Binomial Theorem Test

Result

Binomial Theorem Test - 69

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Weekly Quiz Competition

Question 1
1 / -0

The cooeficient of $${ x }^{ n }$$ in the expension of $$\left( 1-2x \right) ^{ -1/2 }$$

A
$$\frac { \left( 2n! \right) }{ { 2 }^{ n }\left( n! \right) }$$

B
$$\frac { \left( 2n! \right) }{ { 2 }^{ n }\left( n! \right) ^{ 2 } }$$

C
$$\frac { \left( 2n! \right) }{ { 2 }^{ n+1 }\left( n! \right) ^{ 2 } }$$

D
$$\frac { \left( 2n! \right) }{ { 2 }^{n-1}\left( n! \right) ^{ 2 } }$$

Solution
Question 2
1 / -0

The coefficient of $${ x }^{ 1 }$$ in the expansion of $$\left( 1-2x \right) ^{ -1/2 }$$ is

A
$$\dfrac { \left( 2r \right) ! }{ \left( r! \right) ^{ 2 } } $$

B
$$\dfrac { \left( 2r \right) ! }{ { 2 }^{ r }\left( r! \right) ^{ 2 } } $$

C
None of these

D
$$\dfrac { \left( 2r \right) ! }{ { 2 }^{ r }\left( r+1 \right) !\left( c-1 \right) ! } $$
Question 3
1 / -0

In the expansion of $$ \left(1+3 x+2 x^{2}\right)^{6} $$ the coefficient of $$ x^{11} $$ is

A
$$144$$

B
$$288$$

C
$$216$$

D
$$576$$

Solution
Question 4
1 / -0

The value of $$ x, $$ for which the $$6 th$$ term in the expansion of $$ \int 2^{\log 2 \sqrt{\left(9^{x-1}+7\right)}}+\frac{1}{_{0}^{(1 / 5) \log _{2}\left(3^{x-1}+1\right)}} )^{7} $$ is 84 is equal to

A
$$4$$,$$3$$

B
$$0$$,$$3$$

C
$$0$$,$$2$$

D
$$1$$,$$2$$
Question 5
1 / -0

The fifth term of $$\left(1 - \dfrac{2x}{3}\right)^{3/4}$$ is

A
$$\dfrac{-5x^4}{1152}$$

B
$$\dfrac{5x^4}{1152}$$

C
$$-\dfrac{5x^4}{1052}$$

D
$$\dfrac{5x^4}{1052}$$

Solution
Question 6
1 / -0

If the middle term in the expansion of $${ \left( { x }^{ 2 }+\dfrac { 1 }{ x } \right) }^{ n }$$ is $$924{ x }^{ 6 }$$ then n=

A
10

B
12

C
14

D
None of these

Solution
Question 7
1 / -0

The coefficient of $$ x^{11} $$ in the expansion of $$ \left(2 x^{2}+x-3\right)^{6} $$ is

A
$$384$$

B
$$192$$

C
$$572$$

D
$$64$$

Solution
Question 8
1 / -0

Coefficient of the middle term in the expansion of the binormial $$\left( 1+x \right) ^{ 40 }$$ is equal to

A
$$\dfrac { { 2 }^{ 20 }\left( 1.3.5....39 \right) }{ \left( 20 \right) ! } $$

B
the sum of the coefficients of the two middle terms in $$\left( 1+x \right) ^{ 39 }$$

C
$$\dfrac { 20.21.22.....40 }{ \left( 20 \right) ! } $$

D
$$\left( { ^{ 20 }{ C } }_{ 0 } \right) ^{ 2 }+\left( { ^{ 20 }{ C }_{ 1 } } \right) ^{ 2 }+\left( ^{ 20 }{ C }_{ 2 } \right) ^{ 2 }+......+\left( ^{ 20 }{ C }_{ 20 } \right) ^{ 2 }$$

Solution
Question 9
1 / -0

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

A
1

B
50

C
81

D
0

Solution
Question 10
1 / -0

If the coefficients of second, third and fourth terms in the expansion of $$ ( 1 + x ) ^ { n } $$ are in A.P.then the value of $$ n $$ is:

A
$$5$$

B
$$6$$

C
$$7$$

D
$$9$$

Solution