CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 3 - MCQExams.com

Which of the following is $$GP?$$
  • $$2, 4, 8, 16$$
  • $$2, -2, 2, 3, 1$$
  • $$0, 3, 6, 9, 12$$
  • $$10, 20, 30, 40$$
Which of the following is a geometric sequence?
  • {$$2, 4, 6, 8, 10$$}
  • {$$-1, 2, 4, 8, -2$$}
  • {$$2, -2, 2, -2, 2$$}
  • {$$3, 13, 23, 33, 43$$}
The difference of the squares of two consecutive even integers is divisible by which of the following integers?
  • $$3$$
  • $$4$$
  • $$6$$
  • $$7$$
The average IQ of $$4$$ people is $$110$$. If three of these people each have an IQ of $$105$$, what is the IQ of the fourth person?
  • 110
  • 115
  • 120
  • 125
$$2, 3, 6, n, 42, . . .$$
Find the value of $$n$$ in the above series.
  • $$9$$
  • $$12$$
  • $$15$$
  • $$18$$
  • $$21$$
The 8th term of the sequence 1, 1, 2, 3, 5, 8 ............... is
  • 25
  • 24
  • 23
  • 21
$$\left( { 2 }^{ 2 }+{ 4 }^{ 2 }+{ 6 }^{ 2 }+.......+{ 20 }^{ 2 } \right) =$$?
  • $$770$$
  • $$1155$$
  • $$1540$$
  • $$385\times 385$$
The common ratio is calculated in
  • A.P.
  • G.P.
  • H.P.
  • I.P.
Complete the addition square by finding the missing numbers.
Find $$(A-B)-(C-D)$$
$$+$$$$10,923$$$$8,473$$
$$18,732$$$$A$$$$B$$
$$9,018$$$$C$$$$D$$
  • $$0$$
  • $$450$$
  • $$1000$$
  • $$300$$
The models are shaded to show which of the following?
723095_3a54dd16138f4183a63141589df65446.png
  • $$\cfrac { 1 }{ 3 } =\cfrac { 2 }{ 4 } $$
  • $$\cfrac { 1 }{ 4 } >\cfrac { 1 }{ 3 } $$
  • $$\cfrac { 2 }{ 3 } <\cfrac { 2 }{ 4 } $$
  • $$\cfrac { 2 }{ 4 } <\cfrac { 2 }{ 3 } $$
Fathom is a unit once used by sailors to measure the depth of water. If a sunken ship was located underwater at $$240$$ feet, which expression would describe the location of the ship in fathoms?
$$ { 1\ fathom=6\ feet } $$
  • $$240\times 6$$
  • $$240\div 6$$
  • $$240-6$$
  • $$240+6$$
Consider the sequence of numbers $$2, 5, 5, 8, 8, 8, 11, 11, 11, 11, ....$$ The $$150^{th}$$ term of the sequence is
  • $$48$$
  • $$50$$
  • $$47$$
  • $$53$$
$$1 \, + \, 2 \, \cdot \, 2 \, + \, 3 \, \cdot \, 2^2 \, + \, 4 \, \cdot \, 2^3 \, + \, ..... \, + \, 100 \, \cdot \, 2^{99}$$
  • $$S=50502^{100}$$
  • $$S=5050.2^{99}$$
  • $$S=5050.2^{101}$$
  • $$S=5050.2^{98}$$
A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices given below. The columns and rows of Matrix I are numbered from $$0$$ to $$4$$ and that of Matrix $$I$$ are numbered from $$5$$ to $$9$$. A letter from these matrices can be represented first by its row and next by its column, e.g. $$'A'$$ can be represented by $$00, 12, 23$$ etc., and $$'P'$$ can be represented by $$58, 69, 75$$ etc. Similarly, you have to identify the set for the word 'POET'.
