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CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 9 - MCQExams.com

The value of n=2(11n2) equals 
  • ln3
  • 0
  • ln2
  • ln5
solve that :- 
1179763_5300b9e093224c43a86f8c6d71177d45.png
  • 14
  • 18
  • 11
  • 26
The numbers {\log _{180}}12,{\log _{2160}}12,{\log _{25920}}12 are in
  • AP
  • GP
  • HP
  • None of these
If [x] denotes the greates integer \le x, then \left[\dfrac{2}{3} \right] + \left[\dfrac{2}{3} + \dfrac{1}{99} \right] + \left[\dfrac{2}{3} + \dfrac{2}{99} \right] + .... + \left[\dfrac{2}{3} + \dfrac{98}{99} \right] =
  • 99
  • 98
  • 66
  • 65
If (1+ax)^{n }=1+8x+24x^{2}+...; then \cfrac {a-n}{a+n} is equal to
  • 3
  • \dfrac {-1}{3}
  • -3
  • \dfrac {1}{3}
If S={1}^{2}-{2}^{2}+{3}^{2}-{4}^{2}.... upto n terms and n is even, then S equals _____
  • \cfrac{n(n+1)}{2}
  • \cfrac{n(n-1)}{2}
  • \cfrac{-n(n+1)}{2}
  • \cfrac{-n(n-1)}{2}
The sum \sum _{ i=0 }^{ m }{ \left( \begin{matrix} 10 \\ i \end{matrix} \right) \left( \begin{matrix} 20 \\ m-i \end{matrix} \right)  } (where \left( \begin{matrix} p \\ q \end{matrix} \right)=0 if p<q) is maximum where m is
  • 5
  • 10
  • 15
  • 20
The series {1}^{2}-{2}^{2}+{3}^{2}-{4}^{2}+.....+{99}^{2}-{100}^{2}= _____
  • -5050
  • 5050
  • 11000
  • -11000
If x and y are the number of possibilities that A can assume such that the unit digit of A and A^3 are same and the unit digit of A^2 and A^3 are same respectively ,then the value of x-y is (where A is a single digit number)
  • 4
  • 2
  • 3
  • 5
\begin{bmatrix} 12 & 47 & 21 \\ 10 & 52 & 4 \\ 64 & ? & 24 \end{bmatrix} 
  • 40
  • 83
  • 62
  • 16
In a triangle ABC
acos^2(\frac{C}{2})+c\;cos^2(\frac{A}{2})=\dfrac{3b}{2}, then the sides a,b,c 
  • Satisfy a+b=c
  • are in A.P.
  • are in G.P.
  • are in H.P.
The value of \displaystyle \sum^{n-1}_{r=1}\sin^{2}\dfrac {r \pi}{n} is equal to
  • n
  • \dfrac {n}{2}
  • n+1
  • Zero
The sum of the series 10.^{n}C_{0}+10^{2}.^{n}C_{1}+10^{3}.^{n}C_{2}+...10^{n+1}.^{n}C_{n} is 
  • 11^{n}
  • 10.11^{n}
  • 11^{n+1}
  • 11^{n}-1
1 + \left( {1 + a} \right)x + 1\left( {1 + a + {a^2}} \right){x^2} + \left( {1 + a + {a^2} + {a^3}} \right){x^3} +  -  -  -  -  - \;{\text{where}}\;0 < a,x < 1,\;{\text{is}} -
  • \frac{1}{{\left( {1 - x} \right)\left( {1 - a} \right)}}
  • \frac{1}{{\left( {1 - x} \right)\left( {1 - ax} \right)}}
  • \frac{1}{{\left( {1 - a} \right)\left( {1 - ax} \right)}}
  • None of these
The sum of the series \displaystyle \sum_{r = 1}^{n} (-1)^{r - 1}.^{n}C_{r} (a - r) is
  • a
  • 0
  • n.2^{n - 1} + a
  • None of these
1.3.4+2.5.8+3.6.9+ upto n terms is equal to ________ .
