CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set 03

Case Study Based Questions

I. Your friend Veer wants to participate in a 200 m race. Presently, he can run 200 m in 51 seconds and during each day practice it takes him 2 seconds less. He wants to do in 31 seconds.

Question. Which of the following terms are in AP for the given situation?
(a) 51, 53, 55, ...
(b) 51, 49, 47, ...
(c) –51, –53, –55, ...
(d) 51, 55, 59, …
Answer : B

Question. What is the minimum number of days he needs to practice till his goal is achieved?
(a) 10
(b) 12
(c) 11
(d) 9
Answer : C

Question. Which of the following term is not in the AP of the above given situation?
(a) 41
(b) 30
(c) 37
(d) 39
Answer : B

Question. If nth term of an AP is given by an = 2n + 3 then common difference of an AP is
(a) 2
(b) 3
(c) 5
(d) 1
Answer : A

Question. The value of x, for which 2x, x + 10, 3x + 2 are three consecutive terms of an AP is
(a) 6
(b) – 6
(c) 18
(d) –18
Answer : A
 

II. India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.

Question. The production during first year is
(a) 3000 TV sets
(b) 5000 TV sets
(c) 7000 TV sets
(d) 10000 TV sets
Answer : B

Question. The production during 8th year is
(a) 10500
(b) 11900
(c) 12500
(d) 20400
Answer : D

Question. The production during first 3 years is
(a) 12800
(b) 19300
(c) 21600
(d) 25200
Answer : C

Question. In which year, the production is 29,200?
(a) 10th year
(b) 12th year
(c) 15th year
(d) 18th year
Answer : B

Question. The difference of the production during 7th year and 4th year is
(a) 6600
(b) 6800
(c) 5400
(d) 7200
Answer : A

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): Common difference of the AP: –5, –1, 3, 7, ... is 4.
Reason (R): Common difference of the AP : a, a + d, a + 2d, ... is given by d = 2^nd term – 1^st term.
Answer : A

Question. Assertion (A): If n^th term of an AP is 7 – 4n, then its common difference is – 4.
Reason (R): Common difference of an AP is given by d = a_n+1 – a_n.
Answer : A

Question. Assertion (A): Common difference of an AP in which a₂₁ – a₇ = 84 is 14.
Reason (R): n^th term of an AP is given by a_n = a + (n – 1) d.
Answer : D

Very Short Answer Type Questions

Question. If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20^th term.
Answer : 200

Question. Which term of the AP : 3, 8, 13, 18, . . . ,is 78?
Answer : 16^th term

Question. Find the sum of the first 15 multiples of 8.
Answer : 960

Question. Determine the AP whose third term is 16 and the 7^th term exceeds the 5^th term by 12.
Answer : 4, 10, 16, 22, . . .

Question. Find the number of terms in the AP : 7, 13, 19, . . . , 205
Answer : 34

Question. The sum of the 4^th and 8^th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Answer : –13, –8, –3

Arithmetic Progression

Question. If 5 times the 5^th term of an AP is equal to 10 times the 10th term, show that its 15th term is zero.
Answer : Let 1st term = a and common difference = d.
a₅ = a + 4d, a₁₀ = a + 9d
According to the question, 5 × a₅ = 10 × a₁₀
=> 5(a + 4d) = 10(a + 9d)
=> 5a + 20d = 10a + 90d a = -14d
Now, a15 = a + 14d
=> a₁₅ = -14d + 14d = 0. 

Please click the link below to download CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set C