Binomial Theorem Test

Result

Binomial Theorem Test - 66

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Weekly Quiz Competition

Question 1
1 / -0

Coefficient of $$x ^ { 10 }$$ in $$\left( 1 + 2 x ^ { 4 } \right) ( 1 - x ) ^ { 8 }$$ is

A
$$-56$$

B
$$56$$

C
$$112$$

D
$$-112$$

Solution
Question 2
1 / -0

The coefficient of $$x^{-2}$$ in $$(1+3x^2+x^4)\left(1+\dfrac{1}{x}\right)^8$$ is

A
$$266$$

B
$$161$$

C
$$162$$

D
none of these
Question 3
1 / -0

$$ {1 \choose 0} ^2 + {2 \choose 1}^2 + {3 \choose 2}^2 + ... + { n+1 \choose n}^2 = $$

A
$$(n+1){{2n}\choose{n}}$$

B
$$(\frac{n+2}{2}){{2n}\choose{n}}$$

C
$$(n+2).2^{n-1}$$

D
$$(n){{2n}\choose{n}}$$

Solution
Question 4
1 / -0

The coefficient of $$x^2$$ in expansion of the product
(2 $$x^2$$).($$(1 + 2x + 3x^2)^6$$ + $$(1 4x^2)^6$$) is :

A
107

B
106

C
108

D
155
Question 5
1 / -0

Coefficient of $$x^8$$ in $$(x-1)(x-2)(x-3)..(x-10)$$ is?

A
$$980$$

B
$$1395$$

C
$$1320$$

D
None of these

Solution
Question 6
1 / -0

If $$| x | < 2 / 3$$ then the fourth term in the expansion of $$\left( 1 + \frac { 3 } { 2 } x \right) ^ { 1 / 2 }$$ is

A
$$\frac { 27 } { 128 } x ^ { 3 }$$

B
$$-\frac { 27 } { 128 } x ^ { 3 }$$

C
$$\frac { 81 } { 256 } x ^ { 3 }$$

D
$$-\frac { 81 } { 256 } x ^ { 3 }$$

Solution
Question 7
1 / -0

The number of terms which are free from radical signs in the expansion of $$(y^{1/5} + x^{1/10})^{55}$$ is

A
$$5$$

B
$$6$$

C
$$7$$

D
None of these

Solution
Question 8
1 / -0

Coefficient of $${ x }^{ 2009 }in(1+x+{ x }^{ 2 }+{ x }^{ 3 }+{ x }^{ 4 }{ ) }^{ 1001 }{ \left( 1-x \right) }^{ 1002 }$$ IS...

A
$${ 4. }^{ 1001 }{ c }_{ 501 }$$

B
- 2009

C
0

D
None of these

Solution
Question 9
1 / -0

The sum of the coefficients in the expansion (6a-5b) when n is a positive integer, is

A
$${ 10 }^{ \circ }$$

B
1

C
$${ 11 }^{ n }$$

D
0

Solution
Question 10
1 / -0

The number of irrational terms in the expansion of $$\left( 5 ^ { 1 / 6 } + 2 ^ { 1 / 8 } \right) ^ { 100 }$$ is :

A
$$96$$

B
$$97$$

C
$$98$$

D
$$99$$

Solution