Loading [MathJax]/jax/element/mml/optable/SuppMathOperators.js

CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 10 - MCQExams.com

The sum of n=1tan1(2n2+n+4) is equal to-
  • tan12
  • π2+tan12
  • π2tan12
  • π4
496:204::329:?
  • 90
  • 110
  • 115
  • 135
If sin4α.cos2α=3r=0Cr.cos(2rα) then C0+C1+C2+C3=
  • 0
  • 3
  • 4
  • 7
If Sn=74.1.2+1042.2.3+1343.3.4+.... then S is equal to?
  • 52
  • 98
  • 32
  • 1
Find the missing number.
1306969_c830724f37e04dcebf1e546f99ec639f.png
  • 74
  • 62
  • 91
  • 97
The sum of the following series 1+6+9(12+22+32)7+12(12+22+32+42)9+15(12+22+....+52)11+..... up to 15 terms is:
  • 7820
  • 7830
  • 7520
  • 7510
The value of the series 13!+25!+37!+.....  to    is equal to 
  • 12e
  • 12e
  • 32e
  • 45e
The sum of the series
  9522.1+13533.2+17544.3..........  Infinite terms
  • 125
  • 15
  • Not a finite number
  • 95
The sum to infinity of the series 1+\dfrac {2}{3}+\dfrac { 6 }{ { 3 }^{ 2 } } +\dfrac { 10 }{ { 3 }^{ 3 } } +\dfrac { 14 }{ { 3 }^{ 4 } }+.... is
  • 3
  • 4
  • 6
  • 2
If x_{1},x_{2},.... are in H.P and x_{1},2,x_{20} are in G.P, then \displaystyle \sum _{ 1 }^{ 19 }{ x_{r} .x_{r+1}}= 
  • 76
  • 80
  • 84
  • 70
The value of \dfrac { 1 }{ 4 } \tan\dfrac { \pi  }{ 8 } +\dfrac { 1 }{ 8 } \tan\dfrac { \pi  }{ 16 } +\dfrac { 1 }{ 16 } \tan\dfrac { \pi  }{ 32 } +......\infty terms is equal to -
  • \dfrac { 5 }{ \pi } -\cfrac { 1 }{ 2 }
  • \cfrac { 3 }{ \pi } +\cfrac { 1 }{ 2 }
  • \cfrac { 2}{ \pi } -\cfrac { 1 }{ 2 }
  • \cfrac { 4 }{ \pi } -\cfrac { 1 }{ 4 }
Find the missing number
1312792_39895e31d00e4a2a83fc35377622c5be.png
  • 74
  • 62
  • 91
  • 97
If an =\displaystyle \sum_{r =0}^{n} \dfrac{1}{^{n}C_{r}} then \displaystyle \sum_{r=0}^{n} \dfrac{r}{^{n}C_{r}} equals
  • (n-1)a_{n}
  • na_{n}
  • \dfrac{1}{2}na_{n}
  • None\ of\ these
Find the sum of first 15 terms of the sequence whose {n}^{th} term is 3+4n.
  • 525
  • 425
  • 495
  • None\,of\,thes
If in a series t_n=\dfrac{n+1}{(n+2)!} then \displaystyle\sum^{10}_{n=0}t_n is equal to?
  • 1-\dfrac{1}{10!}
  • 1-\dfrac{1}{11!}
  • 1-\dfrac{1}{12!}
  • None of these
Let \sum _{ r=1 }^{ n }{ { r }^{ 4 } } =f\left( n \right) , then \sum _{ r=1 }^{ n }{ { \left( 2r-1 \right)  }^{ 4 } } is equal to
  • f\left( 2n \right) -16f\left( n \right)
  • f\left( 2n \right) +7f\left( n \right)
  • f\left( 2n+1 \right) 8f\left( n \right)
  • none of these
If the sum of the first 15 terms of the series \lgroup \frac{3}{4} \rgroup^3 + \lgroup 1\frac{1}{2} \rgroup^3 + \lgroup 2\frac{1}{4} \rgroup^3 + 3^3 + \lgroup 3\frac{3}{4} \rgroup^3 + ........... is equal to 225 k. then k is equal to:
  • 9
  • 27
  • 108
  • 54
C_1 + 2C_2 + 3C_3 + ...... + nC_n is equal to
  • 2^{n-1}
  • 2^{n +1}
  • n. 2^{n -1}
  • n. 2^{n +1}
insert the missing number:  5,8,12,17,23,___,38 
  • 29
  • 30
  • 32
  • 25
The sum of the series 1+\dfrac{\log_e x}{1!}+\dfrac{(\log_e x)^2}{2!}+........ is 
  • x
  • x^2
  • x^3
  • none of these
If x<1, then \displaystyle \frac { 1 }{ 1+x } +\frac { 2x }{ 1+{ x }^{ 2 } } +\frac { { 4x }^{ 3 } }{ 1+{ x }^{ 4 } } +.........\infty =
  • x
  • \frac { 1 }{ 1+x }
  • \frac { 1 }{ 1-x }
  • \frac { 1 }{ x }
The sum of the series 1+2(1 +1/n)+ 3{ \left( 1+1/n \right)  }^{ 2 }+....\infty \quad is\quad given\quad by
  • { n }^{ 2 }\quad +\quad 1
  • n\left( n+1 \right)
  • n{ (1+1/n) }^{ 2 }
  • { n }^{ 2 }
The sum of the series 1 + \frac { 1 + 2 } { 2 } + \frac { 1 + 2 + 3 } { 3 } + \ldots to n terms is
  • \frac { n ( n + 1 ) } { 2 }
  • \frac { n ( n + 3 ) } { 4 }
  • \frac { n ( n + 1 ) + n } { 4 }
  • \frac { n ( n - 1 ) } { 2 }
If \sum _{ k=2 }^{ n }{ cos{  }^{ -1 }(\frac { 1+\sqrt { (k-1)(k+2)(k+1)k }  }{ k(k+1) }  } )=\frac { 120\pi  }{ \lambda  },then
  • number of even divisors of \lambda is 24
  • Sum of proper divisors of \lambda is 2418.
  • Sum of proper divisors of \lambda is 197.
  • number of ways in which \lambda can be expressed as product of two co-prime factors is 4
What is the next number in the series 2,12,36,80,150?
  • 194
  • 210
  • 252
  • 258
The sum of the first n terms of the series { 1 }^{ 2 }+2.{ 2 }^{ 2 }+{ 3 }^{ 2 }+2.{ 4 }^{ 2 }+{ 5 }^{ 2 }+2.{ 6 }^{ 2 }+... is \dfrac { n{ \left( n+1 \right)  }^{ 2 } }{ 2 } when n is even. When n is odd the sum is
  • \dfrac { 3n\left( n+1 \right) }{ 2 }
  • \dfrac { { n }^{ 2 }\left( n+1 \right) }{ 2 }
  • \dfrac { { n\left( n+1 \right) }^{ 2 } }{ 4 }
  • { \left[ \dfrac { n\left( n+1 \right) }{ 2 } \right] }^{ 2 }
Value of 1+\dfrac{1^3+2^3}{1+2}+\dfrac{1^3+2^3+3^3}{1+2+3}+...+\dfrac{1^3+2^3+......15^3}{1+2+.....+15}-\dfrac{1}{2}(1+2+.....+15) is?
  • 840
  • 720
  • 680
  • 620
Find the sum of the following series to n terms:
1\times 2+2\times 3+3\times 4+4\times 5+...
  • \dfrac{n}{4}(n-1)(n+2)
  • \dfrac{n}{3}(n-1)(n-2)
  • \dfrac{n}{2}(n-1)(n+1)
  • \dfrac{n}{3}(n+1)(n+2)
Find the sum of the following series to n terms:
1+(1+2)+(1+2+3)+(1+2+3+4)+...
  • \dfrac{n}{6}(n+1)(n+2)
  • \dfrac{n}{6}(n-1)(n-2)
  • \dfrac{n}{6}(n+1)(n-1)
  • None of these
5,5,5,... forms a ______
  • Series
  • Sequence
  • Progression
  • None of the above
Whole numbers from a sequence/progression, as they are formed by the fixed rule of adding 1 to previous whole number.
  • True
  • False
State true/false:
3,4,5,6,7,...... forms a progression. As they are formed by the rule n+1
  • True
  • False
Find the sum of Arithmetic means of 3 , 9 and 12 , 8.

