MCQ Questions for Class 11 Engineering Maths Sequences And Series Quiz 2

Find the missing letters
PTVX, AEGI, ..... WACE, HLNP

0%
KNQT
0%
LPRT
0%
KPQS
0%
HKLO

Explanation

Pattern is combination of two series

$\displaystyle P_{11}T_{7}V_{5}X_{3},A_{26}E_{22}G_{20}I_{18},L_{15}P_{11}R_{9}T_{7},W_{4}A_{26}C_{24}E_{22},H_{19}L_{15}N_{13}P_{11}$

$\displaystyle \therefore$ Missing letter = LPRT

Find the missing letters
AYD, BVF, DRH, ....., KGL

0%
FMI
0%
GMJ
0%
HLK
0%
GLJ

Explanation

Pattern is

$\displaystyle ^{1}AY_{2}^{4}D,^{2}BV_{5}^{6}F,^{4}DR_{9}^{8}H,^{7}GM_{14}^{10}J,^{11}KG_{20}^{12}L,$ .....

$\displaystyle \therefore$ Missing letters = GMJ

ac_cab_baca_aba_acac

0%
aacb
0%
acbc
0%
babb
0%
bcbb

b_abbc_bbca_bcabb_ab

0%
acaa
0%
acba
0%
cabc
0%
cacc

adb_ac_da_cddcb_dbc_cbda

0%
bccba
0%
cbbaa
0%
ccbba
0%
bbcad

a_abbb_ccccd_ddccc_bb_ba

0%
abcda
0%
abdbc
0%
abdcb
0%
abcad

abaa_aab_a_a

0%
abb
0%
aba
0%
bab
0%
aab

aba_baca_ba_bacaabac_aca

0%
cacb
0%
ccab
0%
cabc
0%
abcc

Find the missing letters
B E I N T.........

0%
A
0%
S
0%
U
0%
V

aa_b_abb___bb

0%
abaa
0%
bbaa
0%
baaa
0%
baba

Find the missing letters
Z W S P L I E........

0%
D
0%
F
0%
K
0%
B

abc_bc_c_

0%
acbbab
0%
aabbca
0%
aabacb
0%
aababc

Choose the correct statement(s):

$A$ : Every sequence is a progression.

$B$ : Every progression is a sequence.

0%
Only $A$
0%
Only $B$
0%
Both $A$ and $B$
0%
None

If CAT is

$48$ , Z is

$52$ Then what is TEA equal to ?

0%
$48$
0%
$52$
0%
$60$
0%
$50$

aab....aaa......bba.....

0%
baa
0%
abb
0%
bab
0%
bbb

I thought of a decimal number. After I had multiplied it by 2, then added 1.5 and then divided by 3, I got 3.What was the decimal number?

0%
7.1
0%
5.6
0%
5.8
0%
4.5

Explanation

Let the decimal number be

$x.$

$\dfrac{x\times 2+1.5}{3}=3.5$

$2x+1.5=3.5\times 3$

$2x+1.5=10.5$

$2x=9$

$x=\dfrac{9}{2}$

$x=4.5$

Hence, correct option is D.

$\displaystyle t_{3}=15,S_{10}=120$ then the tenth term of the series i:

0%
$\displaystyle 6\frac{3}{5}$
0%
$\displaystyle 5\frac{3}{5}$
0%
$\displaystyle 6\frac{4}{5}$
0%
$\displaystyle 6\frac{3}{4}$

Explanation

$\displaystyle t_{3}=a+2d=15$ ....(i)

$\displaystyle S_{10}=\frac{10}{2}\left [ 2a+9d \right ]=120$

$\displaystyle S_{10}\Rightarrow 2a+9d=24$ ....(ii)
(i) and (ii) gives

$\displaystyle a=\frac{87}{5}$ and

$\displaystyle d=-\frac{6}{5}$

$\displaystyle \therefore t_{10}=a+9d=\frac{87}{5}+9\times \left ( -\frac{6}{5} \right )$

$\displaystyle =6\frac{3}{5}$

How many numbers are there between 500 and 600 in which 9 occurs only once?

