AP 10th Class Maths 5th Chapter Arithmetic Progressions Bits

Chapter 5 Arithmetic Progressions Bits for 10th Class AP Board

Multiple Choice Questions (MCQs) :

Question 1.
Which of the following is a term of the sequence 3, 7, 11,… ?
A) 185
B) 186
C) 187
D) 188
Answer:
C) 187

Question 2.
Sum of first n terms of an A.P is 0 one of the terms of the A.P is also ‘0’ if…
A) n is even less than 4
B) n is odd greater than 1
C) n is odd greater than 3
D) n is even less than 6
Answer:
B) n is odd greater than 1

Question 3.
If 9^th term from the end of an A.P is 12^th term from the beginning, then the number of terms is ……………………. .
A) 18
B) 20
C) 19
D) 19
Answer:
B) 20

Question 4.
If the first and 10^th terms of an A.P be known, then the common difference of the A.P can be determined by dividing the difference of the tenth and first terms by ……………… .
A) 9
B) 10
C) 8
D) 7
Answer:
A) 9

Question 5.
If x, \(\frac{1}{2}\), \(\frac{1}{3}\) are in A.P, then x = …………….. .
A) \(\frac{3}{2}\)
B) \(\frac{2}{5}\)
C) \(\frac{2}{3}\)
D) \(\frac{5}{2}\)
Answer:
C) \(\frac{2}{3}\)

Question 6.
If n^th terms of 3, 10, 17,… and 63, 65, 67 are equal then the value of n = ……………. .
A) 43
B) 33
C) 23
D) 13
Answer:
D) 13

Question 7.
If 5^th term of an A.P is (x + y) and second term is (x – y), then first term is ……………… .
A) \(\frac{3 x-5 y}{3}\)
B) \(\frac{5 x-3 y}{5}\)
C) \(\frac{3 x-4 y}{3}\)
D) \(\frac{4 x-3 y}{3}\)
Answer:
A) \(\frac{3 x-5 y}{3}\)

Question 8.
The sum of integers from 1 to 100 that are divisible by 2 (or) 5 is ……………. .
A) 2950
B) 2050
C) 3050
D) 2750
Answer:
C) 3050

Question 9.
The sum of n terms of A.Ps are in the ratio is (4n + 27) : (7n + 1), then the ratio of their 11^th terms is ………………… .
A) 148 : 111
B) 111 : 148
C) 131 : 152
D) 152 : 131
Answer:
B) 111 : 148

Question 10.
The sum of first 15 multiples is ……………… .
A) 860
B) 760
C) 960
D) 660
Answer:
C) 960

Question 11.
If (8x + 4), (6x – 2) and (2x + 7) are in A.P., then x = ……………. .
A) \(\frac{7}{2}\)
B) \(\frac{15}{2}\)
C) \(\frac{9}{2}\)
D) \(\frac{13}{2}\)
Answer:
B) \(\frac{15}{2}\)

Question 12.
If a is the first term and l is the last term, then sum of first n terms is
A) S_n = \(\frac{n}{2}\)(a – l)
B) S_n = \(\frac{a}{2}\)(n – l)
C) S_n = \(\frac{n}{2}\)(a + l)
D) S_n = \(\frac{l}{2}\)(a + n)
Answer:
C) S_n = \(\frac{n}{2}\)(a + l)

Question 13.
If the sum of first 15 terms of the A.P whose n^th term 3 + 4n is …………….. .
A) 625
B) 525
C) 425
D) 725
Answer:
B) 525

Question 14.
If S_n = (3n² + 2n) in A.P, then n^th term is ………….. .
A) 5n – 1
B) 4n – 1
C) 6n – 1
D) 7n – 1
Answer:
C) 6n – 1

Question 15.
The sum of 18 consecutive natural numbers is a perfect square. The smallest possible value of the sum is ……………. .
A) 225
B) 235
C) 325
D) 335
Answer:
A) 225

Question 16.
In the sum of q terms of an A.P is p and sum of p terms is q, then sum of (p + q) terms is ……………. .
A) p – q
B) -(p – q)
C) -(p + q)
D) p + q
Answer:
C) -(p + q)

Question 17.
If four numbers in A.P are such that greatest number is 4 times the least and their sum is 50, then the numbers
are ……………… .
A) 6, 12, 24
B) 5, 10, 15, 20
C) 8, 13, 17, 32
D) 4, 12, 16, 18
Answer:
B) 5, 10, 15, 20

