JEE Main 2021 (Online) 18th March Evening Shift | Matrices and Determinants Question 107 | Mathematics

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

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

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

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

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

JEE Main 2021 (Online) 18th March Morning Shift

MCQ (Single Correct Answer)

-1

Let $$A + 2B = \left[ {\matrix{ 1 & 2 & 0 \cr 6 & { - 3} & 3 \cr { - 5} & 3 & 1 \cr } } \right]$$ and $$2A - B = \left[ {\matrix{ 2 & { - 1} & 5 \cr 2 & { - 1} & 6 \cr 0 & 1 & 2 \cr } } \right]$$. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) $$-$$ Tr(B) has value equal to

JEE Main 2021 (Online) 17th March Evening Shift

MCQ (Single Correct Answer)

-1

If x, y, z are in arithmetic progression with common difference d, x $$\ne$$ 3d, and the determinant of the matrix $$\left[ {\matrix{ 3 & {4\sqrt 2 } & x \cr 4 & {5\sqrt 2 } & y \cr 5 & k & z \cr } } \right]$$ is zero, then the value of k² is :