JEE Main 2017 (Online) 8th April Morning Slot | Matrices and Determinants Question 266 | Mathematics

The number of real values of $$\lambda $$ for which the system of linear equations

2x + 4y $$-$$ $$\lambda $$z = 0

4x + $$\lambda $$y + 2z = 0

$$\lambda $$x + 2y + 2z = 0

has infinitely many solutions, is :

JEE Main 2017 (Online) 8th April Morning Slot

MCQ (Single Correct Answer)

-1

Let A be any 3 $$ \times $$ 3 invertible matrix. Then which one of the following is not always true ?

adj (A) = $$\left| \right.$$A$$\left| \right.$$.A^$$-$$1

adj (adj(A)) = $$\left| \right.$$A$$\left| \right.$$.A

adj (adj(A)) = $$\left| \right.$$A$$\left| \right.$$².(adj(A))^$$-$$1

adj (adj(A)) = $$\left| \, \right.$$A $$\left| \, \right.$$.(adj(A))^$$-$$1

JEE Main 2017 (Offline)

MCQ (Single Correct Answer)

-1

If $$A = \left[ {\matrix{ 2 & { - 3} \cr { - 4} & 1 \cr } } \right]$$,

then adj(3A² + 12A) is equal to

$$\left[ {\matrix{ {51} & {63} \cr {84} & {72} \cr } } \right]$$

$$\left[ {\matrix{ {51} & {84} \cr {63} & {72} \cr } } \right]$$

$$\left[ {\matrix{ {72} & {-63} \cr {-84} & {51} \cr } } \right]$$

$$\left[ {\matrix{ {72} & {-84} \cr {-63} & {51} \cr } } \right]$$

JEE Main 2017 (Offline)

MCQ (Single Correct Answer)

-1

If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1
x + ay + z = 1
ax + by + z = 0

has no solution, then S is :

an empty set

an infinite set

a finite set containing two or more elements

a singleton

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