Matrix I
$$0$$$$1$$$$2$$$$3$$$$4$$
$$0$$$$A$$$$R$$$$S$$$$N$$$$C$$
$$1$$$$N$$$$C$$$$A$$$$R$$$$S$$
$$2$$$$S$$$$N$$$$C$$$$A$$$$R$$
$$3$$$$R$$$$S$$$$N$$$$C$$$$A$$
$$4$$$$C$$$$A$$$$R$$$$S$$$$N$$
Matrix II
$$5$$$$6$$$$7$$$$8$$$$9$$
$$5$$$$O$$$$E$$$$L$$$$P$$$$T$$
$$6$$$$T$$$$O$$$$E$$$$L$$$$P$$
$$7$$$$P$$$$T$$$$O$$$$E$$$$L$$
$$8$$$$L$$$$P$$$$T$$$$O$$$$E$$
$$9$$$$E$$$$L$$$$P$$$$T$$$$O$$
  • $$69, 88, 67, 65$$
  • $$75, 56, 65, 67$$
  • $$77, 88, 98, 78$$
  • $$75, 66, 76, 78$$
Find the sum of $$1^3-2^3+3^3-4^3+....+9^3$$
  • $$400$$
  • $$425$$
  • $$450$$
  • $$475$$
In this question, the sets of numbers given in the alternatives are represented by two classes of alphabets as in two matrices given below. The columns and rows of Matrix I are numbered from $$0$$ to $$4$$ and that of Matrix II are numbered from $$5$$ to $$9$$. A letter from these matrices can be represented first by its row and next by its column, e.g., $$'B'$$ can be represented by $$00, 13,$$ etc., and $$'A'$$ can be represented by $$55, 69$$, etc. Similarly you have to identify the set for the word 'GIRL'.
Matrix I
$$0$$$$1$$$$2$$$$3$$$$4$$
$$0$$$$B$$$$N$$$$G$$$$L$$$$D$$
$$1$$$$G$$$$L$$$$D$$$$B$$$$N$$
$$2$$$$D$$$$B$$$$N$$$$G$$$$L$$
$$3$$$$N$$$$G$$$$L$$$$D$$$$B$$
$$4$$$$L$$$$D$$$$B$$$$N$$$$G$$
Matrix II
$$5$$$$6$$$$7$$$$8$$$$9$$
$$5$$$$A$$$$I$$$$K$$$$O$$$$R$$
$$6$$$$I$$$$K$$$$O$$$$R$$$$A$$
$$7$$$$K$$$$O$$$$R$$$$A$$$$I$$
$$8$$$$O$$$$R$$$$A$$$$I$$$$K$$
$$9$$$$R$$$$A$$$$I$$$$K$$$$O$$
  • $$02, 56, 97, 24$$
  • $$31, 79, 68, 42$$
  • $$23, 97, 77, 11$$
  • $$11, 88, 95, 23$$
The two sequence of number $${1,4,16,64,.......}$$ and $${3,12,48,192,........}$$ are mixed as follows:$${1,3,4,12,16,48,64,192,.......}$$. one of the numbers in the mixed in the mixed series is $$1048576$$, then number immediately preceding is-
  • $$3.4^9$$
  • $$3.4^{10}$$
  • $$4^9$$
  • $$4^{10}$$
Select a figure from the options which will replace the question mark to complete the given series.
906786_0c1de64c12e342d0a16109e335cb8bba.jpg
If $$n\in N>1$$, then the sum of real part of roots of $$z^n=(z+1)^n$$ is equal to
  • $$\dfrac {n}{2}$$
  • $$\dfrac {(n-1)}{2}$$
  • $$-\dfrac {n}{2}$$
  • $$\dfrac {(1-n)}{2}$$
The value of $$\left(\displaystyle 1-\frac{1}{2}\right)\left(\displaystyle 1-\frac{1}{3}\right)\left(\displaystyle 1-\frac{1}{4}\right).........\left(\displaystyle 1-\frac{1}{10}\right)=$$ ___________.
  • $$\displaystyle\frac{10}{11}$$
  • $$\displaystyle\frac{1}{9}$$
  • $$\displaystyle\frac{1}{10}$$
  • $$\displaystyle\frac{1}{2}$$
Sum $$1+3x+5{ x }^{ 2 }+7{ x }^{ 3 }+9{ x }^{ 4 }+.....$$ to infinity is $$\left( x<1 \right) $$
  • $$\dfrac { 1+x }{ { \left( 1-x \right) }^{ 2 } } $$
  • $$\dfrac { 1-x }{ { \left( 1+x \right) }^{ 2 } } $$
  • $$\dfrac { 1-x }{ { \left( 1+x \right) } } $$
  • $$\dfrac { 1+x }{ { \left( 1-x \right) } } $$
Select the missing number from the given matrix:
524
447
253
1830?
  • $$43$$
  • $$42$$
  • $$33$$
  • $$32$$
What is the next term of the AP $$\sqrt{2}, \sqrt{8}, \sqrt{18},$$ ____?
