Case Study III

200 logs are stacked in the following manner:
20 logs in the bottom row, 19 in the next row, 18 in the next row and so on.

Based on this information, answer the following questions:

1. In how many rows these 200 logs are placed?
   (a) 25
   (b) 20
   (c) 16
   (d) 14

2. The number of logs in the top row is:
   (a) 1
   (b) 5
   (c) 3
   (d) 8

3. The number of logs in the 8th row from the bottom is:
   (a) 14
   (b) 11
   (c) 12
   (d) 13

4. Total number of logs in the first six rows from the bottom is:
   (a) 105
   (b) 95
   (c) 85
   (d) 75

5. The number of logs in the 5th row from the top is:
   (a) 8
   (b) 9
   (c) 7
   (d) 10

Assertion (A): The sum of first n terms of the A.P. −1, 5, 11, … is 3n² − 4n.

Reason (R): The sum of first n terms of an A.P. is given by S_n = $\dfrac{n}{2}$ [2a + (n − 1)d].

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Assertion (A): For an A.P., T₂₂ = 149 and d = 7. Then S₂₂ is 1661.

Reason (R): The sum of first n terms of an A.P. is given by S_n = $\dfrac{n}{2}[2a − (n − 1)d]$.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Assertion (A): If the sum of first n terms of an A.P. is given S_n = 2n² − n, then its nth term is 4n + 3.

Reason (R): The nth term (t_n) of an A.P. is given by S_n − S_{n + 1}.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false