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CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 6 - MCQExams.com

6,10,18,34,66
The first number in the list above is 6. Determine a rule for finding each successive number in the list.
  • Add 4 to the preceding number.
  • Take 12 of the preceding number and then add 7 to that result.
  • Double the preceding number and then subtract 2 from that result.
  • Subtract 2 from the preceding number and then double that result.
  • Triple the preceding number and then subtract 8 from that result.
The value of the sum 1.2.3+2.3.4+3.4.5+... upto n terms =
  • 16n2(2n2+1)
  • 16(n21)(2n1)(2n+3)
  • 18(n2+1)(n2+5)
  • 14n(n+1)(n+2)(n+3)
m,2m,4m,...
The first term in the sequence above is m, and each term thereafter is equal to twice the previous term. If m is an integer, which of the following could NOT be the sum of the first four terms of this sequence?
  • 26
  • 15
  • 45
  • 75
  • 120
Identify the missing integer: 9,45, ____,1125,5625...
  • 220
  • 223
  • 224
  • 225
The terms of a sequence are defined by an=3an1an2 for n>2. Find the value of a5 given that a1=4 and a2=3.
  • 12
  • 23
  • 25
  • 31
  • 36
For all numbers a and b, let ab be defined by ab=ab+a+b. Then for the numbers x, y and z, which of the following is/are true?
I. xy=yx
II. (x1)(x+1)=(xx)1
III. x(y+z)=(xy)+(xz)
  • I only
  • II only
  • III only
  • I and II only
  • I, II, and III
The sum of 1 st n terms of the series
121+12+221+2+12+22+321+2+3+........
  • n+23
  • n(n+2)3
  • n(n2)3
  • n(n2)6
If mn=m+(m1)+(m2)+......+(mn), evaluate 75.
  • 25
  • 20
  • 27
  • 18
N=a2+b2 is a three-digit number which is divisible bya = 10x + y and b = 10x + z, where z is a prime number, and x and y are natural numbers. If a + b = 31, find the value of N.
  • 565
  • 485
  • 505
  • 485 or 505
If ab=6×a3×b, evaluate (53)20
  • 2
  • 41
  • 66
  • 1
The sum of the series,
12.32+23.422+34.523+...... to n terms is _____.
  • 2n+1n+2+1
  • 2n+1n+21
  • 2n+1n+2+2
  • 2n+1n+22
The value of the infinite series 12+22|3_+12+22+32|4_+12+22+33+42|5_........ is
  • e
  • 5e
  • 5e612
  • 5e6
Let S denote the sum of the infinite series 1+82!+213!+404!+655!+........ Then
  • S<8
  • S>12
  • 8<S<12
  • S=8
x=1+12×|1_+14×|2_+18×|3_
  • e1/2
  • e2
  • e
  • 1e
Find the (2n)th term of the series whose nth term is n2+1n3:
  • n2+18n3
  • 4n2+18n3
  • 4n2+1n3
  • 2n2+12n3
In the series 1+3+6+10+......, find the nth term:
  • n(n1)2
  • n(n+1)2
  • n(2n1)2
  • n(2n+1)2
Consider an incomplete pyramid of balls on a square base having 18 layers; and having 13 balls on each side of the top layer. Then the total number N of balls in that pyramid satisfies
  • 9000<N<10000
  • 8000<N<9000
  • 7000<N<8000
  • 10000<N<12000
With the help of match-sticks, Zalak prepared a pattern as shown below. When 97 matchsticks are used, the serial number of the figure will be ...........
626028_e327aecd938b484db21d45ffb46b1a27.PNG
  • Figure 32
  • Figure 95
  • Figure 49
  • Figure 48
Three bells commenced to toll at the same time and tolled at intervals of 20,30,40 seconds respectively. If they toll together at 6 am, then which of the following is the time at which they can toll together
  • 6:55am
  • 6:56am
  • 6:57am
  • 6:59am
Let an=4n+4n212n+1+2n1 then 144n=1an equals
  • 2456
  • 2645
  • 2466
  • 2546
If 112+122+132+..... upto =π26, then 112+132+152+....=
  • π212
  • π224
  • π28
  • π24
k=16k(32k+1+22k+1)(3k2k+1+2k3k+1) is equal to
  • 3
  • 13
  • 43
  • 65
Let S = \displaystyle \sum_{n = 1}^{99} = \dfrac {5^{100}}{5^{100} + 25^{n}} then find the value of [S], where [.] = G.I.F.
