New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2024 · 30 Jan · Shift 1 · Q39

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

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2024 · 30 Jan · Shift 1 · Q39

Matrices and Determinants question

2024 · 30 Jan · Shift 1 · Q39

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Consider the system of linear equations

x+y+z=4 \mu, x+2 y+2 \lambda z=10 \mu, x+3 y+4 \lambda^2 z=\mu^2+15

where

\lambda, \mu \in \mathbf{R}

. Which one of the following statements is NOT correct ?

A
The system has unique solution if $\lambda eq \frac{1}{2}$ and $\mu eq 1,15$
B
The system has infinite number of solutions if $\lambda=\frac{1}{2}$ and $\mu=15$
C
The system is consistent if $\lambda eq \frac{1}{2}$
D
The system is inconsistent if $\lambda=\frac{1}{2}$ and $\mu eq 1$

More from Matrices and Determinants

Let $R = x 00 0 y 0 00 z$ be a non-zero $3 \times 3$ matrix, where $x sin θ = y sin (θ + \frac{2 π}{3}) = z sin (θ + \frac{4 π}{3}) e q 0, θ \in (0, 2 π)$ …2024 · MCQ
Consider the system of linear equations $x + y + z = 5, x + 2 y + λ^{2} z = 9, x + 3 y + λ z = μ$ , where $λ, μ \in R$ . Then, which of the following statement is NOT correct?2024 · MCQ
If the system of linear equations $x - 2 y + z = - 4 2 x + α y + 3 z = 5 3 x - y + β z = 3$ has infinitely many solutions, then $12 α + 13 β$ is equal to2024 · MCQ
Let $A$ be a $3 \times 3$ real matrix such that $A 101 = 2101, A - 1 01 = 4 - 1 01, A 010 = 2010 .$ …2024 · MCQ
Let A be a $3 \times 3$ matrix and $det (A) = 2$ . If $n = det (2024 - times adj (adj (\dots .. (adj A))))$ , then the remainder when $n$ is divided…2024 · Numerical
Let $S$ denote the set of all real values of $λ$ such that the system of equations $λ x + y + z = 1 x + λ y + z = 1 x + y + λ z = 1$ is inconsistent, then $\sum_{λ \in S} (∣ λ ∣^{2} + ∣ λ ∣)$ is equal to2023 · MCQ
For the system of linear equations $α x + y + z = 1, x + α y + z = 1, x + y + α z = β$ , which one of the following statements is NOT correct?2023 · MCQ
If $A = \frac{1}{2} [1 - 3 31]$ , then :2023 · MCQ