0%
19
0%
18
0%
10
0%
9

Answer the following set of questions by reading the above pitctograph. Number of TV sets sold in the year 2005 is

0%
$1000$
0%
$500$
0%
$50$
0%
$2000$

Observe the following pattern for obtaining the sums then find the sum of numbers from 781 to 790?
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = 255
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 = 555
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 = 1055
251 + 252 + 253 + 254 + 255 + 256 + 257
258 + 259 + 260 = 2555

0%
7055
0%
7855
0%
7955
0%
8155

ab _ bc _ c _ ba _ c

0%
baac
0%
aabb
0%
caab
0%
aaab

In a _______ each term is found by multiplying the previous term by a constant.

0%
arithmetic sequence
0%
geometric sequence
0%
arithmetic series
0%
None of these

A sequence of numbers in which each term is related to its predecessor by same law is called

0%
arithmetic series
0%
progression
0%
geometric series
0%
none of these

$10,$ __

$, 15, 15, 20, 20, 25, 25,...$ . What number should fill the blank?

0%
7
0%
8
0%
10
0%
15

Explanation

Here addition with repetition series, each number in the series repeats itself, and then increases by

$5$ to get the next number.
The next number is

$10$ .

________ can be defined as arrangement of terms in which sequence of terms follow some conditions.

0%
Series
0%
Preceding sequence
0%
Progression
0%
Geometric progression

_______ is a series of successive events.

0%
Series
0%
Preceding sequence
0%
Progression
0%
Geometric progression

Find the next number in the series.

$3, 6, 9, 12, 15,....$

0%
$17$
0%
$18$
0%
$19$
0%
$20$

Explanation

The next number is

$18$ .
Since the numbers are multiple of

$3$ .

$3, 6, 9, 12, 15, \underline {18 }$ .

A _________ is a sequence of numbers where each term in the sequence is found by multiplying the previous term with a unchanging number called the common ratio.

0%
geometric progression
0%
arithmetic series
0%
arithmetic progression
0%
None of these

Explanation

A geometric progression is a sequence of numbers where each term in the sequence is found by multiplying the previous term with a with a unchanging number called the common ratio.
Example:

$2, 6, 18, 54, 108....$
This geometric sequence has a common ratio

$3$ .

State the following statement is true or false:

Progression means increment of quantity in a particular pattern.

0%
True
0%
False

Explanation

Progression means increment of quantity in a particular pattern.

For example:

$2,4,6,8,....$ and

$3,6,12,24,....$

If there are five consecutive integer in a series and the first integer is

$1$ , what is the value of the last consecutive integer?

0%
$2$
0%
$3$
0%
$4$
0%
$5$

Explanation

Let the five consecutive integers be

$x, x + 1, x + 2, x + 3$ and

$x + 4$ .
Therefore, the value of first integer is

$1$ i.e.,

$x = 1$
So, the last integer is

$x + 4$
The value of last integer

$= 5$ .

A progression of the form

$a, ar, ar^2$ , ..... is a

0%
geometric series
0%
arithmetic series
0%
arithmetic progression
0%
geometric progression

Explanation

A progression of the form

$a, ar, ar^2$ , ..... is a geometric progression.
Geometric Progression refers to a sequence in which successor term of each term is obtained by multiplying a constant term.

Identify the geometric progression.

0%
$1, 3, 5, 7, 9, ...$
0%
$2, 4, 6, 8, 10...$
0%
$5, 10, 15, 25, 35..$
0%
$1, 3, 9, 27, 81...$

Explanation

A geometric sequence is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.
So,

$1, 3, 9, 27, 81...$ is a geometric progression.
Here the common ratio is

$3$ .

