JEE Main 2018 (Online) 15th April Evening Slot | Matrices and Determinants Question 252 | Mathematics

Suppose A is any 3$$ \times $$ 3 non-singular matrix and ( A $$-$$ 3I) (A $$-$$ 5I) = O where I = I₃ and O = O₃. If $$\alpha $$A + $$\beta $$A^-1 = 4I, then $$\alpha $$ + $$\beta $$ is equal to :

JEE Main 2018 (Online) 15th April Evening Slot

MCQ (Single Correct Answer)

-1

If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :

a = $$-$$ 1, b = 9

a = $$-$$ 1, b $$ \ne $$ 9

a $$ \ne $$ $$-$$ 1, b = 9

a = 1, b $$ \ne $$ 9

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MCQ (Single Correct Answer)

-1

Let $$A$$ be a matrix such that $$A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right]$$ is a scalar matrix and |3A| = 108.
Then A² equals :

$$\left[ {\matrix{ 4 & { - 32} \cr 0 & {36} \cr } } \right]$$

$$\left[ {\matrix{ {36} & 0 \cr { - 32} & 4 \cr } } \right]$$

$$\left[ {\matrix{ 4 & 0 \cr { - 32} & {36} \cr } } \right]$$

$$\left[ {\matrix{ {36} & { - 32} \cr 0 & 4 \cr } } \right]$$

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MCQ (Single Correct Answer)

-1

Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y $$-$$ z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :

an empty set

equal to {0}

equal to R

equal to R $$-$$ {0}

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