AP EAMCET · Maths · Matrices
If \(A=\left[a_{i j}\right], 1 \leq i, j \leq n\) with \(\mathrm{n} \geq 2\) and \(a_{i j}=i+j\) is a matrix, then the rank of \(A\) is
- A 0
- B 1
- C 2
- D 4
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Given that \(n \geq 2\) and \(a_{\mathrm{ij}}=i+j\) Case-1: Let \(n=2\) \(A=\left[\begin{array}{ll} 2 & 3 \\ 3 & 4 \end{array}\right] \Rightarrow|A|=\left|\begin{array}{ll} 2 & 3 \\ 3 & 4 \end{array}\right|=8-1=-1 \neq 0\) Case-2: Let \(n=3\)…
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
- \(\int \frac{2 \cos 2 x}{(1+\sin 2 x)(1+\cos 2 x)} d x=\)AP EAMCET 2024 Medium
- If \(y=\cos ^{-1}\left(\frac{a^2-x^2}{a^2+x^2}\right)+\sin ^{-1}\left(\frac{2 a x}{a^2+x^2}\right)\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2010 Hard
- In \(\triangle \mathrm{ABC}\), if \(\mathrm{r}=1, \mathrm{R}=4\) and \(\Delta=8\), then \(\frac{1}{\mathrm{ab}}+\frac{1}{\mathrm{bc}}+\frac{1}{\mathrm{ca}}=\)AP EAMCET 2023 Easy
- If \(\alpha, \beta\) are the acute angles such that \(\frac{\sin \alpha}{\sin \beta}=\frac{6}{5}\) and \(\frac{\cos \alpha}{\cos \beta}=\frac{9}{5 \sqrt{5}}\) then \(\sin \alpha=\)AP EAMCET 2025 Medium
- Find the solution of the following differential equation \(\left\{x \cos \left(\frac{y}{x}\right)+y \sin \left(\frac{y}{x}\right)\right\} y\)
\[
d x=\left\{y \sin \left(\frac{y}{x}\right)-x \cos \left(\frac{y}{x}\right)\right\} x d y
\]AP EAMCET 2020 Hard - If \(y=\tan ^{-1} \frac{x}{1+2 x^2}+\tan ^{-1} \frac{x}{1+6 x^2}+\tan ^{-1} \frac{x}{1+12 x^2}\), then \(\left(\frac{d y}{d x}\right)_{x=\frac{1}{2}}=\)AP EAMCET 2024 Easy
More PYQs from AP EAMCET
- If a straight line \(L\) perpendicular to the line \(3 x-4 y=6\) forms a triangle of area 6 square units with coordinate axes, then the minimum perpendicular distance from the point \((1,1)\) to the line \(\mathrm{L}\) isAP EAMCET 2023 Easy
- If \(\int_a^b x^3 d x=0\) and \(\int_a^b x^2 d x=\frac{2}{3}\), thenAP EAMCET 2021 Easy
- In which of the following, ortho/para substitution by an electrophile is very facile?AP EAMCET 2010 Hard
- Let \(n\) be a positive integer. If the coefficients of \(2^{\text {nd }}, 3^{\text {rd }}\) and \(4^{\text {th }}\) terms in the expansion of \((1+x)^n\) are in A.P, then the value of \(n=\)AP EAMCET 2020 Easy
- A and B throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. A wins if he throws 6 before B throws 7 and B wins if he throws 7 before \(A\) throws 6 . If \(A\) begins, the probability of his winning isAP EAMCET 2024 Medium
- A particle of mass \(2.2 \times 10^{-30} \mathrm{~kg}\) and charge \(1.6 \times 10^{-19} \mathrm{C}\) is moving at a speed of \(10 \mathrm{~km} \mathrm{~s}^{-1}\) in a circular path of radius \(2.8 \mathrm{~cm}\) inside a solenoid. The solenoid has \(25 \frac{\text { turns }}{\mathrm{cm}}\) and its magnetic field is perpendicular to the plane of the particle's path. The current in the solenoid is
\(\left(\right.\) Take, \(\mu_0=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\) )AP EAMCET 2022 Medium