JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A = \left[ {\begin{array}{*{20}{c}}2&{ - 3}\\{ - 4}&1\end{array}} \right],\) then \(adj\;\left( {3{A^2} + 12A} \right) = \) . . . .
- A \(\left[ {\begin{array}{*{20}{c}}{72}&{ - 63}\\{ - 84}&{51}\end{array}} \right]\)
- B \(\left[ {\begin{array}{*{20}{c}}{72}&{ - 84}\\{ - 63}&{51}\end{array}} \right]\)
- C \(\left[ {\begin{array}{*{20}{c}}{51}&{63}\\{84}&{72}\end{array}} \right]\)
- D \(\left[ {\begin{array}{*{20}{c}}{51}&{84}\\{63}&{72}\end{array}} \right]\)
Answer & Solution
Correct Answer
(C) \(\left[ {\begin{array}{*{20}{c}}{51}&{63}\\{84}&{72}\end{array}} \right]\)
Step-by-step Solution
Detailed explanation
We have \(A = \left[ {\begin{array}{*{20}{c}} 2&{ - 3}\\ { - 4}&1 \end{array}} \right]\) \( \Rightarrow {A^2} = \left[ {\begin{array}{*{20}{c}} {16}&{ - 9}\\ { - 12}&{13} \end{array}} \right]\)…
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
- Let \(A=\{1,2,3,4\}\) and \(R\) be a relation on the set \(A \times A\) defined by \(R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}\). Then the number of elements in \(R\) is:JEE Mains 2023 Hard
- If \(A\) is a square matrix of order \(3\) such that \( \operatorname{det}(\mathrm{A})=3 \text { and } \) \( \operatorname{det}\left(\operatorname{adj}\left(-4 \operatorname{adj}\left(-3 \operatorname{adj}\left(3 \operatorname{adj}\left((2 \mathrm{~A})^{-1}\right)\right)\right)\right)\right)=2^{\mathrm{m}} 3^{\mathrm{n}},\) then \(m+ 2 n\) is equal to :JEE Mains 2024 Hard
- Let \(P\) be the plane containing the straight line \(\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}\) and perpendicular to the plane containing the straight lines \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\) and \(\frac{x}{3}=\frac{y}{7}=\frac{z}{8}\). If \(d\) is the distance of \(P\) from the point \((2,-5,11)\), then \(d ^{2}\) is equal to.JEE Mains 2022 Hard
- lf \(f(x)\) is a differentiable function in the interval \((0,\infty )\) such that \(f(1) = 1\) and \(\mathop {\lim }\limits_{t \to x} \frac{{{t^2}f(x) - {x^2}f(t)}}{{t - x}} = 1,\) for each \(x > 0,\) then \(f (\frac {3}{2})\) is equal toJEE Mains 2016 Hard
- Let \(f : R \to R\) be a function such that \(\left| {f\left( x \right)} \right| \leq {x^2}\) , for all \(x \in R\) . Then, at \(x\, = 0\), \(f\) isJEE Mains 2014 Hard
- Let \(x=2\) be a root of the equation \(x^2+p x+q=0\) and \(f(x)=\left\{\begin{array}{cc}\frac{1-\cos \left(x^2-4 p x+q^2+8 q+16\right)}{(x-2 p)^4}, & x \neq 2 p \\ 0, & x=2 p\end{array}\right.\) Then \(\lim _{x \rightarrow 22^{+}}[f(x)]\) where [. ] denotes greatest integer function, is \(........\)JEE Mains 2023 Hard
More PYQs from JEE Mains
- The set of all values of \(a\) for which \(\operatorname{Lim}_{x \rightarrow a}([x-5]-[2 x+2])=0\), where \([\propto]\) denotes the greater integer less than or equal to \(\propto\) is equal toJEE Mains 2023 Hard
- Let \(\theta\) be the angle between the planes \(P_1=\vec{r} \cdot(\hat{ i }+\hat{ j }+2 \hat{ k })=9\) and \(P _2=\overrightarrow{ r } \cdot(2 \hat{ i }-\hat{ j }+\hat{ k })=15\).Let \(L\) be the line that meets \(P _2\) at the point \((4,-2,5)\) and makes an angle \(\theta\) with the normal of \(P_{2^*}\) If \(\alpha\) is the angle between \(L\) and \(P_2\) then \(\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)\) is equal to \(...........\).JEE Mains 2023 Easy
- Let \(\left(\begin{array}{l}n \\ k\end{array}\right)\) denotes \({ }^{n} C_{k}\) and \(\left[\begin{array}{l} n \\ k \end{array}\right]=\left\{\begin{array}{cc}\left(\begin{array}{c} n \\ k \end{array}\right), & \text { if } 0 \leq k \leq n \\ 0, & \text { otherwise }\end{array}\right.\) If \(A_{k}=\sum_{i=0}^{9}\left(\begin{array}{l}9 \\ i\end{array}\right)\left[\begin{array}{c}12 \\ 12-k+i\end{array}\right]+\sum_{i=0}^{8}\left(\begin{array}{c}8 \\ i\end{array}\right)\left[\begin{array}{c}13 \\ 13-k+i\end{array}\right]\) and \(A_{4}-A_{3}=190 \mathrm{p}\), then \(p\) is equal to :JEE Mains 2021 Hard
- Let \(A\) and \(B\) be two \(3 \times 3\) real matrices such that \(\left(A^{2}-B^{2}\right)\) is invertible matrix. If \(A^{5}=B^{5}\) and \(A^{3} B^{2}=A^{2} B^{3}\), then the value of the determinant of the matrix \(A^{3}+B^{3}\) is equal to:JEE Mains 2021 Hard
- Let for two distinct values of \(p\) the lines \(y=x+p\) touch the ellipse \(\mathrm{E}: \frac{\mathrm{x}^2}{4^2}+\frac{\mathrm{y}^2}{3^2}=1\) at the points A and B . Let the line \(\mathrm{y}=\mathrm{x}\) intersect E at the points C and \(D\). Then the area of the quadrilateral \(A B C D\) is equal toJEE Mains 2025 Medium
- If the distances of the point (1, 2, a) from the line \(\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}\) along the lines
\(L_{1}:\frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}\) and
\(L_{2}:\frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}\) are equal,
then \(a+b+c\) is equal toJEE Mains 2026 Easy