  • 99
  • 100
  • 25
  • 49
The first term of an AP is 148 and the common difference is -2. If the AM of first n terms of the AP is 125, then the value of n is
  • 18
  • 24
  • 30
  • 36
  • 48
The sum of the series \displaystyle \sum_{n = 8}^{17} \dfrac{1}{(n + 2)(n + 3)} is equal to
  • \dfrac{1}{17}
  • \dfrac{1}{18}
  • \dfrac{1}{19}
  • \dfrac{1}{20}
  • \dfrac{1}{21}
The value of \dfrac {1}{i} + \dfrac {1}{i^{2}} + \dfrac {1}{i^{3}} + .... + \dfrac {1}{i^{102}} is
  • -1 - i
  • -1 + i
  • 1 - i
  • 1 + i
  • 1 - 2i
The sum of the first n terms of the series { 1 }^{ 2 }+2\cdot { 2 }^{ 2 }+{ 3 }^{ 3 }+2\cdot { 4 }^{ 2 }+{ 5 }^{ 2 }+2\cdot { 6 }^{ 2 }+\cdots 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 }
Find the sum of the series 
\displaystyle \frac{1}{2\cdot 3}+\frac {1}{4\cdot 5}+\frac {1}{6\cdot 7}+ ...
  • log\, \frac {e}{2}
  • log\, \frac {e}{4}
  • log\, \frac {2}{3}
  • log\, \frac {2}{4}
If the natural numbers are divided into groups of {1}, {2, 3}, {4, 5, 6}, {7, 8, 9, 10} ....Then the /sum of 50th group is 
693570_f1a93ed930d240ae89ce071c94c93b40.PNG
  • 65225
  • 56225
  • 62525
  • 53625
The value of a for which side of nth square equals the diagonals of (n + 1)^{th} square is 
  • 1/3
  • 1/4
  • 1/2
  • 1\sqrt{2}
If \displaystyle \sum_{r = 1}^{n}t_{n} = \dfrac {n(n +1)(n + 2)(n + 3)}{8}, then \displaystyle \sum_{r = 1}^{n} \dfrac {1}{t_{1}} equals
  • -\left (\dfrac {1}{(n + 1)(n + 2)} - \dfrac {1}{2}\right )
  • \left (\dfrac {1}{(n + 1)(n + 2)} - \dfrac {1}{2}\right )
  • \left (\dfrac {1}{(n + 1)(n + 2)} + \dfrac {1}{2}\right )
  • \left (\dfrac {1}{(n - 1)(n - 2)} + \dfrac {1}{2}\right )
Let r^{th} term of a series is given by, T_r = \dfrac {r}{1-3r^2 + r^4} .
Then \underset {n \rightarrow \infty}{\lim} \sum_{r=1}^n T_r is 
  • \cfrac { 3 }{ 2 }
  • \cfrac { 1 }{ 2 }
  • \cfrac { -1 }{ 2 }
  • \cfrac { -3 }{ 2 }
If \alpha =1 / 4 and P_n denotes the perimeter of the nth square then\sum_{n=1}^{\infty } P_n equals 
  • \dfrac{8}{3}\left ( 4+\sqrt{10} \right )
  • \dfrac{8}{3}
  • \dfrac{16}{3}
  • None of these
If a_1 \in R - \left \{ 0 \right \}, i = 1, 2, 3, 4 and x \in R and \left ( \sum_{i=1}^{3}a_i^2\right ) x^2-2x \left ( \sum_{i=1}^{3}a_i a_{i+1}\right )+\sum_{i=2}^{4}a_i^2\leq 0, then a_1, a_2, a_3, a_4 are in
  • A.P
  • G.P
  • H.P
  • A.G.P
If { b }_{ i }=1-{ a }_{ i },na=\sum _{ i=1 }^{ n }{ { a }_{ i } } ,nb=\sum _{ i=1 }^{ n }{ { b }_{ i } } \quad , then \sum _{ i=1 }^{ n }{ { { a }_{ i }b }_{ i } } +\sum _{ i=1 }^{ n }{ { \left( { a }_{ i }-a \right)  }^{ 2 } } =
  • ab
  • -nab
  • nab
  • (n+1)ab
4,9,25,?,121,169
  • 36
  • 49
  • 64
  • 81
Let S be the infinite sum given by S=\displaystyle \sum_{n=0}^{\infty}\frac{a_n}{10^{2n}}, where (a_n)_{n\geq 0} is a sequence defined by a_0=a_1=1 and a_j=20a_{j-1} for j\geq 2. If S is expressed in the form \displaystyle\frac{a}{b}, where a, b are coprime positive integers, than a equals.
