CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 7 - MCQExams.com

The value of the sum $$1.2.3+2.3.4+3.4.5+.......$$ upto n terms=
  • $$\frac{1}{6}n^{2}(2n^{2}+1)$$
  • $$\frac{1}{6}n^{2}(n^{2}-1)(2n-1)(2n+3)$$
  • $$\frac{1}{8}(n^{2}+1)(n^{2}+5)$$
  • $$\frac{1}{4}(n)(n+1)(n+2)(n+3)$$
If the coefficients of $$x^9,x^{10},x^{11}$$ in the expansion of $$(1+x)^n $$ are in arithmetic progression then $$n^2-41n=$$
  • $$398$$
  • $$298$$
  • $$-398$$
  • $$198$$
The value of $$\cfrac { 1 }{ \left( 2n-1 \right) !0! } +\cfrac { 1 }{ \left( 2n-3 \right) !2! } +\cfrac { 1 }{ \left( 2n-5 \right) !4! } +....+\cfrac { 1 }{ 1!\left( 2n-2 \right) ! } $$ equal to
  • $${ 2 }^{ 2n-1 }$$
  • $${ 2 }^{ 2n-2 }$$
  • $${ 2 }^{ 2n-3 }$$
  • $$\cfrac { { 2 }^{ 2n-2 } }{ \left( 2n-1 \right) ! } $$
If $$x\in R$$, find the minimum value of the expression $$3^x+3^{1-x}$$.
  • $$3 \sqrt 2$$
  • $$2 \sqrt 3$$
  • $$3 \sqrt 3$$
  • none of these
Sum of the series
$${ \left( ^{ 100 }C_{ 1 } \right)  }^{ 2 }+2{ \left( ^{ 100 }C_{ 2 } \right)  }^{ 2 }+3{ \left( ^{ 100 }C_{ 3 } \right)  }^{ 2 }+.....100{ \left( ^{ 100 }C_{ 100 } \right)  }^{ 2 }$$ equals:
  • $$\dfrac { { 2 }^{ 99 }\left[ 1.3.5.....\left( 199 \right) \right] }{ \left( 99 \right) ! }$$
  • $$100.^{ 100 }C_{ 100 }$$
  • $$50.^{ 200 }C_{ 100 }$$
  • $$100.^{ 199 }C_{ 99 }$$
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  $$\dfrac{n(n + 1)^2}{2}$$  when n is even.When n is odd the sum is -
  • $$\displaystyle\frac{3n(n + 1)}{2}$$
  • $$ \cfrac { 8{ n }^{ 3 }+6{ n }^{ 2 }+n }{ 3 } $$
  • $$\displaystyle\frac{n(n + 1)^2}{4}$$
  • $$\displaystyle\left [ \frac{n(n + 1)}{4} \right ]^2$$
Let $$A$$ be the sum of the first $$20$$ terms and $$B$$ be the sum of the first $$40$$ terms of the series $$1^{2} + 2.2^{2} + 3^{2} + 2.4^{2} + 5^{2} + 2.6^{2} + .....$$ If $$B - 2A = 100\lambda$$, then $$\lambda$$ is equal to
  • $$464$$
  • $$496$$
  • $$232$$
  • $$248$$
If $$z^2-2z+4=0$$ then the value of $$\left(\displaystyle\frac{z}{2}+\frac{2}{z}\right)^2+\left(\displaystyle\frac{z^2}{4}+\frac{4}{z^2}\right)^2+\left(\displaystyle\frac{z^3}{8}+\frac{8}{z^3}\right)^2+........+\left(\displaystyle\frac{z^{24}}{2^{24}}+\frac{2^{24}}{Z^{24}}\right)^2$$ is equal to.
  • $$24$$
  • $$32$$
  • $$48$$
  • None of these
The odd natural numbers have been divided in groups as $$(1, 3); (5, 7, 9, 11); (13, 15, 17, 19, 21, 23); .....$$ Then the sum of numbers in the $$10^{th}$$ group is
  • $$4000$$
  • $$4003$$
  • $$4007$$
  • $$4008$$
If $$9@ 3 = 12, 15 @ 4 = 22, 16 @ 14 = 4$$, then what is the value of $$6 @ 2 = ?$$
  • $$26$$
  • $$1$$
  • $$30$$
  • $$8$$
 5 2 7
 ? 3 1
 4 5 2
 -15 7 13
Select the missing number from the given alternatives.
  • $$1$$
  • $$5$$
  • $$9$$
  • $$7$$
Select the missing number from the given alternatives.
$$3$$$$4$$$$2$$$$14$$
$$6$$$$5$$$$4$$$$44$$
$$5$$$$2$$$$7$$?
  • $$58$$
  • $$14$$
  • $$49$$
  • $$4$$
If $$12\times 16 = 188$$ and $$14\times 18 = 248$$, then find the value of $$16\times 20 = ?$$
  • $$320$$
  • $$360$$
  • $$316$$
  • $$318$$
Select the missing number from the given alternatives.
908224_58dcb79bac6e47e4a5a056e98ecf5ebf.png
  • 110
  • 115
  • 121
  • 54
If $$28\div 11 = 8, 39\div 21 = 7, 45\div 27 = 4$$, then $$95\div 25 = ?$$
  • $$11$$
  • $$9$$
  • $$16$$
  • $$5$$
In a row of girls, Mridula is $$18^{th}$$ from the right and Sanjana is $$18^{th}$$ from the left. If both of them interchange their position, Sanjana becomes $$25^{th}$$ from the left, how many girls are there in the row?
  • $$40$$
  • $$41$$
  • $$42$$
  • $$35$$
Choose the correct answer from the alternatives given :
The sum of $$\dfrac{1}{\sqrt 2 + 1} \, + \, \dfrac{1}{\sqrt 3 + \sqrt 2} \, + \, \dfrac{1}{\sqrt 4 + \sqrt 3} \, + \, ..... \, + \dfrac{1}{\sqrt {100} + \sqrt {99}}$$ is
  • $$9$$
  • $$10$$
  • $$11$$
  • None of these
Choose the correct answer alternatives given.
Select the missing number from the given alternatives.
908756_fd63ade1fdca4c419eb6d7cc3bd855da.png
  • 18
  • 21
  • 5
  • 17
If $$1^{3} + 2^{3} + .... + 10^{3} = 3025$$, then the value of $$2^{3} + 4^{3} + ..... + 20^{3}$$ is
  • $$7590$$
  • $$5060$$
  • $$24200$$
  • $$12100$$
In our number system the base is ten. If the base were changed to four you would count as follows: $$1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30,....$$ The twentieth number would be:
  • $$20$$
  • $$38$$
  • $$44$$
  • $$104$$
  • $$110$$
The value of the product 
$${ 6 }^{ \frac { 1 }{ 2 }  }\times { 6 }^{ \frac { 1 }{ 4 } }\times { 6 }^{ \frac { 1 }{ 8 } }\times { 6 }^{ \frac { 1 }{ 16 }  }\times ..$$ up to infinite terms is
  • $$6$$
  • $$36$$
  • $$216$$
  • $$512$$
If a and b are two unequal positive numbers, the:
  • $$\frac{2ab}{a+b}>\sqrt{ab}>\frac{a+b}{2}$$
  • $$\sqrt{ab}>\frac{2ab}{a+b}>\frac{a+b}{2}$$
  • $$\frac{2ab}{a+b}>\frac{a+b}{2}>\sqrt{ab}$$
  • $$\frac{a+b}{2}>\frac{2ab}{a+b}>\sqrt{ab}$$
  • $$\frac{a+b}{2}>\sqrt{ab}>\frac{2ab}{a+b}$$
If $$y = x+x^2+x^3+...$$ up to infinite terms, where $$ x<1$$, then which one of the following is correct?
  • $$x=\dfrac { y }{ 1+y } $$
  • $$x=\dfrac { y }{ 1-y } $$
  • $$x=\dfrac {1+ y }{ y }$$
  • $$x=\dfrac { 1-y }{ y } $$
If $$1.3 + 2.3^2 + 3.3^3 +...+ n.3^n $$= $$\dfrac { (2n-1)3^ a+b }{ 4 }$$ then $$a$$ and $$b$$ are respectively 
  • $$n,2$$
  • $$n,3$$
  • $$n +1,2$$
  • $$n + 1,3$$
The value of $$\dfrac { 1 }{ \log _{ 3 }{ e }  } +\dfrac { 1 }{ \log _{ 3 }{ e^2 }  } +\dfrac { 1 }{ \log _{ 3 }{ e^4 }  } +...$$  up to infinite terms is
  • $$\log _{ e }{ 9 } $$
  • $$0$$
  • $$1$$
  • $$\log _{ e }{ 3 } $$
If $$x =1-y+{ y }^{ 2 }-{ y }^{ 3 }+...$$ upto infinite terms, where |y| < 1, then which one of the following is correct?
  • $$x =\frac { 1 }{ 1+y } $$
  • $$x =\frac { 1 }{ 1-y } $$
  • $$x = \frac { y }{ 1+y }$$
  • $$x=\frac { y }{ 1-y } $$
$$\displaystyle \sum _{ k=1 }^{ 6 }{ \left[ sin\frac { 2k\pi  }{ 7 } -i\quad cos\quad \frac { 2k\pi  }{ 7 }  \right]  } =$$
  • $$-1$$
  • $$0$$
  • $$-i$$
  • $$i$$
Arrange these numbers in ascending order. 
$$756, 567, 657, 676$$ 
  • $$657, 567, 756, 676$$
  • $$567, 657, 676, 756$$
  • $$756, 676, 657, 567$$
  • $$676, 756, 567, 657$$
For some natural $$N$$ , the number of positive integral $$x$$ satisfying the equation, 
$$1!+2!+3!+......+(x)!=(N)^2$$ is :
  • None
  • One
  • Two
  • Infinite
State True or False.
$$1 \, + \, \dfrac{1}{5} \, + \, \dfrac{3}{5^2} \, + \, \dfrac{5}{5^3} \, + \, ..... \infty$$ = $$\dfrac {13}{8}$$
  • True
  • False
State true or false.
$$ 199.1 + 197.3 + 195.5 +.....3.197 + 1.397 = 666700 $$
  • True
  • False
The sum of the given series $$1+3+5+7+9+......+53$$ is $$729$$.
  • True
  • False
If $$S_n=\sum\limits_{r=1}^n \dfrac{2r+1}{r^4+2r^3+r^2}$$ then $$S_{20}$$ =
  • $$\dfrac{220}{221}$$
  • $$\dfrac{420}{441}$$
  • $$\dfrac{439}{221}$$
  • $$\dfrac{440}{441}$$
The sum to $$50$$ terms of the series $$\dfrac {1}{2} + \dfrac {3}{4} + \dfrac {7}{8} + \dfrac {15}{16} + ....$$ is equal to
  • $$2^{50} - 51$$
  • $$1 - 2^{-50}$$
  • $$2^{-50}+49$$
  • $$2^{50} - 1$$
$$\sum\limits_{r=1}^{50}\Big[ \dfrac{1}{49+r}-\dfrac{1}{2r(2r-1)}\Big]=$$
  • $$\dfrac{1}{50}$$
  • $$\dfrac{1}{99}$$
  • $$\dfrac{1}{100}$$
  • $$\dfrac{1}{101}$$
The value of $$x$$ satisfying the equation $$\dfrac{5050-\left(\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+......+\dfrac{5049}{5050}\right)}{1+\dfrac{1}{2}+\dfrac{1}{3}+......+\dfrac{1}{5050}}=\dfrac{x}{5050}$$ is 
  • $$1$$
  • $$5049$$
  • $$5050$$
  • $$5051$$
If $$1 + {x^2} = \sqrt {3}x $$, then $$\displaystyle \prod\limits_{n = 1}^{24} {\left( {x^n} + \dfrac {1} {x^n} \right)} $$ is equal to 
  • $$48$$
  • $$-48$$
  • $$ \pm 48\left( {\omega - {\omega ^2}} \right)$$
  • none of these
If $$\left| a \right| < 1$$ and $$\left| b \right| < 1$$ then $$s = 1 + \left( {1 + a} \right)b + \left( {1 + a + {a^2}} \right){b^2} + \left( {1 + a + {a^2} + {a^3}} \right){b^3} + ...is - .$$
  • $${\dfrac 1 {\left( {1 - b} \right)\left( {1 - ab} \right)}}$$
  • $${\dfrac 1 {\left( {1 + b} \right)\left( {1 - ab} \right)}}$$
  • $${\dfrac 1 {\left( {1 - b} \right)\left( {1 + ab} \right)}}$$
  • $${\dfrac 1 {\left( {1 + b} \right)\left( {1 + ab} \right)}}$$
The sum of the series $$\dfrac{1}{(1\times 2)}+\dfrac{1}{(2\times 3)}+\dfrac{1}{(3\times 4)}+.......+\dfrac{1}{(100\times 101)}$$ is equal to
  • $$\dfrac{200}{101}$$
  • $$\dfrac{100}{101}$$
  • $$\dfrac{50}{101}$$
  • $$\dfrac{25}{101}$$
If $$\left| a \right| < 1$$ and $$\left| b \right| < 1$$ then $$\eqalign{  &   \cr   & S = 1 + \left( {1 + a} \right)b + \left( {1 + a + {a^2} } \right){b^2} + ...} $$=
  • $${1 \over {\left( {1 - b} \right)\left( {1 - ab} \right)}}$$
  • $${1 \over {\left( {1 + b} \right)\left( {1 - ab} \right)}}$$
  • $${1 \over {\left( {1 - b} \right)\left( {1 + ab} \right)}}$$
  • $${1 \over {\left( {1 + b} \right)\left( {1 + ab} \right)}}$$
If $$(1+3+5+....+p)+(1+3+5+....+q)=(1+3+5+.....+r),$$ where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of $$p+q+r$$, (where $$P>6$$ ) is :
  • $$12$$
  • $$21$$
  • $$27$$
  • $$24$$
Let $$T_{n}=\displaystyle  \sum _{ r=1 }^{ n }{ \dfrac { n }{ { r }^{ 2 }-2r.n+2{ n }^{ 2 } } ,{ S }_{ n }=\displaystyle  \sum _{ r=0 }^{ n-1 }{ \dfrac { n }{ { r }^{ 2 }-2r.n+{ 2n }^{ 2 } }  }  }$$, then
  • $$T_{n} > S_{n} \forall n \epsilon N$$
  • $$T_{n} > \dfrac{\pi}{4}$$
  • $$S_{n} < \dfrac{\pi}{4}$$
  • $$\displaystyle \lim _{ n-\infty }{ { S }_{ n }=\dfrac { \pi }{ 4 } }$$
If $$S_{n}=\dfrac {3}{2}+\dfrac {33}{2^{2}}+\dfrac {333}{2^{2}}+....$$ upto $$n$$ terms $$=\dfrac {a^{n+1}+b^{b-n}-c}{d}$$ (where $$a,b,c,d \epsilon\ N$$), then ?
  • $$a+b+c+d=28$$
  • $$b+d=a+c$$
  • $$a-c=b+d$$
  • $$d-c=a-b$$
Sum of the series $$1+2.2+3.2^{2}+4.2^{3}+..+100.2^{99}$$ is
  • $$100.2^{100}+1$$
  • $$99.2^{100}+1$$
  • $$99.2^{100}-1$$
  • $$100.2^{100}-1$$
The value of sum $$\sum _{ n=1 }^{n=\infty  }{ \frac { 2 }{ { 3 }^{ n } }  is\ equal\ to: } $$
  • 1
  • 3
  • 15/4
  • 7/3
Pam likes the numbers 1689 and 6891. Knowing this, which pair of numbers will she like among the ones below?
  • 1981 and 1891
  • 19 and 91
  • 190 and 160
  • 1198911 and 1168611
Let $${S_n} = \frac{3}{{{1^2}}} + \frac{5}{{{1^2} + {2^3}}} + \frac{7}{{{1^2} + {2^3} + {3^3}}} + \frac{9}{{{1^2} + {2^3} + {3^3} + {4^3}}} + .......{\text{ up to n terms, then }}\mathop {\lim }\limits_{n \to \infty } {S_n}{\text{ }}$$ is equal to  
  • 2
  • 3
  • 6
  • 1
$$A = (2 + 1)({2^2} + 1)({2^4} + 1).....\left( {{2^{2016}} + 1} \right)$$. The value of $${\left( {A + 1} \right)^{\frac{1}{{2016}}}}$$ is
  • $$4$$
  • $$2016$$
  • $$^{{2^{4032}}}$$
  • $$2$$
Let $${n}^{th}$$ term of sequence $$1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,.....$$ is given by $${t}_{n}$$ , then ?
  • $${t}_{100}=14$$
  • $${t}_{200}=20$$
  • $${t}_{300}=24$$
  • $${t}_{400}=28$$

given relation is  $$\frac{1}{n+1} + \frac{1}{n+2}+.....+ \frac{1}{2n}
> \frac{13}{24}$$< for all natural numbers $$n>1$$
  • True
  • False
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers