CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 5 - MCQExams.com

The value of $$\displaystyle \sum_{n=1}^{10}\left (\sin \dfrac {2n\pi}{11}-\cos\dfrac {2n\pi}{11}\right )$$ is equal to
  • $$2$$
  • $$1$$
  • $$0$$
  • $$-1$$
For $$\frac {2^2+4^2+6^2+...+(2n)^2}{1^2+3^2+5^2+...+(2n-1)^2}$$ to exceed 1.01, the maximum value of n is
  • 99
  • 100
  • 101
  • 150
The sum of the first n terms of the series $$\displaystyle 1^{2}+2.2^{2}+3^{3}+2.4^{2}+5^{2}+2.6^{2}+....$$ is $$\displaystyle \frac{n\left ( n+1 \right )^{2}}{2}$$ when n is even. When n is odd the sum is
  • $$\displaystyle \frac{n\left ( n+1 \right )^{2}}{4}$$
  • $$\displaystyle \frac{n^{2}\left ( n+2 \right )}{4}$$
  • $$\displaystyle \frac{n^{2}\left ( n+1 \right )}{4}$$
  • $$\displaystyle \frac{n\left ( n+2 \right )^{2}}{4}$$
The infinite sum $$1\, +\, \displaystyle {\frac{4}{7}\, +\, \frac{9}{7^2}\, +\, \frac{16}{7^3}\, +\, \frac{25}{7^4}\, +\, ......}$$ equals
  • $$\displaystyle \frac{27}{14}$$
  • $$\displaystyle \frac{21}{13}$$
  • $$\displaystyle \frac{49}{27}$$
  • $$\displaystyle \frac{256}{147}$$
If $$\displaystyle x_{i}> 0,i=1,2,....,50\: \: and\: \: x_{1}+x_{2}+...+x_{50}=50 $$ then the minimum value of $$\displaystyle \frac{1}{x_{1}}+\frac{1}{x_{2}}+...+\frac{1}{x_{50}}$$ equals to
  • $$50$$
  • $$\displaystyle \left ( 50 \right )^{2}$$
  • $$\displaystyle \left ( 50 \right )^{3}$$
  • $$\displaystyle \left ( 50 \right )^{4}$$
If $$\displaystyle \sum_{r=1}^{n}t_{r}=\frac{1}{12}n\left ( n+1 \right )\left ( n+2 \right )$$, then the value of $$\displaystyle \sum_{r=1}^{n}\frac{1}{t_{r}}$$ is
  • $$\displaystyle \frac{2n}{n+1}$$
  • $$\displaystyle \frac{n}{\left ( n+1 \right )}$$
  • $$\displaystyle \frac{4n}{ n+1 }$$
  • $$\displaystyle \frac{3n}{ n+1 }$$
The value of $$\displaystyle\frac{1}{1\cdot2\cdot3}+\displaystyle\frac{1}{2\cdot3\cdot4}+\displaystyle\frac{1}{3\cdot4\cdot5}+\displaystyle\frac{1}{4\cdot5\cdot6}$$ is equal to
  • $$\displaystyle\frac{7}{30}$$
  • $$\displaystyle\frac{11}{30}$$
  • $$\displaystyle\frac{13}{30}$$
  • $$\displaystyle\frac{17}{30}$$
Value of $$9 + 99 + 999 + .... $$ upto $$n$$ terms is
  • $$\displaystyle \frac{10^{n}-9n-10}{9}$$
  • $$\displaystyle \frac{10^{n}-9n-10}{81}$$
  • $$\displaystyle \frac{10^{n+1}-9n-10}{81}$$
  • $$\displaystyle \frac{10^{n+1}-9n-10}{9}$$
In the following question, the numbers/letters are arranged based on some pattern or principle. Choose the correct answer for the term marked by the symbol (?) 
$$0,\,3,\,9,\,18,\,30,\,?$$
  • $$48$$
  • $$42$$
  • $$36$$
  • $$45$$
Evaluate $$7 + 77 + 777 + .............$$ upto $$n$$ terms.
