NIMCET Matrices Previous Year Question Paper and Solution with PDF

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Previous Year Questions

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Previous Year Questions
NIMCET

NIMCET Previous Year Questions (PYQs)

NIMCET Matrices PYQ

Qus : 1

If A and B are square matrices such that

$B=-A^{-1} BA$ , then

$(A + B)^2$ is

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Solution

Qus : 2

If A is an invertible skew-symmetric matrix, then

is a

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Solution

Qus : 3

Consider the matrix

$B=\begin{pmatrix}{-1} & {-1} & {2} \\ {0} & {-1} & {-1} \\ {0} & {0} & {-1}\end{pmatrix}$ . The sum of all the entries of the matrix

$B^{19}$ is

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Solution

Qus : 4

$F(\theta)=\begin{bmatrix}{\cos \theta} & {-\sin \theta} & {0} \\ {\sin \theta} & {\cos \theta} & {0} \\ {0} & {0} & {1}\end{bmatrix}$ , then

$F(\theta)F(\alpha)$ is equal to

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Solution

Qus : 5

Let A and B be two square matrices of same order satisfying

$A^2+5A+5I =0$ and

$B^2+3B+I=0$ repectively. Where I is the identity matrix. Then the inverse of the matrix

$C= BA+2B+2A+4I$ is

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Solution

Qus : 6

Find a matrix X such that 2A + B + X = 0, whose A =

and B =

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Solution

Qus : 7

and

, then f(A)=

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Solution

Qus : 8

$A=\begin{bmatrix} a &b &c \\ b & c & a\\ c& a &b \end{bmatrix}$ , where

$a, b, c$ are real positive numbers such that

$abc = 1$ and

$A^{T}A=I$ then the equation that not holds true among the following is

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Solution

Qus : 9

If the matrix $\begin{bmatrix} -1 &3 &2 \\ 1& K &-3 \\ 1&4 &5 \end{bmatrix}$ has an inverse matrix, then the value of K is:

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Qus : 10

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Qus : 11

$f(x)=\left\{\begin{matrix} \frac{sin[x]}{[x]} &, [x]\ne0 \\ 0 &, [x]=0 \end{matrix}\right.$ , where [x] is the largest integer but not larger than x, then

$\lim_{x\to0}f(x)$ is

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Solution

Qus : 12

A matrix

$M_r$ is defined as

$M_r=\begin{bmatrix} r &r-1 \\ r-1&r \end{bmatrix} , r \in N$ then the value of

$det(M_1) + det(M_2) +...+ det(M_{2015})$ is

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Solution

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