1

JEE Main 2021 (Online) 26th February Evening Shift

Numerical

+4

-1

If the matrix $$A = \left[ {\matrix{
1 & 0 & 0 \cr
0 & 2 & 0 \cr
3 & 0 & { - 1} \cr
} } \right]$$ satisfies the equation

$${A^{20}} + \alpha {A^{19}} + \beta A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & 0 \cr 0 & 0 & 1 \cr } } \right]$$ for some real numbers $$\alpha$$ and $$\beta$$, then $$\beta$$ $$-$$ $$\alpha$$ is equal to ___________.

$${A^{20}} + \alpha {A^{19}} + \beta A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & 0 \cr 0 & 0 & 1 \cr } } \right]$$ for some real numbers $$\alpha$$ and $$\beta$$, then $$\beta$$ $$-$$ $$\alpha$$ is equal to ___________.

Your input ____

2

JEE Main 2021 (Online) 25th February Morning Shift

Numerical

+4

-1

If $$A = \left[ {\matrix{
0 & { - \tan \left( {{\theta \over 2}} \right)} \cr
{\tan \left( {{\theta \over 2}} \right)} & 0 \cr
} } \right]$$ and

$$({I_2} + A){({I_2} - A)^{ - 1}} = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]$$, then $$13({a^2} + {b^2})$$ is equal to

$$({I_2} + A){({I_2} - A)^{ - 1}} = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]$$, then $$13({a^2} + {b^2})$$ is equal to

Your input ____

3

JEE Main 2021 (Online) 25th February Morning Shift

Numerical

+4

-1

Out of Syllabus

Let $$A = \left[ {\matrix{
x & y & z \cr
y & z & x \cr
z & x & y \cr
} } \right]$$, where x, y and z are real numbers such that x + y + z > 0 and xyz = 2. If $${A^2} = {I_3}$$, then the value of $${x^3} + {y^3} + {z^3}$$ is ____________.

Your input ____

4

JEE Main 2021 (Online) 25th February Morning Shift

Numerical

+4

-1

If the system of equations

kx + y + 2z = 1

3x $$-$$ y $$-$$ 2z = 2

$$-$$2x $$-$$2y $$-$$4z = 3

has infinitely many solutions, then k is equal to __________.

kx + y + 2z = 1

3x $$-$$ y $$-$$ 2z = 2

$$-$$2x $$-$$2y $$-$$4z = 3

has infinitely many solutions, then k is equal to __________.

Your input ____

Questions Asked from Matrices and Determinants (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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