  • $$\displaystyle \frac{7}{81}[10^{n\, +\, 1}\, -\, 9n]$$
  • $$\displaystyle \frac{7}{81}[10^{n\, +\, 1}\, -\, 9n\, -\, 10]$$
  • $$\displaystyle \frac{7}{81}[10^n\, -\, 9n\, -\, 10]$$
  • $$\displaystyle \frac{7}{81}[10^{n\, +\, 1}\, -\, n\, -\, 10]$$
4, 9, 25, 49, ....
  • 64
  • 81
  • 121
  • 125
Find a wrong number in the series:
9, 19, 37, 75, 149, 297
  • 75
  • 37
  • 19
  • 149
  • 299
Find pair of consecutive odd natural numbers, both of which are larger than 13 such that their sum is less than 40
  • (15, 17)
  • (13, 17)
  • (19, 21)
  • (21, 17)
In  the following question, the numbers/letters are arranged based on some pattern or principle.Choose the correct answer for the term marked by the symbol (?) 
325102_22cb04bab72c40da93cf75ddfe9760a1.png
  • $$18$$
  • $$40$$
  • $$21$$
  • $$24$$
The sum of 'n' terms of series $$1^2+(1^2+2^2)+(1^2+ 2^2+ 3^2)+(1^2+2^2+ 3^2+4^2)+ .......$$ will be
  • $$\displaystyle \frac{1}{4} n (n + 1)^2 (n + 2)$$
  • $$\displaystyle \frac{1}{3} n (n + 1)^2 (n + 2)$$
  • $$\displaystyle \frac{1}{12} n (n + 1) (n + 2)^2$$
  • $$\displaystyle \frac{1}{12} n (n + 1)^2 (n + 2)$$
$$11, 26, 56, 101, 161, .....$$
  • $$236$$
  • $$226$$
  • $$216$$
  • $$206$$
3, 15, 35, 63, 99, ...
  • 133
  • 143
  • 153
  • 165
10, 12, 16, 24, 40, ....
  • 60
  • 56
  • 70
  • 72
Find the Odd one among : 97, 77, 59, 43, 26, 17
  • 77
  • 59
  • 43
  • 26
- nmmn - mmnm - mnnm -
  • nmmn
  • mnnm
  • nnmm
  • nmnm
7th term of $$\displaystyle\frac{1}{2}$$, $$\displaystyle\frac{1}{4}$$, $$\displaystyle\frac{1}{6}$$ $$\dots\dots$$ is
  • $$\displaystyle\frac{1}{10}$$
  • $$\displaystyle\frac{1}{12}$$
  • $$\displaystyle\frac{1}{14}$$
  • $$\displaystyle\frac{1}{16}$$
Find the missing letters
A, B, D, G, .....
  • L
  • M
  • J
  • K
Find the Odd one among : 49, 121, 169, 225, 289, 361
  • 225
  • 121
  • 49
  • 361
In a series, $$T_n=2n+5$$, find $$S_4$$.
  • 40
  • 30
  • 20
  • 10
$$\displaystyle \frac{1}{3^{2}-1}+\frac{1}{5^{2}-1}+\frac{1}{7^{2}-1}+......+\frac{1}{35^{2}-1}=$$
  • $$\displaystyle \frac{4}{17}$$
  • $$\displaystyle \frac{17}{72}$$
  • $$\displaystyle \frac{19}{72}$$
  • $$\displaystyle \frac{17}{36}$$
There is no symmetry in symmetry in legs of Fig
The value of $$1^2+2^2+3^2+\cdots+ n^2$$ is
  • $$\displaystyle\frac{n(n+1)}{2}$$
  • $$\displaystyle\frac{n(n+1)(2n+1)}{6}$$
  • $$\displaystyle\frac{n(n+1)(2n-1)}{6}$$
  • $$\displaystyle\left[\frac{n(n+1)}{2}\right]^2$$
The product $$ \displaystyle \left ( 1-\frac{1}{n} \right )\left ( 1-\frac{1}{n+1} \right )\left ( 1-\frac{1}{n+2} \right )..\left ( 1-\frac{1}{2n} \right ) $$  Equals
  • $$ \displaystyle \frac{n-1}{2n} $$
  • $$ \displaystyle \frac{1}{2n} $$
  • $$ \displaystyle \frac{2n}{n-1} $$
  • $$ \displaystyle \frac{1}{n} $$
Find the sum of first three terms of the following sequence whose $$n^{th}$$ term is $$5n^2-2$$.