$5, 25, 125, .....$ is an example of

0%
arithmetic progression
0%
arithmetic series
0%
geometric series
0%
geometric progression

Explanation

In geometric progression, the ratio of consecutive terms should be equal.

Here

$5, 25, 125, ...$ is an example of geometric progression as their common ratio is

$5$ .

A ______ is the sum of the numbers in a geometric progression.

0%
arithmetic progression
0%
arithmetic series
0%
geometric series
0%
geometric sequence

Identify the geometric series.

0%
$1 + 3 + 5 + 7 +....$
0%
$2 + 12 + 72 + 432...$
0%
$2 + 3 + 4 + 5 +...$
0%
$11 + 22 + 33 + 44+...$

Explanation

Geometric series is of the following form:

$a+ar+ar^2+ar^3 +ar^4+..........+ar^n$

Series

$2+12+72+432+......$ follows the same with

$a=2$ and

$r=6$ .

Hence, option B is correct.

A sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence is known as

0%
geometric series
0%
arithmetic progression
0%
arithmetic series
0%
geometric sequence

Explanation

A sequence of number,

${ a }_{ 1 }+{ a }_{ 2 }+......{ a }_{ n }$ quotient of any two successive number is a constant,

$\cfrac { { a }_{ 2 } }{ { a }_{ 1 } } =\cfrac { { a }_{ 3 } }{ { a }_{ 2 } } =........=\cfrac { { a }_{ n } }{ { a }_{ n-1 } } =$ common ratio

$(r)$

So we can write

${ a }_{ 1 }+{ a }_{ 1 }r+{ a }_{ 2 }r+{ a }_{ 3 }r.......{ a }_{ n-1 }r\\ ={ a }_{ 1 }+{ a }_{ 1 }r+{ a }_{ 1 }{ r }^{ 2 }..........{ a }_{ n-2 }{ r }^{ 2 }$

and in the end in terms of

${ a }_{ 1 }$

$={ a }_{ 1 }+{ a }_{ 1 }r+{ a }_{ 1 }{ r }^{ 2 }+{ a }_{ 1 }{ r }^{ 3 }.........{ a }_{ 1 }{ r }^{ n-1 }$

We can clearly say this series is in

$GP$ .

Answer

$(D)$

$10,20,40,80$ is an example of

0%
arithmetic series
0%
geometric series
0%
arithmetic sequence
0%
geometric sequence

Explanation

$10, 20, 40, 80$ is an example of geometric sequence.
In geometric sequence, the ratio of succeeding term to the preceeding term is always equal.

Here the common ratio is

$2$ .

$1, 3, 9, 27, 81$ is a

0%
geometric sequence
0%
arithmetic progression
0%
arithmetic series
0%
geometric series

Explanation

$1, 3, 9, 27, 81$ is a geometric sequence.
A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.

The sequence

$6, 12, 24, 48....$ is a

0%
geometric series
0%
arithmetic sequence
0%
geometric progression
0%
harmonic sequence

Explanation

The sequence

$6, 12, 24, 48....$ is a geometric progression as the ratio here is common.
The common ratio in the given series is

$2$ .

The geometric sequence is also called as

0%
geometric progression
0%
arithmetic sequence
0%
arithmetic series
0%
geometric series

If a sequence of values follows a pattern of multiplying a fixed amount times each term to arrive at the following term, it is called a:

0%
geometric sequence
0%
arithmetic sequence
0%
geometric series
0%
none of these

Explanation

$3,3^2,3^3,3^4,....(r=3)$

In a sequence if a fixed amount/constant is multiplied to each term to get the successive term the sequence is called geometric sequence.

Here

$3$ is the constant which gets multiplied to each term to obtain the successive term.

Which one of the following is a general form of geometric progression?

0%
$1, 1, 1, 1, 1$
0%
$1, 2, 3, 4, 5$
0%
$2, 4, 6, 8, 10$
0%
$-1, 2, -3, 4, -5$

Explanation

Lets see option A:

Sequence is

$1,1,1,1,1$

General form of GP is

$a=1$ and

$r=1$

Here ratio is constant throughout.