  • $$\sqrt{24}$$
  • $$\sqrt{28}$$
  • $$\sqrt{30}$$
  • $$\sqrt{32}$$
$$A$$ is twice as fast as $$B$$ is thrice as fast as $$C$$. The journey covered by $$C$$ in $$42$$ minutes, what will be covered by $$A$$ is 
  • $$21$$ Min
  • $$64$$ Min
  • $$17$$ Min
  • $$40$$ Min
State whether the statement is True/False.

Two numbers between 3 and 81 such that the series $$3,G_{1},G_{2},81$$ forms a GP are 9 and 27.
  • True
  • False

The first three terms of a sequence are 3,3,6 and each term after the second is the sum of two terms preceding it, the 8th term of the sequence is
  • 15
  • 24
  • 39
  • 63
The sum of the infinite series $$1+\left ( 1+\dfrac{1}{5} \right )\left ( \dfrac{1}{2} \right )+\left ( 1+\dfrac{1}{5}+\dfrac{1}{5^2} \right )\left ( \dfrac{1}{2^2} \right )+.......$$
  • $$\dfrac{20}{9}$$
  • $$\dfrac{10}{9}$$
  • $$\dfrac{5}{9}$$
  • $$\dfrac{5}{3}$$
The sum of the series $$\sum_{r=0}6{88} \sec r^o\cdot \sec(r+1)^o$$ is equal to
  • $$cosec\, 1^o\cdot \tan 1^o$$
  • $$cosec\, 1^o\cdot \cot 1^o$$
  • $$\sec\, 1^o\cdot \tan 1^o$$
  • $$\sec\, 1^o\cdot \cot 1^o$$
Let $$S_1=\displaystyle \sum_{K=1}^{n}K,S_2=\sum_{K=1}^{n}K^2$$ and $$S_3=\displaystyle \sum_{K=1}^{n}K^3$$, then $$\dfrac{S_{1}^{4}S_{2}^{2}-S_{2}^{2}S_{3}^{2}}{S_{1}^{2}+S_{3}^{2}}$$ is equal to
  • $$4$$
  • $$2$$
  • $$1$$
  • $$0$$
Choose the most appropriate option which follows the pattern
1190048_11258e088382456eaaeb1f64c6a2bada.png
  • None of the above
Find the next term in the sequence.
$$117, 389, 525, 593, 627 ?$$
  • 644
  • 640
  • 634
  • 630
  • none of these
958, 833, 733, 658, 608 ?
  • 577
  • 583
  • 567
  • 573
  • none of these
The value of the expression
 $$\left(1 + \dfrac{1}{\omega}\right) \left(1 + \dfrac{1}{\omega^2}\right) + \left(2 + \dfrac{1}{\omega}\right) \left(2 + \dfrac{1}{\omega^2}\right) + \left(3 + \dfrac{1}{\omega^2}\right) \left(3 + \dfrac{1}{\omega^2}\right) +.............+ \left(n + \dfrac{1}{\omega}\right) \left(n + \dfrac{1}{\omega^2}\right)$$ 

($$\omega$$ is the root of unity) is
  • $$\dfrac{n(n^2 + 2)}{3}$$
  • $$\dfrac{n(n^2 - 2)}{3}$$
  • $$\dfrac{n(n^2 + 1)}{3}$$
  • None of these
Find the number suitable for blank in given series.
1,2,3,5,8,13,21,___,55
  • 35
  • 33
  • 36
  • 34
33, 43, 65, 99, 145 ?
  • 201
  • 203
  • 205
  • 211
  • none of these
Find the missing number
1313200_e86098c8ee83418a8ea00d9e2743bafc.png
  • 74
  • 62
  • 91
  • 97
If D=4 and COVER = 63, then BASIC is equal to
  • 49
  • 50
  • 34
  • 55
If $$5\times 9=144; 7\times 8=151:4\times 6=102,$$ then $$2\times 5=?$$
  • $$73$$
  • $$77$$
  • $$37$$
  • $$97$$
Last digit in $$2^{2^n} +1, n \displaystyle \in N, n \neq 1 $$ is
  • $$7$$
  • $$3$$
  • $$5$$
  • $$1$$
Find the sum of the following geometric series:
$$ 1,-a,a^2,-a^3,...$$ to n terms $$\left ( a\neq 1 \right )$$
  • $$ \dfrac{1+\left ( -a \right )^n}{1+a}$$
  • $$ \dfrac{1-\left ( a \right )^n}{1+a}$$
  • $$ \dfrac{1-\left ( -a \right )^n}{1+a}$$
  • $$ \dfrac{1+\left ( a \right )^n}{1+a}$$
In a sequence, $$a_{n}=n^{2}-1$$ then $$a_{n+1} $$ is equal to
  • $$a^{2}-5n$$
  • $$n^{2}-2n$$
  • $$a^{2}+10n$$
  • $$n^{2}+2n$$
$$1.4+2.5+...+\mathrm{n}(\mathrm{n}+3)=$$
  • $$\displaystyle \frac{n(n+3)(n+5)}{9}$$
  • $$\displaystyle \frac{n(n+1)(n+5)}{3}$$
  • $$\displaystyle \frac{n(n+5)(n+7)}{6}$$
  • $$\displaystyle \frac{n(n+3)(n+9)}{12}$$
$$ 1+ 3 + 6 + 10 + ...+\displaystyle \frac{(n-1)n}{2}+\frac{n(n+1)}{2}=$$
  • $$\displaystyle \frac{n(n+1)(n+2)}{3}$$
  • $$\displaystyle \frac{(n+1)(n+2)}{6}$$
  • $$\displaystyle \frac{n(n+1)(n+2)}{6}$$
  • $$\displaystyle \frac{(n+2)(n+1)^{2}}{3}$$
Sum of the series 
$$S=1+\dfrac{1}{2} \left ( 1+2 \right )+\dfrac{1}{3}\left ( 1+2+3 \right )+\dfrac{1}{4}\left ( 1+2+3+4 \right )+...$$ upto $$20$$ terms is
  • $$110.5$$
  • $$111$$
  • $$115$$
  • $$116.5$$
If $$S_1,S_2$$ and $$S_3$$. are the sums of first n natural  numbers, their squares and their cubes respectively, then $$S_3\left (1+8S_1  \right )=$$
  • $$S_{2}^{2}$$
  • $$ 9S_2 $$
  • $$9S_{2}^{2}$$
  • None
$$3.6+6.9+9.12+...+3\mathrm{n}(3\mathrm{n}+3)=$$
  • $$\displaystyle \frac{n(n+1)(n+2)}{3}$$
  • $$3\mathrm{n}(\mathrm{n}+1)(\mathrm{n}+2)$$
  • $$\displaystyle \frac{(\mathrm{n}+1)(\mathrm{n}+2)(\mathrm{n}+3)}{3}$$
  • $$\displaystyle \frac{(\mathrm{n}+1)(\mathrm{n}+2)(\mathrm{n}+4)}{4}$$
$$2\cdot1^{2}+3\cdot2^{2}+4\cdot3^{2}+\dots $$ up to $$n$$ terms $$=$$
  • $$\displaystyle \frac{n(n+1)(n+2)(3n+1)}{12}$$
  • $$\displaystyle \frac{n(n+2)(n+3)(n+11)}{12}$$
  • $$\displaystyle \frac{n(n+1)(n+2)(3n-2)}{6}$$
  • $$\displaystyle \frac{n(n+2)(n+5)(n+8)}{6}$$
The sum to infinity of $$\displaystyle\frac{1}{7}+\frac{2}{7^2}+\frac{1}{7^3}+\frac{2}{7^4}+...$$is
  • $$\dfrac{1}{5}$$
  • $$\dfrac{7}{24}$$
  • $$\dfrac{5}{48}$$
  • $$\dfrac{3}{16}$$
$$ 1.3+3.5+5.7+...+(2\mathrm{n}-1)(2\mathrm{n}+1)=$$
  • $$\displaystyle \frac{n(4n^{2}+6n-1)}{3}$$
  • $$\displaystyle \frac{n(3n^{2}+5n+1)}{3}$$
  • $$\displaystyle \frac{n(5n^{2}+7n-1)}{3}$$
  • $$\displaystyle \frac{n(7n^{2}-5n+1)}{3}$$
 $$ 1.4+2.7+3.10+...+\mathrm{n}(3\mathrm{n}+1)=$$
  • $$n(2n+1)^{2}$$
  • $$2\mathrm{n}(\mathrm{2n}+1)^{2}$$
  • $$\mathrm{n}(\mathrm{n}+1)^{2}$$
  • $$(\mathrm{n}+2)(\mathrm{n}+3)$$
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