Teachoo Quiz

Assertion Reasoning Quiz

Chapter 8 - Predicting What Comes Next: Exploring Sequences & Progress | 8 questions | about 6 minutes

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Question 1 of 8
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Question 1 of 8
Assertion: A taxi charges a fixed booking fee of ₹200 and ₹40 per kilometre. The fares for journeys of \(1,2,3,\ldots\) km form the AP \(240,280,320,\ldots\), whose \(n\)th term is \(200+40n\).
Reason: Increasing the journey by one kilometre increases the fare by the constant amount ₹40.
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Question 2 of 8
Assertion: The difference between the sixth and fifth square numbers is \(11\).
Reason: For every natural number \(n\), \(n^2-(n-1)^2=2n-1\), which is an odd number.
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Question 3 of 8
Assertion: In the GP \(2,6,18,54,\ldots\), the number \(4374\) is the \(8\)th term.
Reason: The sequence has the constant common difference \(4\).
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Question 4 of 8
Assertion: The number \(172\) is the \(35\)th term of the sequence \(t_n=5n-3\).
Reason: Solving \(5n-3=172\) gives \(n=\dfrac{175}{5}=35\), which is a natural number.
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Question 5 of 8
Assertion: If a sequence has the explicit rule \(t_n=4n+1\), then \(t_{100}\) can be found without calculating \(t_1,t_2,\ldots,t_{99}\).
Reason: An explicit rule gives each term only after all the preceding terms have been calculated.
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Question 6 of 8
Assertion (A): If the terms 5, 15, 45, 135 ... are in GP, then the ratio of the 10th term to the 9th term is 3.
Reason (R): In a Geometric Progression, the ratio of any term to its immediately preceding term is constant throughout the sequence.
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Question 7 of 8
Assertion: A ball is dropped from a height of \(80\) m and rises to \(60\%\) of its previous height after each bounce. Its height after the fifth bounce is \(6.2208\) m.
Reason: The successive bounce heights form an arithmetic progression because the ball loses \(40\%\) of its height each time.
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Question 8 of 8
Assertion: In a Sierpiński triangle, Stage \(4\) contains \(81\) black triangles and has shaded area \(\left(\dfrac{3}{4}\right)^4\) square units when the Stage \(0\) area is \(1\) square unit.
Reason: A fractal is a pattern that repeats itself at different scales.
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