JEE Main 2013 (Offline) | Matrices and Determinants Question 220 | Mathematics

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

If $$P = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and
$$\left| A \right| = 4,$$ then $$\alpha $$ is equal to :

$$4$$

$$11$$

$$5$$

$$0$$

AIEEE 2012

MCQ (Single Correct Answer)

-1

Let $$P$$ and $$Q$$ be $$3 \times 3$$ matrices $$P \ne Q.$$ If $${P^3} = {Q^3}$$ and
$${P^2}Q = {Q^2}P$$ then determinant of $$\left( {{P^2} + {Q^2}} \right)$$ is equal to :

$$-2$$

$$1$$

$$0$$

$$-1$$

AIEEE 2012

MCQ (Single Correct Answer)

-1

Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 2 & 1 & 0 \cr 3 & 2 & 1 \cr } } \right)$$. If $${u_1}$$ and $${u_2}$$ are column matrices such
that $$A{u_1} = \left( {\matrix{ 1 \cr 0 \cr 0 \cr } } \right)$$ and $$A{u_2} = \left( {\matrix{ 0 \cr 1 \cr 0 \cr } } \right),$$ then $${u_1} + {u_2}$$ is equal to :

$$\left( {\matrix{ -1 \cr 1 \cr 0 \cr } } \right)$$

$$\left( {\matrix{ -1 \cr 1 \cr -1 \cr } } \right)$$

$$\left( {\matrix{ -1 \cr -1 \cr 0 \cr } } \right)$$

$$\left( {\matrix{ 1 \cr -1 \cr -1 \cr } } \right)$$

AIEEE 2011

MCQ (Single Correct Answer)

-1

Let $$A$$ and $$B$$ be two symmetric matrices of order $$3$$.
Statement - 1: $$A(BA)$$ and $$(AB)$$$$A$$ are symmetric matrices.
Statement - 2: $$AB$$ is symmetric matrix if matrix multiplication of $$A$$ with $$B$$ is commutative.

statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.

statement - 1 is true, statement - 2 is false.

statement - 1 is false, statement -2 is true

statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.

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