JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The total number of \(3 \times 3\) matrices \(A\) having enteries from the set \((0,1,2,3)\) such that the sum of all the diagonal entries of \(AA ^{ T }\) is \(9\), is equal to........
- A \(728\)
- B \(712\)
- C \(824\)
- D \(766\)
Answer & Solution
Correct Answer
(D) \(766\)
Step-by-step Solution
Detailed explanation
Let \(A =\left[\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & i \end{array}\right]\) diagonal elements of \(AA ^{ T }, \quad a ^{2}+ b ^{2}+ c ^{2}, d ^{2}+ e ^{2}+ f ^{2}, g ^{2}+ b ^{2}+ c ^{2}\) Sum \(=a^{2}+b^{2}+c^{2}+d^{2}+e^{2}+f^{2}+g^{2}+h^{2}+i^{2}=9\)…
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
- For \(x\,\, \in \,R\,,x\, \ne \,0,\) let \({f_0}(x) = \frac{1}{{1 - x}}\) and \({f_{n + 1}}(x) = {f_0}({f_n}(x)),\) \(n\, = 0,1,2,....\) Then the value of \({f_{100}}(3) + {f_1}\left( {\frac{2}{3}} \right) + {f_2}\left( {\frac{3}{2}} \right)\) is equal toJEE Mains 2016 Hard
- If \(\displaystyle\lim_{x \to 2} \dfrac{\sin(x^3 - 5x^2 + ax + b)}{(\sqrt{x-1} - 1)\log_e(x-1)} = m\), then \(a + b + m\) is equal to :JEE Mains 2026 Hard
- Let the domain of the function \(f(x)=\log _{4}\left(\log _{5}\left(\log _{3}\left(18 x-x^{2}-77\right)\right)\right)\) be \((a, b)\). Then the value of the integral \(\int_{a}^{b} \frac{\sin ^{3} x}{\left(\sin ^{3} x+\sin ^{3}(a+b-x)\right)} d x\) is equal to \(.....\)JEE Mains 2021 Hard
- Let \(f : R \rightarrow R\) be a continuous function such that \(f(3 x)-f(x)=x\). If \(f(8)=7\), then \(f(14)\) is equal to.JEE Mains 2022 Hard
- Let the area of the bounded region \(\left\{(x, y): 0 \leq 9 x \leq y^2, y \geq 3 x-6\right\}\) be A. Then 6 A is equal to ________JEE Mains 2025 Medium
- The number of ways to distribute \(30\) identical candies among four children \(C _{1}, C _{2}, C _{3}\) and \(C _{4}\) so that \(C _{2}\) receives atleast \(4\) and atmost \(7\) candies, \(C _{3}\) receives atleast \(2\)and atmost \(6\) candies, is equal toJEE Mains 2022 Hard
More PYQs from JEE Mains
- If the tangents drawn at the points \(P\) and \(Q\) on the parabola \(y^{2}=2 x-3\) intersect at the point \(R(0,1)\), then the orthocentre of the triangle \(PQR\) is.JEE Mains 2022 Hard
- Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a function such that \(f(x) + 3f\left(\dfrac{\pi}{2} - x\right) = \sin x\), \(x \in \mathbf{R}\). Let the maximum value of \(f\) on \(\mathbf{R}\) be \(\alpha\). If the area of the region bounded by the curves \(g(x) = x^2\) and \(h(x) = \beta x^3\), \(\beta > 0\), is \(\alpha^2\), then \(30\beta^3\) is equal to _______.JEE Mains 2026 Hard
- Let \(S=\{4,6,9\}\) and \(T=\{9,10,11, \ldots, 1000\}\). If \(A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in N, a_{1}, a_{2}, a_{3}, \ldots, a_{k} \in S\right\}\) then the sum of all the elements in the set \(T - A\) is equal to \(......\)JEE Mains 2022 Hard
- If \(\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}\) are in an \(A.P.\) and \(\log _e \mathrm{a}-\) \(\log _e 2 b, \log _e 2 b-\log _e 3 c, \log _e 3 c-\log _e a\) are also in an \(A.P,\) then \(a: b: c\) is equal toJEE Mains 2024 Hard
- The vertices of a triangle are \(\mathrm{A}(-1,3), \mathrm{B}(-2,2)\) and \(\mathrm{C}(3,-1)\). \(A\) new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :JEE Mains 2024 Hard
- If \(\cos \,x\,\frac{{dy}}{{dx}} - y\,\sin \,x = 6x,\,\left( {0 < x < \frac{\pi }{2}} \right)\) and \(y\left( {\frac{\pi }{3}} \right) = 0\), then \(y\left( {\frac{\pi }{6}} \right)\) is equal toJEE Mains 2019 Hard