New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2024 · 27 Jan · Shift 1 · Q41

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2024 · 27 Jan · Shift 1 · Q41

Matrices and Determinants question

2024 · 27 Jan · Shift 1 · Q41

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Consider the matrix

f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]

. Given below are two statements : Statement I :

f(-x)

is the inverse of the matrix

f(x)

. Statement II :

f(x) f(y)=f(x+y)

. In the light of the above statements, choose the correct answer from the options given below :

A
Statement I is false but Statement II is true
B
Both Statement I and Statement II are false
C
Both Statement I and Statement II are true
D
Statement I is true but Statement II is false

More from Matrices and Determinants

Let $A = 211010101, B = [B_{1}, B_{2}, B_{3}]$ , where $B_{1}, B_{2}, B_{3}$ are column matrics, and $AB_{1} = 100, AB_{2} = 230, AB_{3} = 321$ …2024 · Numerical
The values of $α$ , for which $11 2 α + 3 \frac{3}{2} \frac{1}{3} 3 α + 1 α + \frac{3}{2} α + \frac{1}{3} 0 = 0$ , lie in the interval2024 · MCQ
Let $A$ be a $2 \times 2$ real matrix and $I$ be the identity matrix of order 2. If the roots of the equation $∣ A - x I ∣ = 0$ be $- 1$ and 3, then the sum of the diagonal elements of the matrix $A^{2}$ is2024 · Numerical
$Let A = 100 0 α β 0 β α and ∣2 A ∣^{3} = 2^{21} where α, β \in Z, Then a value of α is$ …2024 · MCQ
Let $A$ be a square matrix such that $AA^{T} = I$ . Then $\frac{1}{2} A [(A + A^{T})^{2} + (A - A^{T})^{2}]$ is equal to2024 · MCQ
Let $A = 2631232112$ and $P = 157201025$ . The sum of…2024 · MCQ
Let for any three distinct consecutive terms $a, b, c$ of an A.P, the lines $a x + b y + c = 0$ be concurrent at the point $P$ and $Q (α, β)$ be a point such that the system of equations $x + y + z = 6, 2 x + 5 y + α z = β and$ …2024 · Numerical
Consider the system of linear equations $x + y + z = 4 μ, x + 2 y + 2 λ z = 10 μ, x + 3 y + 4 λ^{2} z = μ^{2} + 15$ where $λ, μ \in R$ . Which one of the following statements is NOT correct ?2024 · MCQ