  • $$68$$
  • $$86$$
  • $$69$$
  • $$82$$
In a certain language '$$ \displaystyle +\div ?   $$' means 'where are you' , '$$ \displaystyle @-\div    $$' means ' we are here' , and '$$ \displaystyle +@\times    $$' means ' you come here' What is the code for ' Where' ?
  • +
  • $$ \displaystyle \div $$
  • ?
  • @
How is 'red written in that code ?
  • hee
  • silk
  • be
  • cannot be determined
Image
414387.JPG
  • 70
  • 75
  • 65
  • 80
How is 'vegetables are red flowers' written in this code ?
  • Pec silk mit hee
  • silk peehee be
  • il silk mit hee
  • none
Find the sum of odd numbers between $$2$$ and $$76$$.
  • $$1,350$$
  • $$1,443$$
  • $$1,342$$
  • $$1,360$$
Find the next number of the series.
$$7, 10, 8, 11, 9, 12,....$$
  • 9
  • 10
  • 8
  • 7
In a certain sequence of 8 numbers, each number after the first is 1 more than the previous number .If the first number is -5, how many of the numbers in the sequence are positive? 
  • None
  • One
  • Two
  • Three
  • Four
Find the value of $$'?'$$ in the series: $$12, 17, 15, ?, 18, 23, 21,....$$
  • 20
  • 21
  • 22
  • 24
Find the value of $$'x'$$ in the series: $$144, 169, x, 225, 256, 289$$.
  • 190
  • 192
  • 196
  • 195
Find the missing number in the pattern: $$2, 5, 8, 11,$$ __$$, 17, 20, 23, 26$$
  • 11
  • 12
  • 13
  • 14
Complete the pattern: $$3, 5, 8, 13,$$ ___ 
  • 21
  • 22
  • 23
  • 24
Which pair of numbers comes next?
$$25, 23, 5, 20, 16, 5,....$$
  • $$11, 5$$
  • $$5, 6$$
  • $$10, 5$$
  • $$9, 5$$
Which number comes next?
$$5, 9, 13, 17, 21, 25, 29,...$$
  • $$31$$
  • $$32$$
  • $$30$$
  • $$33$$
$$2, 3,$$ __$$, 4, 4, 5, 6, 6, 6, 7, 7, 7...$$ What number should fill the blank?
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
Which pair of numbers comes next?
$$10, 18, 12, 21, 15 ,25, ,....$$
  • $$19, 30$$
  • $$19, 27$$
  • $$30, 19$$
  • $$27, 19$$
Fill in the blank: $$62, 66, 63, 66, 64,$$ __$$, 65,....$$
  • 60
  • 61
  • 62
  • 63
Look at this series: $$32, 31, 33, 32, 34, 33,...$$. What is the next number?
  • 34
  • 32
  • 35
  • 36
Choose the missing number in the series: $$2, 2, 3, 4, 4,$$__$$, 6, 6, 7, 8, 8, 9....$$
  • 5
  • 6
  • 7
  • 8
The value of $$\displaystyle \tan { \alpha  } +2\tan { \left( 2\alpha  \right)  } +4\tan { \left( 4\alpha  \right)  } +...+{ 2 }^{ n-1 }\tan { \left( { 2 }^{ n-1 }\alpha  \right)  } +{ 2 }^{ n }\cot { \left( { 2 }^{ n }\alpha  \right)  } $$ is
  • $$\displaystyle \cot { \left( { 2 }^{ n }\alpha \right) } $$
  • $$\displaystyle { 2 }^{ n }\tan { \left( { 2 }^{ n }\alpha \right) } $$
  • $$\displaystyle 0$$
  • $$\displaystyle \cot { \alpha } $$
What is the missing number in the sequence $$1, 5, 10, 16, 23, 31,$$ ____?
  • $$37$$
  • $$38$$
  • $$39$$
  • $$40$$
  • $$41$$
The sum of $$24$$ terms of the following series $$2+4+6.....$$
  • $$100$$
  • $$200$$ 
  • $$600$$ 
  • $$250$$ 
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers