MCQ Questions for Class 11 Engineering Maths Binomial Theorem Quiz 9

In the expansion of $$(1+x)^{30}$$, the sum of the coefficients of odd powers of $$x$$, is

0%
$$2^{30}$$
0%
$$2^{31}$$
0%
$$0$$
0%
$$2^{29}$$

The coefficient of $$x^{10}$$ in the expansion of $$(1+x)^{2}(1+x^{2})^{3}(1+x^{3})^{4}$$ is qual to:

0%
$$52$$
0%
$$56$$
0%
$$50$$
0%
$$44$$

If $$P$$ be the sum of odd terms and $$Q$$ be the sum of even terms in the expansion of $$(x+a)^n$$, then $$P ^ { 2 } - Q ^ { 2 } = \left( x ^ { 2 } - a ^ { 2 } \right) ^ { n }$$

0%
True
0%
False

If $$(1+x-2x^2)^8=1+a_1x+a_2x^2+........ + a_{16}x^{16}$$, then $$a_1+a_3+a_5+......a_{15}$$=

0%
$$2^7$$
0%
$$-2^7$$
0%
$$3^2$$
0%
$$4^6$$

The sum of coefficients of the two middle terms in the expansion of $$( 1 + x ) ^ { 2 n - 1 }$$ is equal to

0%
$$( 2 n - 1 ) C _ { n }$$
0%
$$^ { ( 2 n - 1 ) } C _ { n + 1 }$$
0%
$$^ { 2 n } C _ { n - 1 }$$
0%
$$^ { 2 n } C _ { n }$$

$$^{2007}C_0-8.^{2007}C_1+13.^{2007}C_2-18.^{2007}C_3+....$$ upto 2008 terms =

0%
$$0$$
0%
$$2007$$
0%
$$-2007$$
0%
$$2008$$

If the coefficients of $$x^{-7}$$ and $$x^{-8}$$ to the expansion of $$\left(2+\dfrac {1}{3x}\right)^{n}$$ are equal then $$n=$$

0%
$$56$$
0%
$$15$$
0%
$$45$$
0%
$$55$$

The coefficient of $$x^{4}$$ in the expansion of $$\left(\dfrac{x}{2}-\dfrac{3}{x^{2}}\right)^{10}$$, is

0%
$$\dfrac{405}{256}$$
0%
$$\dfrac{504}{259}$$
0%
$$\dfrac{450}{263}$$
0%
$$none\ of\ these$$

The coefficient of $$x^{5}$$ in the expansion of $$(1+x)^{21}+(1+x)^{22}+....+(1+x)^{30}$$ is

0%
$$^{51}C_{5}$$
0%
$$^{9}C_{5}$$
0%
$$^{31}C_{6}-^{21}C_{6}$$
0%
$$^{30}C_{5}-^{20}C_{5}$$

Find the middle term in the expansion of $${ \left( \dfrac { { 2x }^{ 2 } }{ 3 } +\dfrac { 3 }{ { 2x }^{ 2 } } \right) }^{ 10 }$$

0%
$$252$$
0%
$$248$$
0%
$$230$$
0%
$$200$$

The coefficient of $${x}^{3}$$ in the expression of $${(1+{x}^{2}+{x}^{3})}^{10}$$ is

0%
$$10$$
0%
$$220$$
0%
$$211$$
0%
$$None \ of \ these$$

If $$(1+ax)^n=1+8x+24x^2+.....$$ then

0%
$$a=3$$
0%
$$a=4$$
0%
$$a=2$$
0%
$$a=5$$

The coefficient of $$x^{n}$$ in the expansion of $$\dfrac{1}{(1-x)(1-2x)(1-3x)}$$ is

0%
$$\dfrac{1}{2}(2^{n+2}-3^{n+3}+1)$$
0%
$$\dfrac{1}{2}(3^{n+2}-2^{n+3}+1)$$
0%
$$\dfrac{1}{2}(2^{n+3}-3^{n+2}+1)$$
0%
$$none\ of\ these$$

If the $$6^{th}$$ term in the expansion of $$\left(\dfrac {1}{x^{8/3}}+x^{2}\log ^{x}_{10}\right)^{8}$$ is $$5600$$, then equals

0%
$$1$$
0%
$$\log^{10}_{e}$$
0%
$$10$$
0%
$$No\ such\ x\ exists$$

The number of terms in $$\left(x^{3}+1+\dfrac{1}{x^{3}}\right)^{100}$$ is

0%
$$300$$
0%
$$200$$
0%
$$100$$
0%
$$201$$

The coefficient of $$x^{4}$$ in the expansion $$\left(1+5x+9x^{2}+.+\left(4k+1\right)x^{k}+..\right)\left(1+x^{2}\right)^{11}$$ is

0%
$$^{11}C_{2}+4 ^{11}C_{1}+3$$
0%
$$^{11}C_{2}+3 ^{11}C_{1}+4$$
0%
$$3 ^{11}C_{2}+4 ^{11}C_{1}+3$$
0%
$$171$$

If the coefficients of $$2^{nd}, 3^{rd},$$ and $$4^{th}$$ terms in the expansion of $${(1 + x)^n},n \in N$$ are in A.P.,then $$n=$$

0%
$$7$$
0%
$$14$$
0%
$$2$$
0%
None of these

The coefficient of $$x^8$$ in the expansion of $$(1+x+x^3+x^5+x^9)(1+x^2)^5(1_x^4)^6$$ is equal to

0%
180
0%
100
0%
80
0%
None of these

In the expansion of $$\displaystyle {\left( {\frac{{x + 1}}{{{x^{2/3}} - {x^{1/3}} + 1}} - \frac{{x - 1}}{{x - {x^{1/2}}}}} \right)^{10}}$$, the term which does not contain $$x$$ is -

0%
$$^{11}{C_4}{ - ^{10}}{C_3}$$
0%
$$^{10}{C_7}$$
0%
$$^{10}{C_4}$$
0%
$$^{11}{C_5}{ - ^{10}}{C_5}$$

The coefficient of $${ x }^{ n }$$ in $$(1-x+\frac { { x }^{ 2 } }{ 2! } -\frac { { x }^{ 3 } }{ 3! } +.....+\frac { { (-1) }^{ n }{ x }^{ n } }{ n! } )^{ 2 }$$ is

0%
$$\frac { { (-n) }^{ n } }{ n! } $$
0%
$$\frac { { (-2) }^{ n } }{ n! } $$
0%
$$\frac { 1 }{ (n!)^{ 2 } } $$
0%
$$-\frac { 1 }{ (n!)^{ 2 } } $$

If coefficient of $$2^{nd}, 3^{rd}$$ and $$4^{th}$$ term in the expansion of $$\left(1+x\right)^{2n}$$ are in A.P. then :

0%
$$2n^{2}+9n+7=0$$
0%
$$2n^{2}-9n+7=0$$
0%
$$2n^{2}-9n-7=0$$
0%
$$2n^{2}+9n-7=0$$

The coefficient of $$a^3b^4c$$ in the expansion of $$(1+a+b-c)^9$$ is

0%
$$2.^9C_7.^7C_4$$
0%
$$-2.^9C_2.^7C_3$$
0%
$$^9C_7.^7C_4$$
0%
none of these

The coefficient of $$x^4$$ in the expansion of $$(1-2x+3x^2+4x^3)(1-x)^{-8}$$ is:

0%
$$232$$
0%
$$231$$
0%
$$230$$
0%
None of these

If the fourth term in the expansion of $$\left(px+\dfrac{1}{x}\right)^{n}$$ is independent of $$x$$, then the value of term is :

0%
$$5p^{3}$$
0%
$$10p^{3}$$
0%
$$20p^{3}$$
0%
$$None\ of\ these$$

The coefficient of $$x^6 y^5 z^3$$ in the expansion of $$(3xy - 2xz + zy)^7$$ is

0%
$$\dfrac {7 !}{4! 2! 1!}\cdot 3^4 \cdot 2^2$$
0%
$$-\dfrac {7 !}{4! 2! 1!}\cdot 3^4 \cdot 2^2$$
0%
$$-\dfrac {7 !}{4! 2! 1!}\cdot 3^2 \cdot 2^4$$
0%
$$\dfrac {7 !}{4! 2! 1!}\cdot 3^2 \cdot 2^4$$

Middle term in the expansion of $$(1+3x+3x^2+x^3)^6$$ is

0%
$$4^{th}$$
0%
$$3^{rd}$$
0%
$$10^{th}$$
0%
None of these

If the coefficients of $${ x }^{ -2 }$$ and $${ x }^{ -4 }$$ in the expansion of $${ \left( { x }^{ \frac { 1 }{ 3 } }+\frac { 1 }{ 2x^{ \frac { 1 }{ 3 } } } \right) }^{ 18 },$$ $$(x>0)$$, are $$m$$ and $$n$$ respectively, then $$\frac { m }{ n } $$ is equal to :

0%
$$182$$
0%
$$\dfrac { 4 }{ 5 } $$
0%
$$\dfrac { 5 }{ 4 } $$
0%
$$27$$

The middle term in the expansion of $$\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^{20}$$ is

0%
$$_{ }^{ 20 }{ { C }_{ 10 } }{ x }^{ 10 }{ y }^{ 10 }$$
0%
$${ x }^{ 10 }{ y }^{ 10 }$$
0%
$$_{ }^{ 20 }{ { C }_{ 10 } }{ \left( 2/3 \right) }^{ 10 }{ \left( xy \right) }^{ 10 }$$
0%
$$-x^{ 10 }y^{ 10 }$$

$$ \binom{n}{0}+2\binom{n}{1}+2^{2}\binom{n}{2}+......++2^{n}\binom{n}{n} $$ is equal to

0%
$$ 2^{n} $$
0%
$$0$$
0%
$$ 3^{n} $$
0%
None of these

If the constant term in the expansion of $$\left( { x }^{ 3 }-\dfrac { k }{ { x }^{ 8 } } \right) $$ is $$1320$$ then $$k$$ is equal to

0%
$$11$$
0%
$$8$$
0%
$$2$$
0%
$$6$$

If in the expansion of $$\left(2^{1/3}+\dfrac {1}{3^{1/3}}\right)^{n}$$, the ratio of $$6^{th}$$ term from beginning and from the end is $$1/6$$, then the value of $$n$$ is

0%
$$5$$
0%
$$7$$
0%
$$13$$
0%
$$None\ of\ these$$

Find the number of terms in expansion of $$(1+x)^{2}+(1-x)^{8}$$

0%
$$17$$
0%
$$18$$
0%
$$5$$
0%
$$9$$

The term independent of $$x$$ in the expansion of $$\left(\sqrt{\dfrac{x}{3}}+\dfrac{3}{2x^{2}}\right)^{10}$$ will be

0%
$$3$$
0%
$$5$$
0%
$$9$$
0%
$$None\ of\ these$$

The sum of the coefficients of the first three terms in the expansion of $${\left( {x - \frac{3}{{{x^2}}}} \right)^m},\,x \ne 0$$ $$m$$ being a natural number is , $$559$$. Find the term of the expansion containing $$x^3$$

0%
-5940
0%
1010
0%
1001
0%
1002

Explanation

$$\begin{array}{l} { \left( { x-\frac { 3 }{ { { x^{ 2 } } } } } \right) ^{ m } }{ =^{ m } }{ C_{ o } }{ \left( x \right) ^{ m } }{ \left( { \frac { { -3 } }{ { { x^{ 2 } } } } } \right) ^{ 0 } }{ +^{ m } }{ C_{ 1 } }{ \left( x \right) ^{ m-1 } }{ \left( { \frac { { -3 } }{ { { x^{ 2 } } } } } \right) ^{ 1 } }{ +^{ m } }{ C_{ 2 } }{ x^{ m-2 } }{ \left( { \frac { { -3 } }{ { { x^{ 2 } } } } } \right) ^{ 2 } }+...... \\ { =^{ m } }{ C_{ o } }{ \left( x \right) ^{ m } }+{ \left( { -3 } \right) ^{ m } }{ C_{ 1 } }{ \left( x \right) ^{ m-1-2 } }+{ 9.^{ m } }{ C_{ 2 } }{ \left( x \right) ^{ m-2-4 } }+.... \\ { \Rightarrow ^{ m } }{ C_{ o } }+{ \left( { -3 } \right) ^{ m } }{ C_{ 1 } }+{ 9.^{ m } }{ C_{ 2 } }=559 \\ \Rightarrow 1-3m+9\frac { { m\left( { m-1 } \right) } }{ 2 } =559 \\ \Rightarrow 2-6m+9{ m^{ 2 } }-9m=2\times 559=1118 \\ \Rightarrow 9{ m^{ 2 } }-15m-1116=0 \\ \Rightarrow 3{ m^{ 2 } }-15m-372=0 \\ \Rightarrow 3{ m^{ 2 } }-36m+31m-372=0 \\ \Rightarrow 3m\left( { m-12 } \right) +31\left( { m-12 } \right) =0 \\ \Rightarrow \left( { m-12 } \right) \left( { 3m+31 } \right) =0 \\ \therefore m=12,\, \, and\, m=\frac { { -31 } }{ 3 } \left( { does\, not\, exist } \right) \\ so,\, we\, take\, m=12 \\ { \left( { x-\frac { 3 }{ { { x^{ 2 } } } } } \right) ^{ 12 } } \\ Then \\ { T_{ r+1 } }{ =^{ 12 } }{ C_{ r } }{ x^{ 12r } }{ \left( { \frac { { -3 } }{ { { x^{ 2 } } } } } \right) ^{ r } } \\ ={ \left( { -1 } \right) ^{ r } }{ 3^{ r } }^{ 12 }{ C_{ r } }{ x^{ 12-r-25 } } \\ ={ \left( { -1 } \right) ^{ r } }{ 3^{ r } }^{ 12 }{ C_{ r } }{ x^{ 12-3r } } \\ Containg\, { x^{ 3 } } \\ 12-3r=0 \\ \therefore r=3 \\ Now, \\ { T_{ 4 } }={ T_{ 3+1 } }={ \left( { -1 } \right) ^{ 3 } }{ 3^{ 3 } }\, { \, ^{ 12 } }{ C_{ 3 } }{ x^{ 3 } } \\ =-27\, \, { \, ^{ 12 } }{ C_{ 3 } }{ x^{ 3 } } \\ { T^{ 4 } }=-5940{ x^{ 3 } } \end{array}$$

hence, the option $$A$$ is the correct answer.

If the fourth term in the expansion of $$\left( p x + \dfrac { 1 } { x } \right) ^ { n }$$ is $$\dfrac { 5 } { 2 } ,$$ then $$n + p$$ is equal to

0%
$$\dfrac { 9 } { 2 }$$
0%
$$\dfrac { 11 } { 2 }$$
0%
$$\dfrac { 13 } { 2 }$$
0%
$$\dfrac { 15 } { 2 }$$

The coefficient of $$x^{8}$$ in the polynomial $$\left(x-1\right)\left(x-2\right)\left(x-3\right).\left(x-10\right)$$ is:

0%
$$2640$$
0%
$$1320$$
0%
$$1270$$
0%
$$2740$$

The coefficient of $$x ^ { 8 }$$ in the expansion of $$\left( 1 + x ^ { 4 } \right) ^ { 3 } ( 1 - x ) ^ { 12 }$$ is

0%
$$3 + 4 \times 12 C _ { 4 }$$
0%
$$3 + ^ { 12 } \mathrm { C } _ { 8 }$$
0%
$$^ { 12 } C _ { 8 }$$
0%
$$3 - ^ { 12 } \mathrm { C } _ { 8 }$$

$$C_1 +2C_2 + 3C_3 +4C_4 + ......... + {n+1} nC_n$$

0%
$$n2^{n-1}$$
0%
$$2^{n+1}$$
0%
$$2.2^{n-1}$$
0%
Zero

$$\dfrac{C_0}{1} + \dfrac{C_2}{3} + \dfrac{C_4}{5} + \dfrac{C_6}{7} ..... = $$

0%
$$\dfrac{2^n}{n +1}$$
0%
$$\dfrac{2^{n+1} - 1}{n + 1}$$
0%
$$\dfrac{2^{n +1}}{n +1}$$
0%
None of these

$$(1+x)^{21}+(1+x)^{22}+..+(1+x)^{30}$$ in the expansion of this what is the coefficient of $$x^{5}$$ is

0%
$$^{31} C_5-^{21} C_5$$
0%
$$^{31} C_4-^{21} C_4$$
0%
$$^{31} C_6-^{21} C_6$$
0%
$$None\ of\ these$$

The sum $$^ { 20 } \mathrm { C } _ { 0 } + ^ { 20 } \mathrm { C } _ { 1 } + ^ { 20 } \mathrm { C } _ { 2 } + \ldots \ldots . ^ { 20 } \mathrm { C } _ { 10 }$$ is equal to

0%
$$2 ^ { 19 } + \frac { 20 ! } { ( 10 ! ) ^ { 2 } }$$
0%
$$2 ^ { 19 } - \frac { 1 } { 2 } \cdot \frac { 20 ! } { ( 10 ! ) ^ { 2 } }$$
0%
$$2 ^ { 19 } + ^ { 20 } \mathrm { C } _ { 10 }$$
0%
none of these

Coefficient of $$x^ {79}$$ in the expansion of $$\left(x+x^ {2}+x^ {4}\right)$$ is equal to-

0%
$$0$$
0%
$$150x3^ {19}$$
0%
$$1$$
0%
$$3^ {20}$$

The number of integral terms in the expansion of $$ (\sqrt{3}+\sqrt[8]{5})^{256} $$ is

0%
$$32$$
0%
$$33$$
0%
$$34$$
0%
$$35$$

For a binomial distribution, n = 5.
If P (X = 4) = P (X = 3), then P (X > 2) is

0%
0.69
0%
0.97
0%
0.21
0%
0.79

The coefficient of $$t^{50}$$ in $$(1+t)^{41}(1-t+t^2)^{40}$$ is equal to?

0%
$$1$$
0%
$$50$$
0%
$$81$$
0%
$$0$$

Find the middle term in the expansion of $$(1-2x+x^2)^n$$

0%
$$\dfrac {(2n)!}{(n!)^2}(-1)^n x^n$$
0%
$$\dfrac {(2n)!}{(n!)}(-1)^n x^2n$$
0%
$$\dfrac {(2n)!}{(n!)^2} x^n$$
0%
None of these

If $$\left(1+x+x^ {2}+x^ {3}\right)^ {5}=a_{0}+a_{1}x+a_{2}x^ {2}+....+a_{15}x^ {15}$$, then $$a_{10}$$ equals

0%
$$99$$
0%
$$100$$
0%
$$101$$
0%
$$110$$

The largest coefficient in the expansion of $${ \left( 1+x \right) }^{ 38 }$$ is

0%
$$_{ }^{ 38 }{ { C }_{ 18 } }$$
0%
$$_{ }^{ 38 }{ { C }_{ 15 } }$$
0%
$$_{ }^{ 38 }{ { C }_{ 20 } }$$
0%
$$_{ }^{ 38 }{ { C }_{ 19 } }$$

Given that the term of the expansion $$\displaystyle (x^{1/3}+ x^{-1/2})^{15}$$ which does not contain $$x$$ is $$5$$ m , where m$$\in$$N , m $$=$$

0%
1100
0%
1010
0%
1001
0%
None of these

If the $$6^{th}$$ term in the expansion of $$\displaystyle \left [ \dfrac{1}{x^{8/3}} + x^2log_{10}x \right ]^8$$ is 5600 , then $$x$$ =

0%
10
0%
8
0%
11
0%
9

CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 9 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 9 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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