Practice Questions 4 – Mathematical Reasoning – Class XI
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Question 1 of 15
1. Question
1 point(s)Negation of the statement “All equivalent triangles are isosceles”
CorrectIncorrectHint
P: All equilateral triangles are isosceles.
Some equilateral triangles are not isosceles. -
Question 2 of 15
2. Question
1 point(s)Negation of the statement “Some real numbers are not complex numbers”
CorrectIncorrectHint
P: Some real numbers are not complex numbers.
All real numbers are complex numbers. -
Question 3 of 15
3. Question
1 point(s)Negation of the statement “\(\forall n \in {\text {N}},n + 1 \ge 2\)” is:
CorrectIncorrectHint
P:
are negation of each other. -
Question 4 of 15
4. Question
1 point(s)Negation of the statement “Some quadratic equations have unequal roots” is
CorrectIncorrectHint
P: Some quadratic equations have unequal roots.
All quadratic equations have unequal roots. -
Question 5 of 15
5. Question
1 point(s)“\(\forall x \in {\text{N, }}{x^2}\) + x is an even number”. Find the negation of above statement.
CorrectIncorrectHint
P:
is an even number.
is not an even number. -
Question 6 of 15
6. Question
1 point(s)\(\sim \left[ {p \cap \left( {q \to r} \right)} \right]\) is equal to
CorrectIncorrectHint
![\begin{aligned}\sim \left[ {p \cap \left( {q \to r} \right)} \right] \equiv \sim p \cup \sim \left( {q \to r} \right)\\ \equiv \sim p \cup \left( {q \cap \sim r} \right)\end{aligned}](https://fosterjee.com/wp-content/ql-cache/quicklatex.com-14ea488fdafdb66704ffdc5754fb5021_l3.png "Rendered by QuickLaTeX.com")
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Question 7 of 15
7. Question
1 point(s)\(\sim \left[ {\left( {\sim p \cup q} \right) \cap r} \right]\) is equivalence to
CorrectIncorrectHint
![\begin{aligned}\sim \left[ {\left( {\sim p \cup q} \right) \cap r} \right] \equiv \sim \left( {\sim p \cup q} \right) \cup \sim r\\ \equiv \left[ {\sim \left( {\sim p} \right) \cap \sim q} \right] \cup \sim r\\ \equiv \left[ {p \cap \sim q} \right] \cup \sim r\\ \equiv \left( {p \cup \sim r} \right) \cap \left( {\sim q \cup \sim r} \right)\\ \equiv \left( {p \cup \sim r} \right) \cap \sim \left( {q \cap r} \right)\end{aligned}](https://fosterjee.com/wp-content/ql-cache/quicklatex.com-d8e677ea6f19349e2e2788364811a143_l3.png "Rendered by QuickLaTeX.com")
Hence, the given statement is not equvalence to option 1, 2 and 3. -
Question 8 of 15
8. Question
1 point(s)\(p \cap \left( {q \cup \sim p} \right)\) is equivalence to
CorrectIncorrectHint
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Question 9 of 15
9. Question
1 point(s)\(\left( {p \cap q} \right) \cup \left( {\sim p \cap q} \right) \cup \left( {\sim q \cap r} \right)\) is equivalence to
CorrectIncorrectHint
![\begin{aligned}\left( {p \cap q} \right) \cup \left( {\sim p \cap q} \right) \cup \left( {\sim q \cap r} \right) \equiv \left[ {\left( {p \cup \sim p} \right) \cap q} \right] \cup \left( {\sim q \cap r} \right)\\ \equiv \left[ {T \cap q} \right] \cup \left( {\sim q \cap r} \right)\\ \equiv q \cup \left( {\sim q \cap r} \right)\\ \equiv \left( {q \cup \sim q} \right) \cap \left( { q \cup r} \right)\\ \equiv T \cap \left( { q \cup r} \right)\\ \equiv q \cup r\end{aligned}](https://fosterjee.com/wp-content/ql-cache/quicklatex.com-ee8ea8120597901adecbdf7146c2a287_l3.png "Rendered by QuickLaTeX.com")
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Question 10 of 15
10. Question
1 point(s)\(\sim \left[ {\left( {p \cap q} \right) \to \left( {\sim p \cup r} \right)} \right]\) is equivalence to
CorrectIncorrectHint
![\begin{aligned}\sim \left[ {\left( {p \cap q} \right) \to \left( {\sim p \cup r} \right)} \right] \equiv \left( {p \cap q} \right) \cap \sim \left( {\sim p \cup r} \right)\\ \equiv \left( {p \cap q} \right) \cap \left[ {\sim \left( {\sim p} \right) \cap \sim r} \right]\\ \equiv \left( {p \cap q} \right) \cap \left[ {p \cap \sim r} \right]\end{aligned}](https://fosterjee.com/wp-content/ql-cache/quicklatex.com-a172370abefa71b8015327028aea79ea_l3.png "Rendered by QuickLaTeX.com")
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Question 11 of 15
11. Question
1 point(s)Negation of the statement. ” All students of IIT, Bombay live in the hostal.”
CorrectIncorrectHint
P: All students of IIT, Bombay live in the hostel.
Some students of IIT, Bombay do not live in the hostel. -
Question 12 of 15
12. Question
1 point(s)“\(\exists x \in {\text{R, such that }}{x^2} < x \)". Find the negation of above statement.
CorrectIncorrectHint
P:
.
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Question 13 of 15
13. Question
1 point(s)“Some continuous functions are differentiable.” Find the negation of above statement.
CorrectIncorrectHint
P: Some continuous functions are differentiable.
All continuous functions are not differentiable. -
Question 14 of 15
14. Question
1 point(s)Negation of the preposition\(\left( {q \cup \sim r} \right) \cap \left( {p \cup q} \right)\) is
CorrectIncorrectHint
![\begin{aligned}\sim \left[ {\left( {q \cup \sim r} \right) \cap \left( {p \cup q} \right)} \right] \equiv \sim \left( {q \cup \sim r} \right) \cup \sim \left( {p \cup q} \right)\\ \equiv \left[ {\sim q \cap \sim \left( {\sim r} \right)} \right] \cup \left( {\sim p \cap \sim q} \right)\\ \equiv \left( {\sim q \cap r} \right) \cup \left( {\sim p \cap \sim q} \right)\\ \equiv \left( {\sim q \cap r} \right) \cup \left( {\sim q \cap \sim p} \right)\\ \equiv \sim q \cap \left( {r \cup \sim p} \right)\end{aligned}](https://fosterjee.com/wp-content/ql-cache/quicklatex.com-69a81f4f4bf75e7be43ea04d6c3a8d6f_l3.png "Rendered by QuickLaTeX.com")
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Question 15 of 15
15. Question
1 point(s)Write the negation of the statement. “\( 5 \times 5 = 25 \)”
CorrectIncorrectHint
P:
