Please refer to the MCQ Questions for Class 11 Sequences and Series Maths with Answers. The following Sequences and Series Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Sequences and Series with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

**Sequences and Series Class 11 MCQ Questions with Answers**

See below Sequences and Series Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. Which term of the AP, 19 18 1/5, 18 2/5 , , , . . . is the first negative term?**

(a) 24

(b) 25

(c) 26

(d) 23

## Answer

B

**Question: If a, b, c, dand pare different real numbers such that **

(a) AP

(b) GP

(c) HP

(d) ab = cd

## Answer

B

**Question: 0.14189189189 … can be expressed as a rational number**

(a) 7/3700

(b)7/50

(c)525/111

(d)21/148

## Answer

D

**Question: The sum of 100 terms of the series 0.9 + 0.09 + 0.009 … will be**

## Answer

A

**Question: The value of 0.23&4& is**

(a)232/990

(b)232/9990

(c)232/900

(d)232/9909

## Answer

A

**Question: If the pth and qth terms of a GP are q and p, respectively, then ( p – q)th term is **

## Answer

A

**Question: **

## Answer

B

**Question: **

(a) AP

(b) HP

(c) GP

(d) None of these

## Answer

B

**Question: The sum of the geometric progression 0.15, 0.015, 0.0015, … 20 terms is **

## Answer

A

**Question: If a, b, c be in GP, then log a ^{n} , log b^{n} , log c^{n} will be**

(a) AP

(b) GP

(c) HP

(d) None of these

## Answer

A

**Question: If x,1, zare in AP and x,2, zare in GP, then x, 4, zwill be in**

(a) AP

(b) GP

(c) HP

(d) None of these

## Answer

C

**Question: In a GP the sum of three numbers is 14, if 1 is added to first two numbers and subtracted from third number the series becomes AP, then the greatest number is**

(a) 8

(b) 4

(c) 24

(d) 16

## Answer

A

**Question: **

## Answer

D

**Question: If the AM and GM of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be**

(a) x^{2} -16x – 25 = 0

(b) x^{2} – 8x + 5 = 0

(c) x^{2} -16x + 25 = 0

(d) x^{2} +16x – 25 = 0

## Answer

C

**Question: Three numbers form a GP. If the 3rd term is decreased by 64, then the three numbers thus obtained will constitute an AP. If the second term of this AP is decreased by 8, a GP will be formed again, then the numbers will be**

(a) 4, 20, 36

(b) 4, 12, 36

(c) 4, 20, 100

(d) None of these

## Answer

C

**Question: Which of the following statement is correct ?**

(a) If each term of an AP a number is added or subtracted, then the series so obtained is also an AP.

(b) The nth term of geometric series whose first term is a and common ratio r, is ar ^{n} ^{-1}.

(c) If each term of a GP be raised to the same power the resulting terms are in GP.

(d) All of the above

## Answer

A

**Question: **

**then the value of n is (where n∈N**

(a) 32

(b) 16

(c) 31

(d) 15

## Answer

C

**Question: The number 111…1 (91 times) is a/an **

(a) even number

(b) prime number

(c) not prime

(d) None of these

## Answer

C

**Question:**

## Answer

B

**Question: **

## Answer

C

**Question. If the 4th, 10th and 16th terms of a GP are x, y and z respectively, then x, y, z are in **

(a) AP

(b) GP

(c) AGP

(d) HP

## Answer

B

**Question. If Sn denotes the sum of n terms of an AP, then Sn+ 3 – 3Sn+2 + 3Sn +1 – Sn is equal to **

(a) 0

(b) 1

(c) 1/2

(d) 2

## Answer

A

**Question. If a, b, c are in AP, then the straight line ax + by + c = 0 will always pass through the point**

(a) (-1, – 2)

(b) (1, – 2)

(c) (-1,2)

(d) (1, 2)

## Answer

B

**Question. If Θ1 ,Θ2 ,Θ3,….Θn n are in AP, whose common difference is d, then sin d(secΘ _{1} secΘ_{2} secΘ_{3} +….+ secΘ_{n-1} secΘ_{n} is equal to**(a) tanΘ

_{n}– tanΘ

_{1}

(b) tanΘ

_{n}+tanΘ

_{1}

(c) tanΘ

_{n}– tanΘ

_{1}

(d) None of these

## Answer

C

**Question. If 1/p + q, 1/q + r, 1/r + p are in AP, then**

(a) p, q, r are in AP

(b) q2, p2,r2 are in AP

(c) p2 , q2 , r2 are in AP

(d) None of these

## Answer

B

**Question. The sum of n terms of the sequence 8, 88, 888, 8888,… is **

(a) 80/81(10^{n}-1) -8n/9

(b) 80/81(10^{n}-1) + 8n/9

(c) 80/81(10^{n}-1) + 8n^{2}/9

(d) None of these

## Answer

A

**Question. The sum of all two digit numbers which when divided by 4, yield unity as remainder, is**

(a) 1012

(b) 1201

(c) 1212

(d) 1210

## Answer

D

**Question. If log5 2, log5 (2x 3) x – and log5 (17/2 + 1x-1) are in AP, then the value of x is**

(a) 0

(b) -1**(c) 3**

(d) None of these

## Answer

**Question. If S _{1}, S_{2} and S_{3} denote the sum of n1, n2 and n3 terms respectively of an AP, then S1/n1(n1-n2)+S2/n2(n2-n_{1})+S_{3}+n3(n_{1}-n_{2}) is equal to**

(a) 0

(b) 1

(c) S

_{1}S

_{2}S

_{3}

(d) n

_{1}n

_{2}n

_{3}

## Answer

A

**Question. If a _{2}, b_{2}, c_{2}, are in AP, then a/b + c, b/c + a, c/a + b are in**

(a) AP

(b) GP

(c) HP

(d) None of these

## Answer

A

**Question. If 1, log , y x logz y, -15 logx z are in AP, then**

(a) z x 3 =

(b) x = y-1

(c) z-3 = y

(d) All of these

## Answer

D

**Question. Let a _{1}, a_{2}, a_{3}, …, be in AP and ap, aq, ar be in GP, then aq : ap is equal to**

(a) r-p /q-p

(b) q-p/r-q

(c) r-q/q p

(d) None of these

## Answer

C

**Question. Let < a _{n} > be a GP such that a4/a6 = 1/4 and a_{2} + a_{5} = 216. Then, a_{1} is equal to**

(a) 12 or 108/7

(b) 10

(c) 7 or 54/7

(d) None of these

## Answer

A

**Question. If a, b, c are in GP, then b-a/b-c + b+a/b+c is equal to**

(a) b c 2 – 2

(b) ac

(c) ab

(d) 0

## Answer

D

**Question. If the roots of equation (b2 + c2 ) x2 -2(a b) cx +(c2 + a2 ) = 0 are equal, then**

(a) a, b, c are in GP

(b) a, b, c are in AP

(c) a, c, b are in GP

(d) a, c, b are in AP

## Answer

A

**Question. 4 + 44 + 444 +Kis equal to**

(a) 4/81 [10^{n+1} – 10 – 9n ]

(b) 4/9 [10^{n+1} – 10 – 9n ]

(c) 4/81 [10^{n+1} – 10 +9n ]

(d) 4/9 [10^{n+1} – 10 + 9n ]

## Answer

A

**Question. The sum of sequence 0.15, 0.015, 0.0015, . . . , 20 terms is**

(a) 1/6[1-(0.1)^{20}]

(b) 1/6[1-(0.1)^{20}]

(c) 1/3[1-(0.1)^{20}]

(d) None of these

## Answer

A

**Question. One side of an equilateral triangle is 24 cm. The mid-points of its sides are joined to form another triangle whose mid-points in term are joined to form still another triangle. The process continues indefinitely. The sum of perimeters of all the triangles is**

(a) 144 cm

(b) 140 cm

(c) 145 cm

(d) None of the above

## Answer

A

**Question. If ngeometric means between a and b be G1, G2…. Gn = and a geometric mean beG, then the true relation is**

(a) G_{1}, G_{2}…. G_{n} = G

(b) G_{1}, G_{2}…. G_{n} = G1/n

(c) G_{1}, G_{2}…. G_{n} = G^{n}

(d) G_{1}, G_{2}…. G_{n} = G2/n

## Answer

C

**Question. If 1 + cosα + cos ^{2}α + …2 = -√2 , then a, (0 < a < π) is**

(a) π/8

(b) π/6

(c) π/4

(d) 3π/4

## Answer

D

**Question. The sum1+ 3 + 7 + 15 + 31+Kto n terms is**

(a) 2n – 2 – n

(b) 2^{n-1} – 1- n

(c) 2^{n+1} – 2 -n

(d) None of these

## Answer

C

**Question. Suppose a, b, c are in AP and a2, b2 , c2 are in GP. If a < b < c and a + b + c = 3/2 , then the value of a is**

(a) 1/2√2

(b) 1/2√3

(c) 1/2 – 1/√3

(d) 1/2 – 1/√2

## Answer

D

**Question. If the AM and GM of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be**

(a) x^{2} -16x – 25 = 0

(b) x^{2} – 8x + 5 = 0

(c) x^{2} -16x + 25 = 0

(d) x^{2} + 16x – 25 = 0

## Answer

C

**Question. The sum of series 1+4/5 + 7/52 +10/53 +….∞ is**

(a) 7/16

(b) 5/16

(c) 105/64

(d) 35/16

## Answer

D

**Question. The sum of the series 3×6 + 4×7 + 5×8 + … upto (n – 2) terms is**

(a) n3 + n2 + n +2

(b) 1/6 (2n^{3} + 12n + 10n – 84

(c) n3 + n2 + n

(d) None of these

## Answer

B

**Question. If the sum of n terms of an AP is given by S n n n = 3 + 2 2, then the common difference of the AP is **

(a) 3

(b) 2

(c) 6

(d) 4

## Answer

D

**Question. If 9 times the 9th term of an AP is equal to 13 times the 13th term, then the 22nd term of the AP is**

(a) 0

(b) 22

(c) 220

(d) 198

## Answer

A

**Question. In an AP, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. The 20th term is **

(a) 112

(b) –112

(c) 114

(d) –114

## Answer

B

**Question. If a, b, c, d, e, f are in AP, then the value of e – c will be**

(a) 2(c – a)

(b) 2(f – d)

(c) 2(d – c)

(d) d – c

## Answer

C

**Question. Let Sn denote the sum of the first n terms of an AP. If S S 2n n = 3 , then S S 3n n : is equal to **

(a) 4

(b) 6

(c) 8

(d) 10

## Answer

B

**Question. If the angles of a quadrilateral are in AP, whose common difference is 10°, then the angles of the quadrilateral are**

(a) 65°, 85°, 95°, 105°

(b) 75°, 85°, 95°, 105°

(c) 65°, 75°, 85°, 95°

(d) 65°, 95°, 105°, 115°

## Answer

B

**Question. The interior angles of a polygon are in AP. If the smallest angle be 120° and the common difference be 5, then the number of side is**

(a) 8

(b) 10

(c) 9

(d) 6

## Answer

C

**Question. In an AP, if the pth term is 1/q and qth term is 1/p. Then, the sum of first pq terms is**

(a) (pq + 1)

(b) 1/2 (pq + 1)

(c) 1/2 (pq – 1)

(d) None of these

## Answer

B

**Question. If the sum of a certain n number of terms of the AP,25, 22, 19, … is 116, then the last term is**

(a) 4

(b) 3

(c) 2

(d) –4

## Answer

A

**Question. If 1/b – c , 1/c – a , 1/a – b be consecutive terms of an AP, then (b – c) ^{2}, (c – a)^{2}, (a – b)^{2} will be in**

(a) GP

(b) AP

(c) HP

(d) None of these

## Answer

B

**Question. If log 2, log(2 ^{n} – 1) and log (2^{n} – 3) n + are in AP, then n is equal to**

(a) 5/2

(b) log2 5

(c) log3 5

(d) 3/2

## Answer

B

**Question. If the ratio of the sum of n terms of two AP’s be (7n + 1) :(4n + 27), then the ratio of their 11th terms will be**

(a) 2 : 3

(b) 3 : 4

(c) 4 : 3

(d) 5 : 6

## Answer

C

**Question. Given that n AM’s are inserted between two sets of numbers a,2 b and 2 a, b where a, bÎR. Suppose further that mth mean between these sets of** **numbers is same, then the ratio a:b is equal to**

(a) (n – m + 1) : m

(b) (n – m + 1) : n

(c) n: (n – m + 1)

(d) m: (n – m + 1)

## Answer

D

**Question. A man saved ₹66000 in 20 yr. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did****he save in the first year? **

(a) ₹1450

(b) ₹1400

(c) ₹1470

(d) ₹1480

## Answer

B

**Question. The sum of****(x+2)n-2 + (x+2)n-2 (x+1)+(x+2)n-3 (x+1)2 + (x+1)n-1 is equal to**

(a) (x+2)^{n-2} + (x+1)n

(b) (x+2)^{n-1} + (x+1)^{n-1}

(c) (x+2)^{n} + (x+1)n

(d) None of these

## Answer

C

**Question. Let two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation**

(a) x^{2} – 18x -16 = 0

(b) x^{2} – 18x + 16 = 0

(c) x^{2} +18x -16 = 0

(d) x^{2} + 18x + 16 = 0

## Answer

B

**Question. A carpenter was hired to build 192 window frames.****The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many days did it take him to finish the job? **

(a) 11

(b) 10

(c) 12

(d) 14

## Answer

C

**Question. Inacrickettournament16schoolterms participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last placed team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, amount will the first place team received is **

(a) ₹720

(b) ₹725

(c) ₹735

(d) ₹780

## Answer

B

**Question. A farmer buys a used tractor of ` 12000. He pays ` 6000 cash and agrees to pay the balance in annual instalment of ` 500 plus 12% interest on the unpaid amount. The tractor cost for farmer is**

(a) ` 16680

(b) ` 16670

(c) ` 16650

(d) None of these

## Answer

A

**Question. A circle is completely divided into n sectors in such a way that the angles of the sectors are in AP. If the smallest of these angles is 8° and the largest is 72°, then the angle in the fifth sector is**

(a) 40°

(b) 35°

(c) 42°

(d) 43°

## Answer

A

**Question. If a1, a2 ,a3, a24 , , , …, are in arithmetic progression and a1 + a5 + a10 + a15 + a20+ a24 + = 225, then a1 + a2 + a3+ a23 + a24 + + + …+ + is equal to**

(a) 909

(b) 75

(c) 750

(d) 900

## Answer

D

**Question. If a1 , a2 , a3….. a 4001 are terms of an AP such that 1/a1a2 + 1/a2a3 +…+ 1/a4000a _{4001} = 10 and a_{2} + a_{4000} = 50 ,then|a1 – a4001 | is equal to**

(a) 20

(b) 30

(c) 40

(d) None of these

## Answer

B

**Question. If a _{1} , a_{2} , a_{n} , , …, are in AP with common difference d, then the sum of the series sin d(cosec a1 cosec a_{2} + cosec a_{2} cosec a_{3} + … + cosec a_{n} coseca_{3} +….+ cosec a_{n-1} coseca_{n} ) is**

(a) sec a

_{1}– sec an

(b) cot a

_{1}– cot an

(c) tan a

_{1}– tan an

(d) coseca

_{1}– coseca

_{n}

## Answer

B

**Question. length of Sn equals the length of a diagonal of S _{n+1}. If the length of a side of a side of S_{1} is 10 cm, then for which of the following values of n, the area of Sn less than 1 sq cm ?**

(a) 7

(b) 6

(c) 9

(d) None of these

## Answer

C