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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

__Mathematics__

__Multiple Choice Questions (MCQ)__

__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__

__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 n^{th} term of an A.P.?

a) a_{n} = a + (n - 1) d

b) a_{n }= a + (n) d

c) a_{n} = ar^{n-1}

d) a_{n} = ar^{n }

Ans: a

^{th}term of the A.P.

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

^{th}terms.

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

^{th}term is 2 more than three times of its third term, then the sum of its first 20 terms is

(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

^{th}and 13

^{th}terms of an AP be 34 and 64 respectively, then its 18

^{th}term is

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)

_{p}= q and S

_{q}= p and then subtract these two

^{2 }- n and its common difference is 6, then its first term is

a) 2

b) 3

c) 1

d) 4

a) 5

b) 6

c) 7

d) 8

^{2}+ 5n then which of its term is 164 ?

a) 26

^{th}

b) 27

^{th}

c) 28

^{th}

d) None of these

^{rd}term of an A.P. is 6 and 5

^{th}term of that A.P. is 12. Then find the 21

^{st}term of that A.P.

a) 40

b) 42

c) 60

d) 63

^{th}term is 120. Find the sum up to 12

^{th}term.

a) 420

b) 840

c) 140

d) 1680

a) 127

b) 1204

c) 1408

d) 1604

^{2 }+ 5n then find general term.

a) n + 1

b) 2n + 4

c) 3n

d) n

^{2 }+ 3n

Ans: b

a) 6

b) 8

c) 4

d) None of these

a) True

b) False

a) True

b) False

^{th}term.

a) 10240

b) 40960

c) 5120

d) 2560

(a) 4^{3}

(b) 4^{5}

(c) 4^{4}

(d) none of these

Ans: b

(a) 1

(b) 2

(c) 3

(d) 4

Q 30) If a sequence is in the form 2x5

^{n}then which of the following may be the sequence?

a) Arithmetic progression

b) Geometric Progression

c) Harmonic Progression

d) Special Progression

^{th}term of a G.P.?

a) a_{n} = a + (n-1)
d

b) a_{n} = a + (n) d

c) a_{n} = ar^{n-1}

d) a_{n} = ar^{n}

a) na

b) a/ n

c) (n - 1) a

d) (n + 1) a

Ans: a

Explanation

Then sum to n terms becomes na.

^{th}term.

a) 95

b) 82

c) 93

d) 97

^{th}term.

a) 16

b) 64

c) 128

d) 124

a) 63/32

b) 32/63

c) 26/53

d) 53/26

^{th}term is 27 and 8

^{th}term is 729. Find its 11

^{th}term.

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

^{3}= 27 ⇒ a = 3

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

^{2}+ r + 1) = (7/2) r

^{2}– (5/2) r +1 = 0

⇒ 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, G_{1}, G_{2},
G_{3}, 512.

⇒ a = 4 and t_{5} = ar^{4} = 512 (Given)

⇒ 4 x r^{4} = 512

⇒ r^{4} = 512/4 = 128 ⇒
r = 4.

G_{1} = a_{2} = a r = 4 x 4 = 16.

G_{2} = G_{1} x r = 16 x 4 = 64.

G_{3} = G_{2} 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

^{2 }+ 2

^{2 }+ 3

^{2 }+ …………… + 10

^{2}.

a) 325

b) 365

c) 385

d) 435

^{3 }+ 2

^{3 }+ 3

^{3 }+ …………… + 8

^{3}.

a) 1225

b) 1184

c) 1475

d) 1296

^{th}term whose n

^{th}term is given by n

^{2}+ 3

^{n}.

a) 91

b) 1284

c) 1183

d) 1092

a) 784

b) 882

c) 928

d) 966

a) 70

b) 490

c) 340

d) 420

^{2}+7

^{2}+…………………..+15

^{2}.

a) 55

b) 1185

c) 1240

d) 1385

Q 50) Find the sum of series 6

^{3}+7

^{3}+ ………………..…..+20

^{3}.

a) 43875

b) 83775

c) 43775

d) 43975

^{2 }+ 3

^{2 }+ 5

^{2 }+ ………………………….. + 11

^{2}.

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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