WB JEE 2019 | Matrices and Determinants Question 48 | Mathematics

WB JEE 2019

MCQ (Single Correct Answer)

-0.25

If $$A = \left( {\matrix{ 5 & {5x} & x \cr 0 & x & {5x} \cr 0 & 0 & 5 \cr } } \right)$$ and $$|A{|^2} = 25$$, then | x | is equal to

$${1 \over 5}$$

5²

WB JEE 2019

MCQ (Single Correct Answer)

-0.25

Let A and B be two square matrices of order 3 and AB = O₃, where O₃ denotes the null matrix of order 3. Then,

must be A = O₃ , B = O₃

if A $$ \ne $$ O₃, must be B $$ \ne $$ O₃

if A = O₃, must be B $$ \ne $$ O₃

may be A $$ \ne $$ O₃, B $$ \ne $$ O₃

WB JEE 2019

MCQ (Single Correct Answer)

-0.5

The system of equations

$$\eqalign{ & \lambda x + y + 3z = 0 \cr & 2x + \mu y - z = 0 \cr & 5x + 7y + z = 0 \cr} $$

has infinitely many solutions in R. Then,

$$\lambda $$ = 2, $$\mu $$ = 3

$$\lambda $$ = 1, $$\mu $$ = 2

$$\lambda $$ = 1, $$\mu $$ = 3

$$\lambda $$ = 3, $$\mu $$ = 1

WB JEE 2018

MCQ (Single Correct Answer)

-0.25

If $$\left| {\matrix{ { - 1} & 7 & 0 \cr 2 & 1 & { - 3} \cr 3 & 4 & 1 \cr } } \right| = A$$, then $$\left| {\matrix{ {13} & { - 11} & 5 \cr { - 7} & { - 1} & {25} \cr { - 21} & { - 3} & { - 15} \cr } } \right|$$ is

$${A^2}$$

$${A^2} - A + {I_3}$$

$${A^2} - 3A + {I_3}$$

$$3{A^2} + 5A - 4{I_3}$$

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