CBSE Class 10 Arithmetic Progression Printable Worksheet Set B

Case Based MCQs

A. In a flower bed, there are 43 rose plants in the first row, 41 in the second, 39 in the third and so on.

Question. If there are 11 rose plants in the last row, then number of rose required are
(a) 16
(b) 15
(c) 17
(d) 10
Answer : C

Question. Difference of rose plants in 7th row and 13th row is
(a) 11
(b) 12
(c) 13
(d) 14
Answer : B

Question. If there are x rose plants in 15 rose, then x is equal to
(a) 10
(b) 12
(c) 13
(d) 15
Answer : D

Question. The rose plants in 6th row is
(a) 35
(b) 37
(c) 33
(d) 31
Answer : A

Question. The total number of rose plants in 5th and 8th row is
(a) 64
(b) 54
(c) 46
(d) 45
Answer : A

B. The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167.
The sum of the first ten terms of this AP is 235.

Question. Let first term and common difference of an AP be a and d, respectively. Then pair of linear equations for given problem is
(a) 13a + 31d = 167, 2a + 9d = 47
(b) 13a + 31d = 169, 2a + 9d = 45
(c) 12a + 31d = 167, 2a + 9d = 47
(d) 12a + 31d = 169, 2a + 9d = 45
Answer : C

Question. Common difference of given AP is
(a) 5
(b) 7
(c) 9
(d) 11
Answer : A

Question. First term of given AP is
(a) 3
(b) 4
(c) 2
(d) 1
Answer : D

Question. Fourth term of the AP is
(a) 15
(b) 16
(c) 17
(d) 18
Answer : B

Question. Sum of first twenty terms is
(a) 970
(b) 990
(c) 950
(d) 980
Answer : A

C. Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of ` 118000 by paying every month starting with the first installment of ` 1000. If he increases the installment by ` 100 every month, answer the following :

Question. The amount paid by him in 30th installment is
(a) 3900
(b) 3500
(c) 3700
(d) 3600
Answer : A

Question. The amount paid by him in the 30 installments is
(a) 37000
(b) 73500
(c) 75300
(d) 75000
Answer : B

Question. What amount does he still have to pay after 30th installment?
(a) 45500
(b) 49000
(c) 44500
(d) 54000
Answer : C

Question. If total installments are 40, then amount paid in the last installment?
(a) 4900
(b) 3900
(c) 5900
(d) 9400
Answer : A

Question. The ratio of the 1st installment to the last installment is
(a) 1 : 49
(b) 10 : 49
(c) 10 : 39
(d) 39 : 10
Answer : B

D. 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.

Based on the above information, answer the following questions:

Question. Find the production during first year.
(a) 4000 sets
(b) 5000 sets
(c) 6000 sets
(d) 7000 sets
Answer : B

Question. Find the production during 8th year.
(a) 48000 sets
(b) 20400 sets
(c) 43000 sets
(d) None of these
Answer : B

Question. Find the production during first 3 years.
(a) 20000 sets
(b) 25000 sets
(c) 31000 sets
(d) 21600 sets
Answer : D

Question. In which year, the production is ₹ 29200.
(a) 11
(b) 12
(c) 10
(d) 8
Answer : B

Question. Find the difference of the production during 7th year and 4th year.
(a) 5500
(b) 6700
(c) 5400
(d) 6600
Answer : D

E. Your friend Veer wants to participate in a 200 m race. He can currently run that distance in 51 seconds and with each day of 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

Very Short Answer Type Questions

Question. How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Answer : 12

Question. Find the sum of the odd numbers between 0 and 50.
Answer : 625

Question. For what value of k: 2k, k + 10 and 3k + 2 are in AP?
Answer : k+10 = 2𝑘+3𝑘+2/2 = k+10 = 5𝑘+2/2 Also by cross multiplying we get 2(k+10) = 5k+2
2k+20 = 5k+2, 18 = 3k, k = 6

Question. Find the common difference of the AP 1/𝑝, 1−𝑝/𝑝 , 1−2𝑝/𝑝,…
Answer : d = a₂-a₁ = 1−𝑝/𝑝 - 1/𝑝 = 1−𝑝−1/𝑝 = −𝑝/𝑝 = -1

Question. Write first four terms of the AP,when first term is 1.25 and common difference is -0.25.
Answer : a, a+d, a+2d, a+3d = 1.25, 1 ,0.75, 0.50

Question. Find the missing terms in the given AP 2, --------, 26 ------------ SHORT ANSWER 
Answer : a₂  = a1+a3/2 , a₂  = 2+26/2 = 14, d = a₂ - a₁ = 12, a₄ = a₃+d = 26+12 = 38

Question. If the nth term of an AP is 2n+1, then find the sum of its first three terms.
Answer : a_n = 2n+1, a₁ = 2x1+1=3 , a₃ = 2x3+1 = 7, S₃ = 3/2(3+7) = 15

Question. Find the sum of all natural numbers from 1 to 100.
Answer : 𝑛(𝑛+!)/2 = 100(100+!)/2 = 5050

Question. Find the 9th term from the end (towards the first term) of the AP 5, 9, 13, …, 185.
Answer : nth term from the end = l- (n-1)d, where l is the last term.
9^th term from the end = 185-(9-1)4, 185-32 = 153

Question. Find the common difference of an AP in which a₁₈ – a₁₄ = 32
Answer : a₁₈ – a14 = 32.,a+17d-(a+13d) = 32, 4d = 32,d = 32÷4 = 8

Question. The first, second and last terms of an AP are respectively 4, 7 and 31. How many terms are there in the given AP?
Answer : a1 = 4 , a₂ = 7 , an = 31 ,d = a₂- a₁ = 7-4 = 3
31 = 4+(n-1)3,(n-1)3 = 27,n-1 = 9,n = 10

Question. In an AP,if the common difference is -4 and the seventh term is 4,then find thefirst term.
Answer : a₇ = 4,d = -4, a+6d = 4, a+6x-4 = 4, a-24 = 4,a = 28.

Question. Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
(i) – 1.2, – 3.2, – 5.2, – 7.2, . . . (ii) 3, 3 + √2 , 3 + 2 √2 , 3 + 3√2 , . . .
(iii) 0.2, 0.22, 0.222, 0.2222, . . . (iv) 12, 32, 52, 72, . . .
Answer : (i) Yes. d = – 2; – 9.2, –11.2, – 13.2,
(ii) Yes. d = √2 ; 3 + 4 √2 , 3 + 5 √2 , 3 + 6 √2 ,
(iii) No
(iv) No

Question. Subba Rao started work in 1995 at an annual salary of ₹ 5000 and received an increment of ₹ 200 each year. In which year did his income reach ₹ 7000?
Answer : 11^th year

Question. How many multiples of 4 lie between 10 and 250?
Answer : 60

Question. A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, find the value of each of the prizes. 
Answer : Values of the prizes (in Rs) are 160, 140, 120, 100, 80, 60, 40.

Please click on below link to download CBSE Class 10 Arithmetic Progression Printable Worksheet Set B