1
JEE Main 2021 (Online) 22th July Evening Shift
Numerical +4 -1
Let $$A = \left[ {\matrix{
0 & 1 & 0 \cr
1 & 0 & 0 \cr
0 & 0 & 1 \cr
} } \right]$$. Then the number of 3 $$\times$$ 3 matrices B with entries from the set {1, 2, 3, 4, 5} and satisfying AB = BA is ____________.
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2
JEE Main 2021 (Online) 20th July Evening Shift
Numerical +4 -1
Let $$A = \{ {a_{ij}}\} $$ be a 3 $$\times$$ 3 matrix,
where $${a_{ij}} = \left\{ {\matrix{ {{{( - 1)}^{j - i}}} & {if} & {i < j,} \cr 2 & {if} & {i = j,} \cr {{{( - 1)}^{i + j}}} & {if} & {i > j} \cr } } \right.$$
then $$\det (3Adj(2{A^{ - 1}}))$$ is equal to _____________.
where $${a_{ij}} = \left\{ {\matrix{ {{{( - 1)}^{j - i}}} & {if} & {i < j,} \cr 2 & {if} & {i = j,} \cr {{{( - 1)}^{i + j}}} & {if} & {i > j} \cr } } \right.$$
then $$\det (3Adj(2{A^{ - 1}}))$$ is equal to _____________.
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3
JEE Main 2021 (Online) 20th July Morning Shift
Numerical +4 -1
Let $$A = \left( {\matrix{
1 & { - 1} & 0 \cr
0 & 1 & { - 1} \cr
0 & 0 & 1 \cr
} } \right)$$ and B = 7A20 $$-$$ 20A7 + 2I, where I is an identity matrix of order 3 $$\times$$ 3. If B = [bij], then b13is equal to _____________.
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4
JEE Main 2021 (Online) 20th July Morning Shift
Numerical +4 -1
Let a, b, c, d in arithmetic progression with common difference $$\lambda$$. If $$\left| {\matrix{
{x + a - c} & {x + b} & {x + a} \cr
{x - 1} & {x + c} & {x + b} \cr
{x - b + d} & {x + d} & {x + c} \cr
} } \right| = 2$$, then value of $$\lambda$$2 is equal to ________________.
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Questions Asked from Matrices and Determinants (Numerical)
Number in Brackets after Paper Indicates No. of Questions
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