Binomial Theorem Test

Result

Binomial Theorem Test - 74

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Weekly Quiz Competition

Question 1
1 / -0

After simplification, the total number of terms in the expansion of $$ ( x + \sqrt { 2 } ) ^ { 4 } + ( x - \sqrt { 2 })^4 $$ is-

A
10

B
5

C
4

D
3

Solution
Question 2
1 / -0

The number of integral terms in expansion $$(\sqrt [2]{3} + \sqrt [ 8 ]{ 5 } )^{256}$$ is

A
32

B
33

C
34

D
35

Solution
Question 3
1 / -0

If x=1/3, then the greatest term in the expansion of $$(1+4x)^{8}$$ is

A
$$56(\frac{3}{4})^{4}$$

B
$$56(\frac{4}{3})^{4}$$

C
$$56(\frac{3}{4})^{5}$$

D
$$56(\frac{2}{5})^{4}$$
Question 4
1 / -0

The coefficient of the term independent of $$x$$ in the expansion of $$(1 - x)^2 \cdot \left(x + \dfrac{1}{x}\right)^{10}$$ is

A
$$^{11}C_3$$

B
$$^{10}C_3$$

C
$$^{10}C_4$$

D
None of these

Solution
Question 5
1 / -0

$$\left (5^{\dfrac {1}{2}} + 7^{\dfrac {1}{6}}\right )^{642}$$ contains $$n$$ integral terms then $$n$$ is

A
$$108$$

B
$$106$$

C
$$107$$

D
$$109$$

Solution
Question 6
1 / -0

Number of irrational terms in the expansion of $$\left( \sqrt { 2 } +\sqrt { 3 } \right) ^{ 15 }\quad are$$

A
9

B
7

C
16

D
10

Solution
Question 7
1 / -0

The coefficient of $${ x }^{ 4y }\quad in\quad the\quad expansion\quad of\quad (x-1)\left( x-\frac { 1 }{ 2 } \right) \left( x-\frac { 1 }{ { 2 }^{ 2 } } \right) ......\left( x-\frac { 1 }{ { 2 }^{ 49 } } \right) $$ is equal to

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

B
+ve cocfficient of x.

C
-ve coefficient of x

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

Solution
Question 8
1 / -0

The coefficient of $$x ^ { 15 }$$ in the product of $$( 1 - x )( 1 - 2 x ) \left( 1 - 2 ^ { 2 } x \right) \dots \ldots \ldots \ldots \left( 1 - 2 ^ { 15 } x \right)$$ is equal to

A
$$2 ^ { 105 } - 2 ^ { 121 }$$

B
$$2 ^ { 121 } - 2 ^ { 105 }$$

C
$$2 ^ { 120 } - 2 ^ { 104 }$$

D
none of these

Solution
Question 9
1 / -0

In the expansion of $${ x }^{ 2 }{ \left( \sqrt { x } +\frac { \lambda }{ { x }^{ 2 } } \right) }^{ 10 }$$. The coefficient of $${ x }^{ 2 }$$ is $$720$$ then $$\lambda $$ is

A
4

B
9

C
2

D
3
Question 10
1 / -0

The number of integral terms in the expansion of $$\displaystyle (5^ \frac{1}{2}+7^\frac {1}{6})^ {642}$$ is?

A
$$ 1 0 6$$

B
$$1 0 8$$

C
$$1 0 3$$

D
$$ 1 0 0$$

Solution