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Recent questions tagged determinant

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NIELIT 2017 OCT Scientific Assistant A (IT) - Section B: 7
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiplied by $2,$ its determinant value becomes $40.$ The value of $’n’$ is$2$3$5$4$
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NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 9
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiple by $2,$ its determinant value becomes $40.$ The value of $’n’$ is$2$3$5$4$
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NIELIT 2016 MAR Scientist B - Section B: 4
What is the determinant of the matrix $\begin{bmatrix}5&3&2\\1&2&6\\3&5&10\end{bmatrix}$-76$-28$+28$+72$
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NIELIT 2016 MAR Scientist B - Section B: 12
If $A$ and $B$ are square matrices of size $n\times n$, then which of the following statements is not true?$\det(AB)=\det(A) \det(B)$\det(kA)=k^n \det(A)$\det(A+B)=\det(A)+\det(B)$\det(A^T)=1/\det(A^{-1})$
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NIELIT 2016 DEC Scientist B (IT) - Section B: 26
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+​ \sqrt-1)$ and $3$. The determinant of $P$ is ________.$0$1$15$-1$
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NIELIT 2016 DEC Scientist B (CS) - Section B: 21
Let $A,B,C,D$ be $n\times n$ matrices, each with non-zero determinant. If $ABCD=1$, then $B^{-1}$ is:$D^{-1}C^{-1}A^{-1}$CDA$ADC$Does not necessarily exist.
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ISI2014-DCG-25
The determinant $\begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix}$ ... $3\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$None of these
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ISI2015-MMA-37
Let $a$ be a non-zero real number. Define$f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$ for $x \in \mathbb{R}$. Then, the number of distinct real roots of $f(x) =0$ is$1$2$3$4$
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ISI2015-DCG-3
The value of $\begin{vmatrix} 1+a & 1 & 1 & 1 \\ 1 & 1+b & 1 & 1 \\ 1 & 1 & 1+c & 1 \\ 1 & 1 & 1 & 1+d \end{vmatrix}$ ... \frac{1}{d})$1+\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}$None of these
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ISI2015-DCG-22
The value of $\begin{vmatrix} 1 & \log _x y & \log_x z \\ \log _y x & 1 & \log_y z \\ \log _z x & \log _z y & 1 \end{vmatrix}$ is$0$1$-1$None of these
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ISI2015-DCG-31
Let $A$ be an $n \times n$ matrix such that $\mid A^{2} \mid\: =1$. Here $\mid A \mid $ stands for determinant of matrix $A$. Then$\mid A \mid =1$\mid A \mid =0 \text{ or } 1$\mid A \mid =-1, 0 \text{ or } 1$\mid A \mid =-1 \text{ or } 1$
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ISI2015-DCG-34
Let $A_{ij}$ denote the minors of an $n \times n$ matrix $A$. What is the relationship between $\mid A_{ij} \mid $ and $\mid A_{ji} \mid $ ... is a symmetric matrixIf $\mid A_{ij} \mid =0$ then $\mid A_{ji} \mid =0$
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ISI2016-DCG-3
The value of $\begin{vmatrix} 1+a& 1& 1& 1\\ 1&1+b &1 &1 \\ 1&1 &1+c &1 \\ 1&1 &1 &1+d \end{vmatrix}$ ... frac{1}{d})$1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}$None of these
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ISI2016-DCG-22
The value of $\:\:\begin{vmatrix} 1&\log_{x}y &\log_{x}z \\ \log_{y}x &1 &\log_{y}z \\\log_{z}x & \log_{z}y&1 \end{vmatrix}\:\:$ is$0$1$-1$None of these
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ISI2016-DCG-31
Let $A$ be an $n\times n$ matrix such that $\mid\: A^{2}\mid=1.\:\: \mid A\:\mid$ stands for determinant of matrix $A.$ Then$\mid\:(A)\mid=1$\mid\:(A)\mid=0\:\text{or}\:1$\mid\:(A)\mid=-1,0\:\text{or}\:1$\mid\:(A)\mid=-1\:\text{or}\:1$
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ISI2017-DCG-7
If $\begin{vmatrix} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{vmatrix} = k(10!)(11!)(12!)$, then the value of $k$ is$1$2$3$4$
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ISI2017-DCG-23
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability of choosing a non-zero determinant is$\frac{3}{16}$\frac{3}{8}$\frac{1}{4}$none of these
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ISI2017-DCG-25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is$\pi$\frac{\pi}{2}$0$1$
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ISI2018-MMA-14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals$-4$-2$2$4$
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ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is$2$2(1+i)$0$2^{10}$
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