JEE Main 2021 (Online) 20th July Morning Shift | Matrices and Determinants Question 103 | Mathematics

JEE Main 2021 (Online) 20th July Morning Shift

MCQ (Single Correct Answer)

-1

Let $$A = \left[ {\matrix{ 2 & 3 \cr a & 0 \cr } } \right]$$, a$$\in$$R be written as P + Q where P is a symmetric matrix and Q is skew symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to :

JEE Main 2021 (Online) 18th March Evening Shift

MCQ (Single Correct Answer)

-1

Let the system of linear equations

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

2x $$-$$ y + z = 0

$$\mu$$x + 2y + 3z = 0, $$\lambda$$, $$\mu$$$$\in$$R.

has a non-trivial solution. Then which of the following is true?

$$\mu$$ = 6, $$\lambda$$$$\in$$R

$$\lambda$$ = 3, $$\mu$$$$\in$$R

$$\mu$$ = $$-$$6, $$\lambda$$$$\in$$R

$$\lambda$$ = 2, $$\mu$$$$\in$$R

JEE Main 2021 (Online) 18th March Evening Shift

MCQ (Single Correct Answer)

-1

Define a relation R over a class of n $$\times$$ n real matrices A and B as

"ARB iff there exists a non-singular matrix P such that PAP^$$-$$1 = B".

Then which of the following is true?

R is reflexive, transitive but not symmetric

R is symmetric, transitive but not reflexive.

R is reflexive, symmetric but not transitive

R is an equivalence relation

JEE Main 2021 (Online) 18th March Morning Shift

MCQ (Single Correct Answer)

-1

The solutions of the equation $$\left| {\matrix{ {1 + {{\sin }^2}x} & {{{\sin }^2}x} & {{{\sin }^2}x} \cr {{{\cos }^2}x} & {1 + {{\cos }^2}x} & {{{\cos }^2}x} \cr {4\sin 2x} & {4\sin 2x} & {1 + 4\sin 2x} \cr } } \right| = 0,(0 < x < \pi )$$, are

$${\pi \over {12}},{\pi \over 6}$$

$${\pi \over 6},{{5\pi } \over 6}$$

$${{5\pi } \over {12}},{{7\pi } \over {12}}$$

$${{7\pi } \over {12}},{{11\pi } \over {12}}$$

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