COMEDK · Maths · 22. Determinants
If \(A=\left[\begin{array}{cc}2-k & 2 \\ 1 & 3-k\end{array}\right]\) is a singular matrix, then the value of \(5 k-k^2\) is
- A 0
- B 6
- C -6
- D 4
Answer & Solution
Correct Answer
(D) 4
Step-by-step Solution
Detailed explanation
A matrix \(A\) is singular if its determinant is zero, so \(\det(A) = 0\). Given \(A = \begin{bmatrix} 2-k & 2 \\ 1 & 3-k \end{bmatrix}\), the determinant is calculated as: \(\det(A) = (2-k)(3-k) - (2)(1) = 0\) Expanding the expression: \(6 - 2k - 3k + k^2 - 2 = 0\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The foci of a hyperbola are the same as those of the ellipse with equation \(9x^2 + 16y^2 = 144\). If the length of the transverse axis of this hyperbola is \(2\cos\alpha\), then its equation is:COMEDK 2026 Medium
- The projection of \(=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) on \(\hat{v}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{R}}\) isCOMEDK 2019 Easy
- A batch of 10 cupcakes consists of 5 chocolate, 3 vanilla, and 2 strawberry. If 4 cupcakes are selected to be put into a gift box, find the number of different ways they can be chosen if the selection must include at least 2 chocolate, at most 1 vanilla, and exactly 1 strawberry cupcake.COMEDK 2026 Medium
- If \(x^{x}=y^{y}\), then \(\frac{d y}{d x}\) isCOMEDK 2020 Medium
- If \(\omega\) is a cube root of unity, then the value of \(\operatorname{determinant}\left|\begin{array}{ccc}1+\omega & \omega^{2} & \omega \\ \omega^{2}+\omega & -\omega & \omega^{2} \\ 1+\omega^{2} & \omega & \omega^{2}\end{array}\right|\) is equal toCOMEDK 2012 Easy
- If \(x=a\left(\cos t+\log \tan \frac{t}{2}\right), y=a \sin t\), then \(\frac{d y}{d x}=\)COMEDK 2018 Easy
More PYQs from COMEDK
- The value of \(\left|\begin{array}{ccc}441 & 442 & 443 \\ 445 & 446 & 447 \\ 449 & 450 & 451\end{array}\right|\) isCOMEDK 2013 Medium
- An electric current \(I\) enters and leaves a uniform circular wire of radius \(r\) through diametrically opposite points. A charged particle \(q\) moves along the axis of circular wire passes through its centre with speed \(v\). The magnetic force on the particle when it passes through the centre has a magnitudeCOMEDK 2022 Hard
- In the ionic equation, \(\mathrm{BiO}_{3}^{-}+6 \mathrm{H}^{+}+x e^{-} \longrightarrow \mathrm{Bi}^{3+}+3 \mathrm{H}_{2} \mathrm{O}\) the value of \(x\) isCOMEDK 2020 Medium
- An electric field and magnetic field \(1.8 \times 10^4\ Vm^{-1}\) and \(6 \times 10^{-3}\ T\) respectively are applied simultaneously on an electron beam such that path of the beam remains undeviated, then the speed of the electron will be:COMEDK 2026 Easy
- In which of the following case, does the reaction go farthest to completion ifCOMEDK 2014 Easy
- The imaginary part of \(i^{i}\) isCOMEDK 2020 Easy