Binomial Theorem Test

Result

Binomial Theorem Test - 65

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Weekly Quiz Competition

Question 1
1 / -0

The coefficient of $${x}^{24}$$ in the expansion of $$ { \left( 1+{ x }^{ 2 } \right) }^{ 12 }\left( 1+{ x }^{ 12 } \right) \left( 1+{ x }^{ 24 } \right)$$ is

A
$$^{12}{C}_{6}$$

B
$$^{12}{C}_{6}+2$$

C
$$^{12}{C}_{6}+4$$

D
$$^{12}{C}_{6}+6$$

Solution
Question 2
1 / -0

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

A
$$9$$

B
$$7$$

C
$$16$$

D
$$10$$

Solution
Question 3
1 / -0

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

A
$$1-2n-\dfrac {3}{2^{n+1}}$$

B
$$1-2n-\dfrac {3}{2^{n-1}}$$

C
$$1+2n+\dfrac {3}{2^{n+1}}$$

D
$$1+2n-\dfrac {3}{2^{n-1}}$$

Solution
Question 4
1 / -0

If the coefficient of $${ x }^{ 2 }{ y }^{ 3 }{ z }^{ 4 }$$ in $$\left( x+y+z \right) ^{ n }$$ is A, then the coefficient of $${ x }^{ 4 }{ y }^{ 4 }{ z }$$

A
2A

B
$$\frac { nA }{ 2 } $$

C
$$\frac { A }{ 2 } $$

D
None of these

Solution
Question 5
1 / -0

The term independent of $x$ in the expansion of $$\left( \sqrt { \left( \frac { x } { 3 } \right) } + \sqrt { \left( \frac { 3 } { 2 x ^ { 2 } } \right) } \right) ^ { 10 }$$ is:-

A
$$5$$$$/ 12$$

B
$$^ { 10 } C _ { 1 }$$

C
$$1$$

D
none of these
Question 6
1 / -0

The 4th term in the expansion of $${ \left( \sqrt { x } +\frac { 1 }{ x } \right) }^{ 2 }$$ is

A
$$110{ x }^{ \frac { 3 }{ 2 } }$$

B
$$220{ x }^{ \frac { 3 }{ 2 } }$$

C
$$220{ x }^{ 2 }$$

D
$$110{ x }^{ 2 }$$

Solution

$$\left(\sqrt{x}+\frac{1}{x}\right)^{12}$$

$$T_4={}^{12} C_{3}(\sqrt{x})^{12-3}\left(\frac{1}{x}\right)^{3}$$

$$={12 C_{3}(\sqrt{x})^{9}\left(x^{-3}\right)}$$

$$= \frac{12 !}{9! \times 3 !}(x)^{\frac{3}{2}}$$

= $$220 x^{\frac{3}{2}}=$$ Ans

Option (b)
Question 7
1 / -0

In how many terms in the expansion of $$(x^{1/5}+y^{1/10})^{55}$$ do not have fractional power of the variable :

A
$$6$$

B
$$7$$

C
$$8$$

D
$$10$$
Question 8
1 / -0

In the expansion of $$(a-b)^{n},n\ge 5$$, if the sum of the $$5^{th}$$ and $$6^{th}$$ terms is zero, then $$a/b$$=

A
$$(x-5)/6$$

B
$$(x-4)/5$$

C
$$5/(x-4)$$

D
$$6/(x-5)$$
Question 9
1 / -0

The value of the sum $$\sum _{ j=0 }^{ 8 }{8 \choose j}{ \frac { 1 }{ (j+1)(j+2) } } $$ is

A
$$\frac { 1003 }{ 90 } $$

B
$$\frac { 1013 }{ 90 } $$

C
$$\frac { 1023 }{ 90 } $$

D
$$\frac { 1033 }{ 90 } $$

Solution
Question 10
1 / -0

Find the number of terms in the expression $$5x^ {2}-x^ {2}y+2xy+7$$

A
$$3$$

B
$$4$$

C
$$1$$

D
$$2$$

Solution