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If $${\left( {1 + x} \right)^{10}} = {a_0} + {a_1}x + {a_2}{x^2} + ..... + {a_{10}}{x^{10}}$$ then $${\left( {{a_0} - {a_2} + {a_4} - {a_6} + {a_8} - {a_{10}}} \right)^2} + {\left( {{a_1} - {a_3} + {a_5} - {a_7} + {a_9}} \right)^2}$$ is equal to

A. $${3^{10}}$$

B. $${2^{10}}$$

C. $${2^{9}}$$

D. None of these

Answer : $${2^{10}}$$

Solution :
Putting $$x = i, - i$$ and multiplying both the results, we get the value of the required expression.

Releted MCQ Question on
Algebra >> Binomial Theorem

Releted Question 1

Given positive integers $$r > 1, n > 2$$ and that the co - efficient of $${\left( {3r} \right)^{th}}\,{\text{and }}{\left( {r + 2} \right)^{th}}$$ terms in the binomial expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal. Then

A. $$n = 2r$$

B. $$n = 2r + 1$$

C. $$n = 3r$$

D. none of these

View Answer

Releted Question 2

The co-efficient of $${x^4}$$ in $${\left( {\frac{x}{2} - \frac{3}{{{x^2}}}} \right)^{10}}$$ is

A. $$\frac{{405}}{{256}}$$

B. $$\frac{{504}}{{259}}$$

C. $$\frac{{450}}{{263}}$$

D. none of these

View Answer

Releted Question 3

The expression $${\left( {x + {{\left( {{x^3} - 1} \right)}^{\frac{1}{2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{\frac{1}{2}}}} \right)^5}$$ is a polynomial of degree

A. 5

B. 6

C. 7

D. 8

View Answer

Releted Question 4

If in the expansion of $${\left( {1 + x} \right)^m}{\left( {1 - x} \right)^n},$$ the co-efficients of $$x$$ and $${x^2}$$ are $$3$$ and $$- 6\,$$ respectively, then $$m$$ is

A. 6

B. 9

C. 12

D. 24

View Answer

If $${\left( {1 + x} \right)^{10}} = {a_0} + {a_1}x + {a_2}{x^2} + ..... + {a_{10}}{x^{10}}$$ then $${\left( {{a_0} - {a_2} + {a_4} - {a_6} + {a_8} - {a_{10}}} \right)^2} + {\left( {{a_1} - {a_3} + {a_5} - {a_7} + {a_9}} \right)^2}$$ is equal to

Releted MCQ Question on
Algebra >> Binomial Theorem

Given positive integers $$r > 1, n > 2$$ and that the co - efficient of $${\left( {3r} \right)^{th}}\,{\text{and }}{\left( {r + 2} \right)^{th}}$$ terms in the binomial expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal. Then

The co-efficient of $${x^4}$$ in $${\left( {\frac{x}{2} - \frac{3}{{{x^2}}}} \right)^{10}}$$ is

The expression $${\left( {x + {{\left( {{x^3} - 1} \right)}^{\frac{1}{2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{\frac{1}{2}}}} \right)^5}$$ is a polynomial of degree

If in the expansion of $${\left( {1 + x} \right)^m}{\left( {1 - x} \right)^n},$$ the co-efficients of $$x$$ and $${x^2}$$ are $$3$$ and $$- 6\,$$ respectively, then $$m$$ is

Practice More Releted MCQ Question on
Binomial Theorem

Practice More MCQ Question on Maths Section

If $${\left( {1 + x} \right)^{10}} = {a_0} + {a_1}x + {a_2}{x^2} + ..... + {a_{10}}{x^{10}}$$ then $${\left( {{a_0} - {a_2} + {a_4} - {a_6} + {a_8} - {a_{10}}} \right)^2} + {\left( {{a_1} - {a_3} + {a_5} - {a_7} + {a_9}} \right)^2}$$ is equal to

Releted MCQ Question on Algebra >> Binomial Theorem

Given positive integers $$r > 1, n > 2$$ and that the co - efficient of $${\left( {3r} \right)^{th}}\,{\text{and }}{\left( {r + 2} \right)^{th}}$$ terms in the binomial expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal. Then

The co-efficient of $${x^4}$$ in $${\left( {\frac{x}{2} - \frac{3}{{{x^2}}}} \right)^{10}}$$ is

The expression $${\left( {x + {{\left( {{x^3} - 1} \right)}^{\frac{1}{2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{\frac{1}{2}}}} \right)^5}$$ is a polynomial of degree

If in the expansion of $${\left( {1 + x} \right)^m}{\left( {1 - x} \right)^n},$$ the co-efficients of $$x$$ and $${x^2}$$ are $$3$$ and $$- 6\,$$ respectively, then $$m$$ is

Practice More Releted MCQ Question on Binomial Theorem

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Algebra >> Binomial Theorem

Practice More Releted MCQ Question on
Binomial Theorem