  • 60
  • 75
  • 80
  • 81
Find the missing number in the circle:
716190_432c83cc262449fb9c49be0336e200ad.jpg
  • 66
  • 72
  • 71
  • 78
\displaystyle \sum_{r = 0}^{n}{ \left( \frac{ 2^{r-2} . ^nC_r}{(r+1)(r+2)} \right) } is equal to
  • \displaystyle \frac{3^{n+2} - 2n + 5}{(n+1)(n+2)}
  • \displaystyle \frac{3^{n+2} - 4n + 5}{(n+1)(n+2)}
  • \displaystyle \frac{3^{n+2} - 2n - 5}{(n+1)(n+2)}
  • None of these
13, 74, 290, 650,.......
  • 1248
  • 1370
  • 1346
  • 1452
  • 1625
Figures 1 and 2 are related in a particular manner. Establish the same relationship between figures 3 and 4 by choosing a figure from amongst the options.
726593_93a844c1ede949b2b2fa594a3d0af569.png
Select the INCORRECT match
  • 3249-MMMCCXLIX
  • 1667-MDCLXVII
  • 207-CCXVII
  • 499-CDXCIX
The value of \sum _{ n=1 }^{ \infty  }{ { \left( -1 \right)  }^{ n+1 }\left( \cfrac { n }{ { 5 }^{ n } }  \right)  } equals
  • \cfrac { 5 }{ 12 }
  • \cfrac { 5 }{ 24 }
  • \cfrac { 5 }{ 36 }
  • \cfrac { 5 }{ 16 }
If the p^{th} term of the series of positive numbers 25, 22\dfrac {3}{5}, 20\dfrac {1}{2}, 18\dfrac {1}{4}, .... is numerically the smallest, then the p^{th} is.
  • \dfrac{1}{4}
  • \dfrac{1}{7}
  • \dfrac{1}{3}
  • \dfrac{1}{5}
The sum of first 20 terms of the series 1,6,13,22- is
  • 5580
  • 5780
  • 7789
  • 1237
If \begin{vmatrix} x \end{vmatrix}<1  then the coefficient of x^5 in the expansion of \dfrac{3x}{(x-2) (x-1)} is
  • \dfrac{33}{32}
  • -\dfrac{33}{32}
  • \dfrac{31}{32}
  • -\dfrac{33}{34}
2.4+4.7+6.10+..... upto (n-1) terms 
  • 2{ n }^{ 3 }+2{ n }^{ 2 }
  • \cfrac { 1 }{ 6 } \left( { n }^{ 3 }+3{ n }^{ 2 }+1 \right)
  • 2{ n }^{ 3 }-2{ n }^{ 2 }
  • \cfrac { 1 }{ 6 } \left( { n }^{ 2 }-3{ n }+1 \right)
Sum of the series \sum _{ r=1 }^{ n }{ \left( { r }^{ 2 }+1 \right) r! } is ______
  • (n+1)!
  • (n+2)!-1
  • n(n+1)!
  • none of these
Given S_n=1+q+q^2+...+q^n & S_n=1+\displaystyle\frac{q+1}{2}+\left(\frac{q+1}{2}\right)^2+....+\left(\displaystyle\frac{q+1}{2}\right)^n, q\neq 1. then ^{n+1}C_1+ {^{n+1}C_2\cdot s_1}+ {^{n+1}C_3}\cdot s_2+....+{^{n+1}C_{n+1}}\cdot s_n=2^n\cdot S_n.
  • True
  • False
Suppose a_2,a_3,a_4,a_5,a_6,a_7 are integers such that
\dfrac {5}{7}=\dfrac {a_2}{2!}+\dfrac {a_3}{3!}+\dfrac {a_4}{4}+\dfrac {a_5}{5!}+\dfrac {a_6}{6!}+\dfrac{a_7}{7!}
where 0 \le a < j for j=2,4,5,6,7. The sum a_2+a_3+a_4+a_5+a_6+a_7 is 
  • 8
  • 9
  • 10
  • 11
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