  • 6
  • 9
  • 20
  • 16
The arithmetic mean of 4 and 14 is 
  • 9
  • 18
  • 10
  • 4
If AM of two numbers a and 17 isThen a is ___
  • 15
  • 13
  • 17
  • None of the above
Insert an arithmetic mean between 7 and 21
  • 10
  • 14
  • 28
  • 30
Arithmetic mean of two numbers a+d and a-d is 
  • a
  • b
  • Cannot be determined
  • None of the above
Sum of the series S=1^2-2^2+3^2-4^2+.....-2002^2+2003^2 is
  • 2007006
  • 1005004
  • 2000506
  • 1005040
The sum of n terms of the series 1^2-2^2+3^2-4^2+5^2-6^2+... is 
  • \dfrac{-n(n+1)}{2} if n is even
  • \dfrac{n(n+1)}{2} if n is odd
  • -n(n+1) if n is even
  • \dfrac{n(n+1)(2n+1)}{6} if n is odd
\displaystyle \frac{1^{3}}{1}+\frac{1^{3}+2^{3}}{1+3}+\frac{1^{3}+2^{3}+3^{3}}{1+3+5}+\ldots.n terms =
  • \displaystyle \frac{\mathrm{n}(2\mathrm{n}^{2}+9\mathrm{n}+13)}{24}
  • \displaystyle \frac{n(2n^{3}+9n+13)}{8}
  • \displaystyle \frac{n(n^{2}+9n+13)}{24}
  • \displaystyle \frac{n(n^{2}+9n+13)}{8}

