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Maths MCQ Class 11 Ch-9 | Sequence & Series
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Mathematics
SEQUENCE AND SERIES
MCQ | Class 11 | Chapter 9
Multiple Choice Questions (MCQ)
MCQ Based on the ARITHMATIC PROGRESSION (AP).
MCQ Based on the GEOMETRIC PROGRESSION (GP)
MCQ Based on the ARITHMATIC MEAN (AM) AND GEOMETRIC MEAN (GM).
Features- In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
- Solution Hints are also given to some difficult problems.
- Each MCQ contains four options from which one option is correct.
- On the right hand side column of the pdf Answer option is given.
Action Plan
- First of all students should Learn and write all basic points and Formulas related to the Continuity and Differentiability.
- Start solving the NCERT Problems with examples.
- Solve the important assignments on the SEUENCE AND SERIES Chapter 9 Class XI.
- Then start solving the following MCQ.
MCQ | CHAPTER 9 | CLASS 11
SEQUENCE AND SERIES.
Q 1) If a, b, c are in AP then
(a) b = a + c
(b) 2b = a + c
(c) b² = a + c
(d) 2b² = a + c
Ans: b
Q 2) What is the nth term of an A.P.?
a) an = a + (n - 1) d
b) an = a + (n) d
c) an = arn-1
d) an = arn
Ans: a
a) 12
b) 21
c) 22
d) 25
a) 2
b) 3
c) 5
d) 6
a) 0
b) - 2
c) - 6
d) – 9
a) 4, 8, 12, 16
b) 5, 9, 13, 17
c) 4, 10, 15, 19
d) 6, 10, 14, 18
Q 7) If two numbers are 2 and 6 then find their arithmetic mean.
a) 3
b) 4
c) 5
d) 8
a) 4 : 5
b) 5 : 4
c) 9 : 31
d) 31 : 9
a) 10
b) 11
c) 12
d) 14
Q 10) If 1/(b + c), 1/(c + a), 1/(a + b) are in AP then
(a) a, b, c are in AP
(b) a², b², c² are in AP
(c) 1/1, 1/b, 1/c are in AP
(d) None of these
Ans: b
Given, 1/(b + c), 1/(c + a), 1/(a + b)
⇒ 2/(c + a) = 1/(b + c) + 1/(a + b)
⇒ a², b², c² are in AP
(a) 3557
(b) 3775
(c) 3757
(d) 3575
Ans: b
Solution
Given, AP is 2, 5, 8, …..up to 50
Now, first term a = 2
common difference d = 5 – 2 = 3
Number of terms = 50
Now, Sum = (n/2) × {2a + (n – 1)d}
= (50/2) × {2 × 2 + (50 – 1)3}
= 25 × {4 + 49 × 3}
= 25×(4 + 147)
= 25 × 151 = 3775
(a) 31/24
(b) 31/48
(c) 24/31
(d) 48/31
Ans: b
⇒ 2k = 2/3 + 5/8
⇒ 2k = 31/24
⇒ k = 31/48
So, the value of k is 31/48
(a) 228
(b) 74
(c) 740
(d) 1090
Ans: c
Solution
Given the third term of an A.P. is 7 and its 7th term is 2 more than three times of its third term
⇒ a + 2d = 7 ………….. (1)
and
3(a + 2d) + 2 = a + 6d
⇒ 3×7 + 2 = a + 6d
⇒ 21 + 2 = a + 6d
⇒ a + 6d = 23 ………….. (2)
From equation 1 – 2, we get
4d = 16 ⇒ d = 16/4 ⇒ d = 4
From equation 1, we get
a + 2×4 = 7 ⇒ a + 8 = 7 ⇒ a = -1
Now, the sum of its first 20 terms
= (20/2) × {2 × (- 1) + (20 - 1) × 4} = 10 × {- 2 + 19 × 4)}
= 10 × {- 2 + 76)} = 10 × 74 = 740
(a) 10
(b) 12
(c) 11
(d) 13
Ans: c
⇒ (2n/2) × {2 × 2 + (2n - 1) 3} = (n/2) × {2 × 57 + (n - 1)2}
⇒ n × {4 + 6n – 3} = (n/2) × {114 + 2n – 2}
⇒ 6n + 1 = {2n + 112}/2
⇒ 6n + 1 = n + 56
⇒ 6n – n = 56 – 1
⇒ 5n = 55
⇒ n = 55/5
⇒ n = 11
a) 87
b) 88
c) 89
d) 90
Q 16) If sum of p terms of an AP is q and sum of q terms is p then what is the sum of p + q terms
a) 0
b) p - q
c) p + q
d –(p + q)
a) 2
b) 3
c) 1
d) 4
a) 5
b) 6
c) 7
d) 8
a) 26th
b) 27th
c) 28th
d) None of these
a) 40
b) 42
c) 60
d) 63
a) 420
b) 840
c) 140
d) 1680
a) 127
b) 1204
c) 1408
d) 1604
a) n + 1
b) 2n + 4
c) 3n
d) n2 + 3n
Ans: b
a) 6
b) 8
c) 4
d) None of these
a) True
b) False
a) True
b) False
a) 10240
b) 40960
c) 5120
d) 2560
(a) 43
(b) 45
(c) 44
(d) none of these
Ans: b
(a) 1
(b) 2
(c) 3
(d) 4
Q 30) If a sequence is in the form 2x5n then which of the following may be the sequence?
a) Arithmetic progression
b) Geometric Progression
c) Harmonic Progression
d) Special Progression
a) an = a + (n-1)
d
b) an = a + (n) d
c) an = arn-1
d) an = arn
a) na
b) a/ n
c) (n - 1) a
d) (n + 1) a
Ans: a
Explanation
Then sum to n terms becomes na.
a) 95
b) 82
c) 93
d) 97
a) 16
b) 64
c) 128
d) 124
a) 63/32
b) 32/63
c) 26/53
d) 53/26
a) 729
b) 2187
c) 6561
d) 19683
a) 4
b) 5
c) 6
d) 7
a) 2
b) 1/ 2
c) 2 or 1/ 2
d) neither 2 nor 1/2
a) 3
b) 2/3
c) 3/2
d) 6
Ans: b
Explanation:
Product = 27
⇒ (a/r) (a) (ar) = 27
Sum = 21/ 2
⇒ (a / r + a + ar) = 21/2
⇒ a (1 / r + 1 + 1r) = 21/2
⇒ 3 (1 / r + 1 + 1r) = 21/2
⇒ (1 / r + 1 + 1r) = (21/2)/3 = 7/2
⇒ r = 2 and 1/2.
Terms are 3/2, 3, 3 x 2 i.e. 3/2, 3, 6.
Q 40) Which of the following is the geometric mean of 3 and 12 ?
a) 4
b) 6
c) 9
d) 10
a) 256
b) 16
c) 64
d) 128
Ans: a
Explanation:
Let G.P. be 4, G1, G2,
G3, 512.
⇒ a = 4 and t5 = ar4 = 512 (Given)
⇒ 4 x r4 = 512
⇒ r4 = 512/4 = 128 ⇒
r = 4.
G1 = a2 = a r = 4 x 4 = 16.
G2 = G1 x r = 16 x 4 = 64.
G3 = G2 x r = 64 x 4 = 256.
a) 6 and 8
b) 12 and 3
c) 24 and 6
d) 27 and 3
Ans: b
Explanation:
⇒ (a + b)/2 = 15/2 ⇒ a + b = 15.
Also, G.M. of two numbers a and b is
⇒ = 6 ⇒ ab = 36.
For a = 3, b = 12.
For a = 12, b = 3.
So, the two numbers are 3 and 12.
a) A > G
b) A ≥ G
c) G < A
d) G ≤ A
a) 325
b) 365
c) 385
d) 435
a) 1225
b) 1184
c) 1475
d) 1296
a) 91
b) 1284
c) 1183
d) 1092
a) 784
b) 882
c) 928
d) 966
a) 70
b) 490
c) 340
d) 420
a) 55
b) 1185
c) 1240
d) 1385
Q 50) Find the sum of series 63+73+ ………………..…..+203.
a) 43875
b) 83775
c) 43775
d) 43975
a) 279
b) 286
c) 309
d) 409
Q 52) The ratio of the A.M. and G.M. of two positive numbers a and b is 5: 3. Find the ratio of a to b.
a) 9 : 1
b) 3 : 5
c) 1 : 9
d) 3 : 1
Ans: a
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