Thus in all options, option A is correct.

The geometric progression is

$1,1,1,1,1,............$ .

The number of terms in a sequence

$6, 12, 24, ....1536$ represents a

0%
arithmetic progression
0%
arithmetic series
0%
geometric progression
0%
geometric series

Explanation

Given sequence is

$6,12,24,....1536$

Since,

$\dfrac {12}{6} =2$ and

$\dfrac {24}{12} =2$

i.e. the given sequence is a geometric sequence / progression.

$4, \dfrac{8}{3}, \dfrac{16}{9}, \dfrac{32}{27}..$ is a

0%
arithmetic sequence
0%
geometric sequence
0%
geometric series
0%
harmonic sequence

Explanation

lets check the ratio between the consecutive terms.

$\dfrac {\frac {8}{3}}{4}=\dfrac {8}{12}=\dfrac {2}{3}$

Again take the ratio between next consecutive terms.

$\dfrac {\frac {16}{9}}{\frac {8}{3}}=\dfrac {16\times 3}{9\times 8}=\dfrac {2}{3}$

Here the common ratio is same

$\dfrac{2}{3}$ throughout.

Hence,

$4, \dfrac{8}{3}, \dfrac{16}{9}, \dfrac{32}{27}..$ is a geometric sequence.

An example of G.P. is

0%
$-1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$
0%
$-1, \dfrac{3}{2}, \dfrac{1}{2}, -\dfrac{1}{2}$
0%
$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{6}...$
0%
$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$

Explanation

For a G.P., the ratio of consecutive terms must be equal.

Here only D satisfies this condition.

So, an example of G.P. is

$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$
Here the common ratio is

$\dfrac{1}{2}$ .

Identify a geometric progression.

0%
$1, 3, 5, 7, 9.....$
0%
$2, 4, 6, 8, 10.....$
0%
$4, 8, 16, 32, 64....$
0%
$1, -1, 3, -2, 4$

Explanation

For a G.P., the ratio must be common throughout.

Thus the sequence

$4, 8, 16, 32, 64....$ is a geometric progression because the common ratio is

$2.$

The common ratio is used in _____ progression.

0%
arithmetic
0%
geometric
0%
harmonic
0%
series

Explanation

The common ratio is used in geometric progression.

For example:

$2,4,8,16,....$

Here the common ratio is

$2$ .

Which of the following is not in the form of G.P.?

0%
$2, 6, 18, 54, ....$
0%
$3, 12, 48, 192, ....$
0%
$1, 4, 7, 10, ....$
0%
$1, 3, 9, 27, ....$

Explanation

In option A, the common ratio is

$3$ .

In option B, the common ratio is

$4$ .

In option D, the common ratio is

$3$ .

$1, 4, 7, 10, ....$ . is not a G.P., since the sequence is in the form of A.P.

Which one of the following is not a geometric progression?

0%
$1, 2, 4, 8, 16, 32$
0%
$4, -4, 4, -4, 4$
0%
$12, 24, 36, 48$
0%
$6, 12, 24, 48$

Explanation

For geometric progression, the ratio of the consecutive terms should be equal.

Here

$12, 24, 36, 48$ is not a geometric progression. Here only the difference is common i.e.

$12$ .

Rest all options have same common ratio i.e., in option A, the ratio is

$2$ . In option B, the ratio is

$-1$ .

And in option D, the ratio is

$2$ .
Here the given sequence is an arithmetic progression.

Which one of the following is a geometric progression?

0%
$3, 5, 9, 11, 15$
0%
$4, -4, 4, -4, 4$
0%
$12, 24, 36, 48$
0%
$6, 12, 24, 36$

Explanation

$4, -4, 4, -4, 4$ is a geometric progression.
Here the common ratio is

$-1$ .

Option B is correct.

CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 2 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 2 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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