JEE MATHEMATICS MCQ: MATRICES

1 Easy

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Analyzing +4 | -1

\left(1+a x+b x^2\right)^4=a_0+a_1 x+a_2 x^2+\ldots+a_8 x^8

, where

a, b, a_0, a_1, \ldots, a_8 \in R

such that

a_0+a_1+a_2 \neq 0

and

\left|\begin{array}{lll}a_0 & a_1 & a_2 \\ a_1 & a_2 & a_0 \\ a_2 & a_0 & a_1\end{array}\right|=0

, then

View answer and explanation

Correct option: B

a=\frac{1}{4}, b=\frac{5}{32}

The correct answer is B (

a=\frac{{1}}{{4}}, b=\frac{{5}}{{32}}

) because substituting the given conditions into the determinant equation leads to these values for a and b.

More Questions from MATRICES

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\left|\begin{array}{ccc}a & b-c & b+c \\ c+a & b & c-a \\ a-b & a+b & c\end{array}\right|=0

a, b, c

a x+b y+c=0

{x_2} - {x_3} = 1,\; - {x_1} + 2{x_3} = - 2,\;{x_1} - 2,\;{x_1} - 2{x_2} = 3

2x + 3y + 1 = 0,3x + y - 2 = 0

ax + 2y - b = 0

\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

\omega

\left| {\begin{array}{cccccccccccccccccccc} 1&\omega &{{\omega ^2}}\\ \omega &{{\omega ^2}}&1\\ {{\omega ^2}}&1&\omega \end{array}} \right|

A

2 \times 2

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

|A|