Question 18.
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k = ……………….. .
A) \(\frac{2 a b}{3(b-a)}\)
B) \(\frac{3 a b}{2(b-a)}\)
C) \(\frac{\mathrm{ab}}{\mathrm{b}+\mathrm{a}}\)
D) \(\frac{\mathrm{ab}}{\mathrm{b}-\mathrm{a}}\)
Answer:
B) \(\frac{3 a b}{2(b-a)}\)

Question 19.
If \(\frac{4}{5}\), a, 2 are three consecutive terms of A.P, then the value of a is …………….. .
A) \(\frac{7}{5}\)
B) \(\frac{5}{7}\)
C) \(\frac{3}{7}\)
D) \(\frac{7}{3}\)
Answer:
A) \(\frac{7}{5}\)

Question 20.
If the sum of first n even natural numbers is equal to p times the sum of first n odd natural numbers, then
P = …………….. .
A) \(\frac{\mathrm{n}}{\mathrm{n}+1}\)
B) \(\frac{\mathrm{n}+1}{\mathrm{n}}\)
C) \(\frac{2 n+1}{n}\)
D) \(\frac{n}{2 n+1}\)
Answer:
B) \(\frac{\mathrm{n}+1}{\mathrm{n}}\)

Question 21.
The common difference of the A.P :
\(\frac{1}{2 b}\), \(\frac{1-6 b}{2 b}\), \(\frac{1-12 b}{2 b}\), ….. is …………………. .
A) 2b
B) -2b
C) 3
D) -3
Answer:
D) -3

Question 22.
The sum of first 20 odd natural numbers is ………………. .
A) 100
B) 210
C) 400
D) 420
Answer:
C) 400

Question 23.
The n^th term of an A.P the sum of whose n terms is S_n is ………….. .
A) S_{n + 1} – S_n
B) S_n – S_{n + 1}
C) S_n – S_{n – 1}
D) S_{n + 1} – S_{n – 1}
Answer:
C) S_n – S_{n – 1}

Question 24.
If 18, a, b, -3 are in A.P, then a – b = ………………. .
A) 7
B) 15
C) 10
D) 12
Answer:
A) 7

Question 25.
If \(\frac{5+9+13+\ldots n \text { terms }}{7+9+11+\ldots(n+1) \text { terms }}\) = \(\frac{17}{16}\), then n = ………………. .
A) 5
B) 6
C) 7
D) 8
Answer:
C) 7

Question 26.
If the sum of n terms of two A.P.s are in the ratio (5n + 7): (3n + 5), then the ratio of their n^th terms is …………………. .
A) (3n + 1) : (5n + 1)
B) (5n + 1) : (3n + 1)
C) (3n – 1) : (5n – 1)
D) (5n – 1) : (3n – 1)
Answer:
B) (5n + 1) : (3n + 1)

Question 27.
Sum of n terms of the series √3 + \(\sqrt{12}\) + \(\sqrt{27}\) +… is ……………….. .
A) \(\frac{\mathrm{n}(\mathrm{n}+1)}{\sqrt{2}}\)
B) \(\frac{\mathrm{n}(\mathrm{n}+1)}{\sqrt{3}}\)
C) √2n(n + 1)
D) \(\frac{\sqrt{3} \cdot \mathrm{n}(\mathrm{n}+1)}{2}\)
Answer:
D) \(\frac{\sqrt{3} \cdot \mathrm{n}(\mathrm{n}+1)}{2}\)

Question 28.
The sum of first n odd natural numbers is ……………… .
A) 2n + 1
B) (2n – 1)²
C) 2n²
D) n²
Answer:
D) n²

Question 29.
The sum of first n even natural numbers is ……………. .
A) \(\frac{\mathrm{n}(\mathrm{n}+1)}{2}\)
B) 2n²
C) n (n + 1)
D) \(\frac{\mathrm{n}(\mathrm{n}+1)}{3}\)
Answer:
C) n (n + 1)

Question 30.
The value of a₃₀ – a₁₀ for the A.P is 4, 9, 14, 19, ………………. .
A) 100
B) 200
C) 150
D) 50
Answer:
A) 100

Question 31.
The sum of first 30 natural numbers is ……………. .
A) 600
B) 700
C) 800
D) 900
Answer:
D) 900

Question 32.
The sum of first 50 natural numbers is ……………….. .
A) 2500
B) 1600
C) 2550
D) 1650
Answer:
C) 2550

