JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Medium

1 of 1

Application +4 | -1

Let

\left(1-x-2 x^2\right)^6=1+a_1 x+a_2 x^2+\ldots . .+a_{12} x^{12}

. Then

\frac{a_2}{2^2}+\frac{a_4}{2^4}+\frac{a_6}{2^6}+\ldots .+\frac{a_{12}}{2^{12}}

is equal to

View answer and explanation

Correct option: B

-1 / 2

Option B (-1/2) is correct because by substituting x = 1/2 and x = -1/2 into the given equation and adding the resulting equations, we can isolate the desired sum.

More Questions from THEORY OF EQUATION

Practice All Chapter MCQs →

The maximum number of real roots of the equation

{x^{2n}} - 1 = 0

is The number of roots of the equation

\frac{1}{x}+\frac{1}{\sqrt{\left(1-x^2\right)}}=\frac{35}{12}

is How many real solutions does the equation

x^7+14 x^5+16 x^3+30 x-560=0

have? If

x_1, x_2, x_3, \ldots, x_n

are the roots of the equation

x^n+a x+b=0

, the value of

\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_1-x_4\right) \ldots\left(x_1-x_n\right)

is The polynomials

P(x)=k x^3+3 x^2-3

and

Q(x)=2 x^3-5 x+k

, when divided by

(x-4)

leave the same remainder, then

k

is equal to: If

{\left( {x - 1} \right)^3}

is a factor of

{x^4} + a{x^3} + b{x^2} + cx - 1,

then the other factor is