Assertion Reasoning Quiz

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.

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.

Assertion (A): The sequence 3, -6, 12, -24, ... is a geometric progression.
Reason (R): The common ratio of this given sequence is 2.

Assertion: The \(23\)rd term of the AP \(11,7,3,-1,\ldots\) is \(-77\).
Reason: An arithmetic progression may have a negative common difference.

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.

Assertion (A): In the Sierpiński square carpet, the number of red squares at Stage 3 is 512.
Reason (R): The number of red squares at Stage \(n\) follows the geometric progression rule \(8^n\).

Assertion (A): If the terms of a geometric progression are plotted on a graph (position number on x-axis, term value on y-axis), the points lie on a straight line.
Reason (R): The explicit formula for the \(n^{th}\) term of an Arithmetic Progression is a linear equation in \(n\), given by \(t_n = a + (n-1)d\).