Binomial Theorem Test

Result

Binomial Theorem Test - 72

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Weekly Quiz Competition

Question 1
1 / -0

The coefficient of $${x^{49}}$$in the expansion of $$\left( {x - 1} \right)\left( {x - \frac{1}{2}} \right)\left( {x - \frac{1}{{{2^2}}}} \right).....\left( {x - \frac{1}{{{2^{49}}}}} \right)$$ is equal to

A
$$ - 2\left( {1 - \frac{1}{{{2^{50}}}}} \right)$$

B
$$ + \,\,ve\,\,coefficient\,\,of\,\,x$$

C
$$ - \,\,ve\,\,coefficient\,\,of\,\,x$$

D
$$ - 2\left( {1 - \frac{1}{{{2^{49}}}}} \right)$$
Question 2
1 / -0

Number of different terms in the sum $$ ( 1 + x ) ^ { 2009 } \cdot \left( 1 + x ^ { 2 } \right) ^ { 2008 } + \left( 1 + x ^ { 3 } \right) ^ { 2007 } , $$ is

A
3683

B
4007

C
4017

D
4352

Solution
Question 3
1 / -0

The middle term of $$\left( { x-\cfrac { 1 }{ x } } \right) ^{ 2n+1 }$$

A
$$^{ 2n+1 }{ { c }_{ n }.x }$$

B
$$^{ 2n+1 }{ { c }_{ n } }$$

C
$${ (-1) }^{ n\quad 2n+1 }{ c }_{ n }$$

D
$${ (-1) }^{ n\quad 2n+1 }{ c }_{ n }.x$$

Solution
Question 4
1 / -0

Sum of coefficients of even powers of $$x$$ in expansion of $${\left( {1 + x + {x^2} + {x^3}} \right)^5}$$ is

A
$$16$$

B
$$64$$

C
$$128$$

D
$$512$$

Solution
Question 5
1 / -0

If $$n$$ is even, then the middle term in the expansion of $$\Bigg ( x^2 + \dfrac{1}{x} \Bigg )^n$$ is $$924 x^6$$, then n is equal to

A
10

B
12

C
14

D
none of these

Solution
Question 6
1 / -0

If the second, third and fourth terms in the expansion of $${\left( {a + b} \right)^n}$$ are 135, 30 and 10/3 respectively, then the value of a is

A
3

B
4

C
5

D
7

Solution
Question 7
1 / -0

The number of terms in the expansion of $$\left( x ^ { 2 } + 1 + \dfrac { 1 } { x ^ { 2 } } \right) ^ { n } , n \in { N } ,$$ is :

A
$$2 n $$

B
$$3 n $$

C
$$2 n + 1$$

D
None

Solution
Question 8
1 / -0

The coefficient of $${ a }^{ 3 }{ b }^{ 4 }{ c }^{ 5 }$$ in the expansion of $${ (bc+ca+ab) }^{ 6 }$$ is

A
40

B
60

C
80

D
100

Solution
Question 9
1 / -0

If the number of terms in $$\left(x+1+\dfrac {1}{x}\right)^n (n\in I^{+})$$ is $$401$$, then $$n$$ is greater then

A
$$201$$

B
$$200$$

C
$$199$$

D
$$None\ of\ these$$

Solution
Question 10
1 / -0

In the expansion of $$\left( { x }^{ 3 }-\dfrac { 1 }{ { x }^{ 2 } } \right) ^{ n },\quad n\quad \epsilon \quad N,$$ if the sum of the coefficient of $${ x }^{ 5 }\quad and\quad { x }^{ 10 }\quad $$ is 0 then n is

A
25

B
20

C
15

D
none of these

Solution