  • \dfrac {n(n+1)(n+2)}{6}
  • \dfrac {n(n+1)(3n^{2}+23n+46)}{12}
  • \dfrac {n(27n^{3}+90n^{2}+45n-5)}{4}
  • \dfrac {n(n+1)(2n+1)}{6}
  • None\ of\ these
The sum of the series  
1+2.2+3.2^{2}+4.2^{3}+5.2^{4}+...+1000.2^{999} is
  • 999.2^{999}-1
  • 999.2^{1000}-1
  • 999.2^{1000}+1
  • 999.2^{999}+1
\displaystyle\sum^n_{r=1}\displaystyle\sum^{r-1}_{p=0} ^{n}C_r\cdot {^{r}C_p}\cdot 2^p is equal to?
  • 4^n-3^n+1
  • 4^n-3^n-1
  • 4^n-3^n+2
  • 4^n-3^n
If | x| < 1 , then the sum of series 1+ 2x + 3x^2 + 4x^3 + .........\infty will be
  • \dfrac{1}{1-x}
  • \dfrac{1}{1+x}
  • \dfrac{1}{(1+x)^2}
  • \dfrac{1}{(1-x)^2}
\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+..n terms =
  • \dfrac{3n}{2(3n+2)}
  • \dfrac{3n}{3n+2}
  • \dfrac{n}{2(3n+2)}
  • \dfrac{n}{3n+2}
The sum of the series {5 \over {13}} + {{55} \over {{{13}^2}}} + {{555} \over {{{13}^3}}} + .........\infty is 
  • {65\over {36}}
  • {65\over {32}}
  • {25\over {36}}
  • none of these
Sum to n terms the following series :
  • 5 + 11 + 19 + 29 + 41 + .......
  • 3 + 7 + 14 + 24 + 37 +......
  • 6 + 9 + 16 + 27 + 42 + .....
  • 5 + 7 + 13 + 31 + 85 + ....
\sum _{ k=1 }^{ 2n+1 }{ (-1)^{k-1} }k^2= 
  • (n+1)(2n+1)
  • (n+1)(2n-1)
  • (n-1)(2n-1)
  • (n-1)(2n+1)
If S = 1 + \frac{1}{{1 + 2}} + \frac{1}{{1 + 2 + 3}} + \frac{1}{{1 + 2 + 3 + 4}}......, then
  • {S_n} = \frac{{2n}}{{n + 1}}
  • {S_n} = \frac{{2n}}{{n - 1}}
  • {S_\infty } = 2
  • {S_\infty } = 1
If S = \tan ^ { - 1 } \left( \frac { 1 } { n ^ { 2 } + n + 1 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { n ^ { 2 } + 3 n + 3 } \right) + \ldots + \tan ^ { - 1 } \left( \frac { 1 } { 1 + ( n + 19 ) ( n + 20 ) } \right) then \tan S is equal to
  • \frac { 20 } { 401 + 20 n }
  • \frac { n } { n ^ { 2 } + 20 n + 1 }
  • \frac { 20 } { n ^ { 2 } + 20 n + 1 }
  • \frac { n } { 401 + 20 n }
7, 11, 23, 51, 103 ?
  • 186
  • 188
  • 185
  • 187
  • none of these
The value of the expression \sum _{ r=0 }^{ n }{ { (-1) }^{ r } } \left( \dfrac { ^nC_r  }{^{r+3}C_r  }  \right) is
  • \dfrac{n(n+1)}{2}
  • \dfrac{n+3}{3}
  • \dfrac{3}{n+3}
  • \dfrac{n+2}{2}
S=\tan^{-1}\left(\dfrac{1}{n^2+n+1}\right)+\tan^{-1}\left(\dfrac{1}{n^2+3n+3}\right)+.....+\tan^{-1}\left(\dfrac{1}{1+(n+19)(n+20)}\right), then \tan S is equal to?
  • \dfrac{20}{401+20n}
  • \dfrac{n}{n^2+20n+1}
  • \dfrac{20}{n^2+20n+1}
  • \dfrac{n}{401+20n}
13, 16, 22, 33, 51 ?
  • 89
  • 78
  • 102
  • 69
  • none of these
Evaluate:-
If \sum\limits_{r - 0}^n {{{\left\{ {\frac{{^n{C_{r - 1}}}}{{^n{C_r}{ + ^n}{C_{r - 1}}}}} \right\}}^3} = \frac{{25}}{{24}}}
  • 3
  • 6
  • 4
  • 5
655, 439, 314, 250, 223 ?
  • 215
  • 210
  • 195
  • 190
  • none of these
If the expansion of \left( x+a \right) ^{ n } if the sum of odd terms be P & sum of even terms be Q, prove that
  • { P }^{ 2 }-{ Q }^{ 2 }=({ x }^{ 2 }-{ a }^{ 2 })^{ n }
  • 4PQ=(x+a)^{ 2n }-(x-a)^{ 2n }
  • P^2-Q^2=(x^2+a^2)^{n}
  • None\ of\ these
Sum of the series
S=1^{2}-2^{2}+3^{2}-4^{2}+..... -2000^{2}+2003^{2} is
  • 2007006
  • 1005004
  • 2000506
  • None
Find the next term
210,209,205,196,180,?
  • 138
  • 77
  • 155
  • 327
Determine the next term 20, 24, 33, 49, 74, 110, ?
  • 133
  • 147
  • 159
  • 163
  • 171
Find the next term of the series 1728, 2744, 4096, 5832, 8000, 10648, ?
  • 2167
  • 13824
  • 15625
  • 9261
  • 17576
4,6,12,30,90,315,?
  • 945
  • 1102
  • 1260
  • 1417.5
  • None\ of\ these
Find next term
462,552,650,756,870,992,?
  • 1040
  • 1122
  • 1132
  • 105
Find the missing number from the given alternatives.
1270336_822c03df2be64fbfb6d26b105230fb9f.png
  • 39,116
  • 52,156
  • 30,117
  • 31,116
8, 31, 122, 485, 1936, 7739, ?
  • 30950
  • 46430
  • 34650
  • 42850
  • 38540
The sum of infinite series \begin{vmatrix} 1 & 2 \\ 6 & 4 \end{vmatrix}+\begin{vmatrix} \frac { 1 }{ 2 }  & 2 \\ 2 & 4 \end{vmatrix}+\begin{vmatrix} \frac { 1 }{ 4 }  & 2 \\ \frac { 2 }{ 3 }  & 4 \end{vmatrix}+.........
  • -10
  • 0
  • 10
  • \infty
If \dfrac{\pi}{4}-1+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{11}-\dfrac{1}{13}+=0 then value of \dfrac{1}{1\times3}+\dfrac{1}{5\times7}+\dfrac{1}{9\times11}+\dfrac{1}{13\times15}+.. is
  • \dfrac{\pi}{8}
  • \dfrac{\pi}{6}
  • \dfrac{\pi}{4}
  • \dfrac{\pi}{34}
Let t_{r}=\frac{r}{1+r^{2}+r^{4}} then, \lim_{n\rightarrow \infty }\sum_{r=1}^{n}t_{r} equals
  • \frac{1}{4}
  • 1
  • \frac{1}{2}
  • None of these
The sum to n terms of the series 
\dfrac {3}{1^{2}}+\dfrac {5}{1^{2}+2^{2}}+\dfrac {7}{1^{2}+2^{2}+3^{2}}+......... is 
  • \dfrac {6n}{n+1}
  • \dfrac {9n}{n+1}
  • \dfrac {12n}{n+1}
  • \dfrac {3n}{n+1}
499, 622, 868, 1237, 1729, 2344, ?
  • 3205
  • 3082
  • 2959
  • 3462
  • 2876
The sum \dfrac{1}{1+1^{2}+1^{4}}+\dfrac{2}{1+2^{2}+2^{4}}+\dfrac{3}{1+3^{2}+3^{4}}+...+\dfrac{99}{1+99^{2}+99^{4}} lies between

  • 0.46 and 0.47
  • 0.52 and 1.0
  • 0.48 and 0.49
  • 0.49 and 0.50
Find : 12,15,21,24,30,33 , ? , ?
  • 39,42
  • 37,42
  • 38,47
  • 39,51
Find the missing number :

1306229_30e87c7078374916b3c099fafe3684b1.png
  • 125
  • 90
  • 105
  • 225
23,29,47,75 , ?
  • 87
  • 93
  • 110
  • 117
The value of \dfrac{1}{6.10}+\dfrac{1}{10.14}+\dfrac{1}{14.18}+....\infty equals to
  • \dfrac{1}{(24)^2}
  • \dfrac{1}{6}
  • \dfrac{1}{24}
  • \dfrac{1}{(24)^3}
0:0:1


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