New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2025 · 29 Jan · Shift 1 · Q44

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

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2025 · 29 Jan · Shift 1 · Q44

Matrices and Determinants question

2025 · 29 Jan · Shift 1 · Q44

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let M and m respectively be the maximum and the minimum values of

f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & 4 \sin 4 x \\ \sin ^2 x & 1+\cos ^2 x & 4 \sin 4 x \\ \sin ^2 x & \cos ^2 x & 1+4 \sin 4 x\end{array}\right|, x \in R

Then

M^4 - m^4

is equal to :

A
1280
B
1040
C
1215
D
1295

More from Matrices and Determinants

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
Let the system of equations $x + 2 y + 3 z = 5, 2 x + 3 y + z = 9, 4 x + 3 y + λ z = μ$ have infinite number of solutions. Then $λ + 2 μ$ is equal to :2024 · MCQ
Let $A = I_{2} - 2 M M^{T}$ , where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^{T} M = I_{1}$ holds. If $λ$ is a real number such that the relation $A X = λ X$ holds for some non-zero real matrix $X$ of order $2 \times 1$ …2024 · Numerical