Observe the following lists List I and  List II

(A) \displaystyle \sum_{n=0}^{\infty}\frac{x^{n}(\log_{e}a)^{n}}{n!}                                     (1)\displaystyle \frac{e^{x}-e^{-x}}{2}
(B) \displaystyle \sum_{n=0}^{\infty}\frac{x^{2n}}{(2n)!}                                                (2) e^{-ax}
(C) \displaystyle \sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)!}=                                    (3) a^{x}
(D) \displaystyle \sum_{n=0}^{\infty}\frac{(-1)^{n}.(ax)^{n}}{n!}                                  (4)\displaystyle \frac{a^{x}-a^{-x}}{2}
                                                                       (5)\displaystyle \frac{e^{x}+e^{-x}}{2}
The correct match of List I to List II is:
  • A - 1, B - 4, C - 3, D - 5
  • A - 4, B - 2, C - 1, D - 3
  • A - 3, B - 5, C - 1, D - 2
  • A - 2, B - 3, C - 5, D - 4
 Sum  the  series  1^3+3^3+5^3+..........   to  n terms  is
  • n^2\left ( 2n^2-1 \right )
  • n\left ( 2n^2-1 \right )
  • n\left ( 2n^2+1 \right )
  • n^2\left ( 2n^2+1 \right )
If \displaystyle f(r)=1+\frac {1}{2}+\frac {1}{3}+.....+\frac {1}{r} and f(0)=0, then value of \displaystyle \sum_{r=1}^{n}(2r+1)f(r) is
  • n^2f(n)
  • \displaystyle (n+1)^2f(n+1)-\frac {n^2+3n+2}{2}
  • \displaystyle (n+1)^2f(n)-\frac {n^2+n+1}{2}
  • (n+1)^2f(n)
If n is an odd integer greater than or equal to 1, then the value of  n^3-(n-1)^3+(n-2)^3-....+(-1)^{n-1}1^3, is
  • \dfrac{(n+1)^2(2n-1)}{4}
  • \dfrac{(n-1)^2(2n-1)}{4}
  • \dfrac{(n+1)^2(2n+1)}{4}
  • \dfrac{(n+1)^2(2n+1)}{8}
The sum to n terms of the series \displaystyle \frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+... is
  • \displaystyle \frac{6n}{n+1}
  • \displaystyle \frac{9n}{n+1}
  • \displaystyle \frac{12n}{n+1}
  • \displaystyle \frac{3n}{n+1}
The sum of the first n terms of the series 1^2+2\cdot2^2+3^2+2\cdot4^2+5^2+2\cdot6^2+.....  is \dfrac{n \left ( n+1\right )^2}{2} when n is even. 
When n is odd, then the sum is
  • \dfrac{3n \left ( n+1\right )}{2}
  • \dfrac{n (n+1)^2}{4}
  • \dfrac{n \left ( n+1\right )^2}{2}
  • \dfrac{n^2 \left ( n+1\right )}{2}
The sum of n terms of the series 1 + (1 + a) + (1 + a + a^2) + (1 + a  + a^2 + a^3) + .... is
  • \displaystyle \frac{n}{1+a} - \frac{1 - a^n}{(1 - a)^2}
  • \displaystyle \frac{n}{1- a} + \frac{a (1 - a^n)}{(1 - a)^2}
  • \displaystyle \frac{n}{1 - a} + \frac{a (1 + a^n)}{(1 - a)^2}
  • none of the above
ABCD is a square of length a, a\epsilon N, a>Let L_{1}L_{2}L_{3},... be points on BC such that BL_{1}=L_{1}L_{2}=L_{2}L_{3}=...=1 and M_{1}M_{2}M_{3},... be points on CD such that CM_{1}=M_{1}M_{2}=M_{2}M_{3}=...=1. Then \sum_{n=1}^{a-1}\left ( A{L_{n}}^{2}+L_{n}{M_{n}}^{2} \right ) is equal to
  • \dfrac{1}{2}a\left ( a-1 \right )^{2}
  • \dfrac{1}{2}a\left ( a-1 \right )\left ( 4a-1 \right )
  • \dfrac{1}{2}a\left ( a-1 \right )\left ( 2a-1 \right )\left ( 4a-1 \right )
  • none of these
If \displaystyle \sum_{r=1}^{n}t_{r}=\frac {n(n+1)(n+2)(n+3)}{8}, then \displaystyle \underset{n\rightarrow \infty}{ \lim} \sum_{r=1}^{n}\frac {1}{t_{r}}
is equal to: 
  • \displaystyle \frac {1}{8}
  • \displaystyle \frac {1}{4}
  • \displaystyle \frac {1}{2}
  • 1
Let x, y, z be three positive prime numbers. The progression in which \sqrt{x}\sqrt{y}\sqrt{z} can be three terms (not necessarily consecutive) is
  • AP
  • GP
  • HP
  • none of these
0:0:2


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers