JEE MAIN Matrices Previous Year Questions (PYQs) – Page 8 of 15
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If $A$ and $B$ are two non-zero $n \times n$ matrices such that $A^{2}+B=A^{2}B$, then:
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Solution
Let $ A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix} $.
If $ \det(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n $, $ m, n \in \mathbb{N} $, then $ m + n $ is equal to
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Solution
Let f : (–1,$\infty $)$ \to $ R be defined by f(0) = 1 andLet A = {X = (x, y, z)T: PX = 0 and
x2 + y2 + z2 = 1} where
$P = \left[ {\matrix{ 1 & 2 & 1 \cr { - 2} & 3 & { - 4} \cr 1 & 9 & { - 1} \cr } } \right]$,
then the set A :
x2 + y2 + z2 = 1} where
$P = \left[ {\matrix{ 1 & 2 & 1 \cr { - 2} & 3 & { - 4} \cr 1 & 9 & { - 1} \cr } } \right]$,
then the set A :
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Solution
Let the system of linear equations $x + 2y + z = 2$, $\alpha x + 3y - z = \alpha $, $ - \alpha x + y + 2z = - \alpha $ be inconsistent. Then $\alpha$ is equal to :
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Solution
Consider the system of linear equations
$x + y + z = 4\mu,\quad x + 2y + 2\lambda z = 10\mu,\quad x + 3y + 4\lambda^2 z = \mu^2 + 15$
where $\lambda, \mu \in \mathbb{R}$.
Which one of the following statements is NOT correct?
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Solution
If the system of linear equations
$7x + 11y + \alpha z = 13$
$5x + 4y + 7z = \beta$
$175x + 194y + 57z = 361$
has infinitely many solutions, then $\alpha + \beta + 2$ is equal to:
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Solution
If the system of equations
$x + 2y + 3z = 3$
$4x + 3y - 4z = 4$
$8x + 4y - \lambda z = 9 + \mu$
has infinitely many solutions, then the ordered pair $(\lambda,\mu)$ is equal to:
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Solution
The number of real values of $\lambda$ for which the system of linear equations
$2x+4y-\lambda z=0$
$4x+\lambda y+2z=0$
$\lambda x+2y+2z=0$
has infinitely many solutions, is :
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Solution
Let α be a solution of $x^2 + x + 1 = 0$, and for some a and b in
$R, \begin{bmatrix} 4 & a & b \end{bmatrix} \begin{bmatrix} 1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8 \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 \end{bmatrix}$. If $\frac{4}{\alpha^4} + \frac{m}{\alpha^a} + \frac{n}{\alpha^b} = 3$, then m + n is equal to _______
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Solution
Let $A$ be any $3\times 3$ invertible matrix. Then which one of the following is not always true?
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Solution
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