Question 33.
Sum of n terms of the series √2 + √8 + \(\sqrt{18}\) + \(\sqrt{32}\) +… is ……………… .
A) \(\frac{\mathrm{n}(\mathrm{n}+1)}{\sqrt{2}}\)
B) \(\frac{\mathrm{n}(\mathrm{n}-1)}{\sqrt{2}}\)
C) 2n (n + 1)
D) 2n (n – 1)
Answer:
A) \(\frac{\mathrm{n}(\mathrm{n}+1)}{\sqrt{2}}\)

Question 34.
Sum of all odd numbers between 100 and 200 is …………………. .
A) 7000
B) 7500
C) 8000
D) 8500
Answer:
B) 7500

Question 35.
The number of two digit numbers are divisible by 3 is ……………… .
A) 30
B) 25
C) 35
D) 40
Answer:
A) 30

Question 36.
The common difference of an Arithmetic Progression, whose 3^rd term is 5 and 7^th term is 9, is …………….. .
A) 1
B) 2
C) 3
D) 4
Answer:
A) 1

Question 37.
The common difference of an Arithmetic Progression in which a₂₅ a₁₂ = -52 is ………………. .
A) 4
B) -4
C) -3
D) 3
Answer:
B) -4

Question 38.
Which term of the Arithmetic Progres-sion 24, 21, 18, ……………… is the first negative term ?
A) 8^th
B) 9^th
C) 10^th
D) 12^th
Answer:
C) 10^th

Question 39.
In an Arithmetic Progression, 4^th term is 11 and 7^th term is 17, then its common difference is
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2

Question 40.
If the common difference of A.P. is 2, then a₁₀ – a₅ =
A) 5
B) 10
C) 2
D) 20
Answer:
B) 10

Question 41.
If a, b, c are in A.P., then b =
A) \(\frac{a+c}{2}\)
B) a + c
C) \(\sqrt{\mathrm{ac}}\)
D) ac
Answer:
A) \(\frac{a+c}{2}\)

Question 42.
The sum of the first 20 even natural numbers is
A) 5050
B) 55
C) 505
D) 420
Answer:
D) 420

Question 43.
If the n^th term of an arithmetic progression is 4n – 2, then its 10^th term is ………………. .
A) 38
B) 28
C) 42
D) 24
Answer:
A) 38

Question 44.
The 30^th term of the A.P. 10, 7, 4, …………. is …………… .
A) 87
B) 77
C) -77
D) -87
Answer:
C) -77

Question 45.
The number of terms in the AP : 2, 5, 8, …., 32 is ……………. .
A) 9
B) 10
C) 11
D) 32
Answer:
C) 11

Fill in the blanks:

1. Number of terms in the sequence 3, 17, 31, ……., 101 is ________ .
Answer:
8

2. n^th term of A.P is 2n + 5. If any term of the A.P is divided by 2, then the remainder is________ .
Answer:
1

3. n^th term of A.P is 20n + 5 and if consisting of 20 terms. Then its common difference is ________ .
Answer:
20

4. Sum of all two digited odd numbers is ________ .
Answer:
2475

5. If the sum of n terms of an A.P is n², then the common difference is ________ .
Answer:
2

6. Sum of the first 10 term of A.P x – 8, x – 2, x + 4 is________ .
Answer:
10x + 190

7. If the first term in A.P is 2 and the sum of first 5 terms is equal to \(\frac{1}{4}\)^th of the sum of the next five terms, then the sum of first 30 terms is ________ .
Answer:
-2550

8. n^th term of an A.P is ________ .
Answer:
a + (n – 1)d

9. If the sum of n terms of A.P is n² + 13n, then its 13th term is ________ .
Answer:
38

10. If the first term of an A.P is p and its common difference is q, then its 10^th term ________ .
Answer:
p + 9q

11. The first and last terms of an A.P. are 1 and 11. If the sum of the terms is 36. Then the number of terms is ________ .
Answer:
6

12. If the sum of first p term of A.P is ap2 + bp then the common difference is __________ .
Answer:
2a

13. The common difference of the A.P is \(\frac{1}{2 q}\), \(\frac{1-2 \mathrm{qq}}{2 \mathrm{q}}\), \(\frac{1-4 q}{2 q}\) ….. is __________ .
Answer:
-1

14. The number of terms of the A.P. 3, 7, 11, 15, to be taken. So that the sum is 406 is __________ .
Answer:
14

15. The sum of n terms of two A.Ps are in the ratio 9n + 6 : 5n + 9 then the ratio of their 18^th terms is __________ .
Answer:
321 : 179

10th Class Maths Bits