New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2025 · 28 Jan · Shift 2 · Q42

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

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2025 · 28 Jan · Shift 2 · Q42

Matrices and Determinants question

2025 · 28 Jan · Shift 2 · Q42

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

\mathrm{A}=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 \\ 0 & 1\end{array}\right]

and

\mathrm{P}=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right], \theta\gt 0

. If

\mathrm{B}=\mathrm{PAP}{ }^{\top}, \mathrm{C}=\mathrm{P}^{\top} \mathrm{B}^{10} \mathrm{P}

and the sum of the diagonal elements of

C

is

\frac{m}{n}

, where

\operatorname{gcd}(m, n)=1

, then

m+n

is :

A
127
B
2049
C
258
D
65

More from Matrices and Determinants

Let $A = [a_{ij}] = [lo g_{5} 128 lo g_{5} 8 lo g_{4} 5 lo g_{4} 25]$ . If $A_{ij}$ is the cofactor of $a_{ij}$ , $C_{ij} = k = 1 \sum 2 a_{ik} A_{j k}, 1 \leq i, j \leq 2$ …2025 · MCQ
Let M and m respectively be the maximum and the minimum values of $f (x) = 1 + sin^{2} x sin^{2} x sin^{2} x cos^{2} x 1 + cos^{2} x cos^{2} x 4 sin 4 x 4 sin 4 x 1 + 4 sin 4 x, x \in R$ …2025 · MCQ
Let $S = {m \in Z : A^{m^{2}} + A^{m} = 3 I - A^{- 6}}$ , where $A = [21 - 1 0]$ . Then $n (S)$ is equal to .2025 · Numerical
Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} \in {0, 1}$ for all $i$ and $j$ . Let the random variable $X$ denote the possible values of the determinant of the matrix $A$ . Then, the variance of $X$ is:2025 · MCQ
Let $α, β (α e q β)$ be the values of $m$ , for which the equations $x + y + z = 1$ , $x + 2 y + 4 z = m$ and $x + 4 y + 10 z = m^{2}$ have infinitely many solutions. Then the value of $n = 1 \sum 10 (n^{α} + n^{β})$ is equal to :2025 · MCQ
Let $A = [a_{ij}]$ be a matrix of order $3 \times 3$ , with $a_{ij} = (2)^{i + j}$ . If the sum of all the elements in the third row of $A^{2}$ is $α + β 2, α, β \in Z$ , then…2025 · MCQ
If $A = [2 - 1 12], B = [1101], C = ABA^{T}$ and $X = A^{T} C^{2} A$ …2024 · MCQ
If the system of equations $2 x + 3 y - z = 5 x + α y + 3 z = - 4 3 x - y + β z = 7$ has infinitely many solutions, then $13 α β$ is equal to :2024 · MCQ