "If x2\displaystyle x^2 is not even, then x\displaystyle x is not even" is converse of the statement
    (A)
    If x2\displaystyle x^2 is odd, then x\displaystyle x is even.
    (B)
    If x\displaystyle x is not even, then x2\displaystyle x^2 is not even.
    (C)
    If x\displaystyle x is even, then x2\displaystyle x^2 is even.
    (D)
    If x\displaystyle x is odd, then x2\displaystyle x^2 is even.

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    NCERT’s answer
    B
    (B) If \(\displaystyle x\) is not even, then \(\displaystyle x^2\) is not even.The converse of \(\displaystyle p \Rightarrow q\) is \(\displaystyle q \Rightarrow p\). The given statement is\[\sim(x^2 \text{ even}) \Rightarrow \sim(x \text{ even}) \]Its converse is\[\sim(x \text{ even}) \Rightarrow \sim(x^2 \text{ even}) \]Answer: (B)

  2. Exercise 32

    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 is not in India.

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    NCERT’s answer
    A
    (A) If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.Let \(\displaystyle p\): Chandigarh is capital of Punjab; \(\displaystyle q\): Chandigarh is in India.\[p \Rightarrow q \quad \text{(given)} \]\[\sim q \Rightarrow \sim p \quad \text{(contrapositive)} \]Answer: (A)

  3. Exercise 33

    Which of the following is the conditional p→q\displaystyle p \rightarrow q ?
    (A)
    q\displaystyle q is sufficient for p\displaystyle p.
    (B)
    p\displaystyle p is necessary for q\displaystyle q.
    (C)
    p\displaystyle p only if q\displaystyle q.
    (D)
    if q\displaystyle q, then p\displaystyle p.

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    NCERT’s answer
    C
    (C) \(\displaystyle p\) only if \(\displaystyle q\).\[p \rightarrow q \;\equiv\; \text{if } p, \text{ then } q \;\equiv\; p \text{ only if } q \] \[\text{(A) } q \text{ is sufficient for } p \;\equiv\; q \rightarrow p \] \[\text{(B) } p \text{ is necessary for } q \;\equiv\; q \rightarrow p \] \[\text{(D) if } q, \text{ then } p \;\equiv\; q \rightarrow p \](A), (B) and (D) are the converse.

  4. Exercise 34

    The negation of the statement "The product of 3\displaystyle 3 and 4\displaystyle 4 is 9\displaystyle 9" is
    (A)
    It is false that the product of 3\displaystyle 3 and 4\displaystyle 4 is 9.
    (B)
    The product of 3\displaystyle 3 and 4\displaystyle 4 is 12.
    (C)
    The product of 3\displaystyle 3 and 4\displaystyle 4 is not 12.
    (D)
    It is false that the product of 3\displaystyle 3 and 4\displaystyle 4 is not 9.

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    NCERT’s answer
    A
    (A) It is false that the product of $\displaystyle 3$ and $\displaystyle 4$ is 9.
    Let \(\displaystyle p\): the product of $\displaystyle 3$ and $\displaystyle 4$ is 9.
    \[\sim p \;:\; \text{It is false that the product of 3 and 4 is 9} \]
    \[\text{(D)} \;:\; \sim(\sim p) \equiv p \]
    (D)
    restates \(\displaystyle p\); (B) and (C) are about a different number, not a denial of \(\displaystyle p\).

  5. Exercise 35

    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

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    NCERT’s answer
    C
    (C)Let \(\displaystyle p\): a natural number is greater than zero.
    \[\text{(A)} \;:\; \sim p \]
    \[\text{(B)} \;:\; \sim p \]
    \[\text{(C)} \;:\; \sim(\sim p) \equiv p \]
    (C)
    is \(\displaystyle p\) itself, not its negation.

  6. Exercise 36

    Which of the following statement is a conjunction ?
    (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.

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    (B) Both Ram and Shyam are tall.\[\text{Ram is tall} \;\wedge\; \text{Shyam is tall} \]Each component is a statement on its own. In (A) and (C), "friends" and "enemies" relate the two people to each other and cannot be split into two statements.

  7. Exercise 37

    State whether the following sentences are statements are not :
    (i)
    The angles opposite to equal sides of a triangle are equal.
    (ii)
    The moon is a satellite of earth.
    (iii)
    May God bless you!
    (iv)
    Asia is a continent.
    (v)
    How are you?

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    NCERT’s answer
    (i), (ii) and (iv) are statement; (iii) and (v) are not statements.
    A sentence is a statement if it is definitely true or definitely false.\[\text{(i)} \;\; \text{statement (true)} \] \[\text{(ii)} \;\; \text{statement (true)} \] \[\text{(iii)} \;\; \text{not a statement (a wish)} \] \[\text{(iv)} \;\; \text{statement (true)} \] \[\text{(v)} \;\; \text{not a statement (a question)} \]Answer: (i), (ii) and (iv) are statements; (iii) and (v) are not.