JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A =\left(\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right)\). If \(B = I -{ }^{5} C _{1} (\operatorname{adj} A )+{ }^{5} C _{2}\) \((\operatorname{adjA})^{2}-\ldots-{ }^{5} C _{5} (\operatorname{adj} A )^{5}\), then the sum of all elements of the matrix \(B\) is
- A \(-5\)
- B \(-6\)
- C \(-7\)
- D \(-8\)
Answer & Solution
Correct Answer
(C) \(-7\)
Step-by-step Solution
Detailed explanation
\(B =( I -\operatorname{adjA})^{5}=\left[\begin{array}{cc} -1 & -1 \\ 0 & -1 \end{array}\right]^{5}=\left[\begin{array}{cc} -1 & -5 \\ 0 & -1 \end{array}\right]\) Sum of its all elements \(=-7\).
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 mean and standard deviation of 100 observations are 40 and 5.1 , respectively, By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are \(\mu\) and \(\sigma\) respectively, then \(10(\mu+\sigma)\) is equal toJEE Mains 2025 Medium
- The locus of the mid points of the chords of the circle \(C_1:(x-4)^2+(y-5)^2=4\) which subtend an angle \(\theta_i\) at the centre of the circle \(C_1\), is a circle of radius \(r_i\). If \(\theta_1=\frac{\pi}{3}, \theta_3=\frac{2 \pi}{3}\) and \(r_1^2=r_2^2+r_3^2\), then \(\theta_2\) is equal toJEE Mains 2023 Hard
- A plane bisects the line segment joining the points \(( 1 , 2, 3)\) and \(( - 3, 4, 5)\) at right angles. Then this plane also passes through the pointJEE Mains 2018 Hard
- If \(\int\left( e ^{2 x }+2 e ^{ x }- e ^{- x }-1\right) e ^{\left( e ^{ x }+ e ^{- x }\right)} d x\) \(=g(x) e^{\left(e^{x}+e^{-x}\right)}+c,\) where \(c\) is a constant of integration, then \(g (0)\) is equal toJEE Mains 2020 Hard
- The curve satisfying the differential equation, \(ydx-(x + 3y^2 )\, dy = 0\) and passing through the point \((1, 1)\) , also passes through the pointJEE Mains 2017 Hard
- Let \(f(x)=3 \sin ^{4} x+10 \sin ^{3} x+6 \sin ^{2} x-3, x \in\left[-\frac{\pi}{6}, \frac{\pi}{2}\right] .\) Then, \(f\) is \(.....\)JEE Mains 2021 Hard
More PYQs from JEE Mains
- If \(f(x)\, = {x^2} - x + 5,\,\,x > \frac{1}{2},\) and \(g(x)\) is its inverse function, then \(g'(7)\) equalsJEE Mains 2014 Hard
- The area (in sq. units) in the first quadrant bounded by the parabola, \(y = x^2 +1\), the tangent to it at the point \((2, 5)\) and the coordinate axes isJEE Mains 2019 Hard
- Let
\(\mathrm{f}(x)=\left\{\begin{array}{lc}3 x, & x \lt 0 \\ \min \{1+x+[x], x+2[x]\}, & 0 \leq x \leq 2 \\ 5, & x\gt2,\end{array}\right.\)
where [.] denotes greatest integer function. If \(\alpha\) and \(\beta\) are the number of points, where f is not continuous and is not differentiable, respectively, then \(\alpha+\beta\) equals __________JEE Mains 2025 Hard - If \(f\left( x \right) = \left| \begin{array}{*{20}{c}}
{\cos x}&x&1\\
{2\sin x}&{{x^2}}&{2x}\\
{\tan x}&x&1
\end{array}\right|\) , then \(\mathop {\lim }\limits_{x \to 0} \frac{{f'\left( x \right)}}{x}\)JEE Mains 2018 Hard - Let \(a _1, \frac{ a _2}{2}, \frac{ a _3}{2^2}, \ldots ., \frac{ a _{10}}{2^9}\) be a G.P. of common ratio \(\frac{1}{\sqrt{2}}\). If \(a _1+ a _2+\ldots+ a _{10}=62\), then \(a _1\) is equal to \(:\)JEE Mains 2026 Medium
- Let \(O\) be the origin and \(A\) be the point \(z _{1}=1+2 i\). If \(B\) is the point \(z _{2}, \operatorname{Re}\left( z _{2}\right)<0\), such that \(OAB\) is a right angled isosceles triangle with \(OB\) as hypotenuse, then which of the following is NOT true?JEE Mains 2022 Hard