WBJEE · Maths · Matrices
An \(n \times n\) matrix is formed using 0,1 and -1 as its elements. The number of such matrices which are skew symmetric is
- A \(\frac{n(n-1)}{2}\)
- B \((n-1)^2\)
- C \(2^{n(n-1) / 2}\)
- D \(3^{n(n-1) / 2}\)
Answer & Solution
Correct Answer
(D) \(3^{n(n-1) / 2}\)
Step-by-step Solution
Detailed explanation
\(3^{\frac{n(n-1)}{2}}\) Each diagonal entry must be ' 0 ' and sum of conjugate elements will be ' 0 '. So, we need to select elements of one side of the diagonal, where each entry has three options.
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 values of \(a, b, c\) for which the function \(f(x)=\left\{\begin{array}{l}\frac{\sin (a+1) x+\sin x}{x}, x < 0 \\ c, x=0 \\ \frac{\left(x+b x^2\right)^{1 / 2}-\sqrt{x}}{b x^{1 / 2}}, x>0\end{array}\right.\) is continuous at \(x=0\), areWBJEE 2022 Medium
- If angles \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are in A.P., then \(\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}}\) is equal toWBJEE 2010 Hard
- If \(a, x\) are real numbers and \(|a| < 1,|x| < 1\) then \(1 (1+a) x+\left(1+a+a^{2}\right) x^{2}+\ldots \infty \quad\) is equal toWBJEE 2016 Hard
- Le the relation \(\rho\) be defined on \(\mathbb{R}\) by a \(\rho\) b holds if and only if \(a-b\) is zero or irrational, thenWBJEE 2020 Medium
- The domain of \(f(x)=\sqrt{\left(\frac{1}{\sqrt{x}}-\sqrt{x+1}\right)}\) isWBJEE 2020 Medium
- If \(F(x)=\int_{0}^{x} \frac{\cos t}{\left(1+t^{2}\right)} d t, 0 \leq x \leq 2 \pi .\) ThenWBJEE 2013 Medium
More PYQs from WBJEE
- The bond order of \(\mathrm{CO}\) molecule isWBJEE 2010 Easy
- Which of the following carbocations will be most stable?WBJEE 2009 Medium
- Two integers \(r\) and \(s\) are drawn one at a time without replacement from the set \(\{1,2, \ldots ., n\}\). Then \(P(r \leq k / s \leq k)=\)WBJEE 2024 Medium
- A uniform rod of length \(L\) pivoted at one end \(P\) is freely rotated in a horizontal plane with an angular velocity \(\omega\) about a vertical axis passing through \(\mathrm{P}\). If the temperature of the system is increased by \(\Delta \mathrm{T}\), angular velocity becomes \(\frac{\omega}{2}\). If coefficient of linear expansion of the rod is \(\alpha(\alpha< < 1)\), then \(\Delta \mathrm{T}\) will beWBJEE 2021 Easy
- A point is in motion along a hyperbola \(y=\frac{10}{x}\) so that its abscissa \(x\) increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate when the point passes through (5,2)WBJEE 2019 Easy
- If the vertex of the conic \(y^{2}-4 y=4 x-4 a\) always lies between the straight lines \(x+y=3\) and \(2 x+2 y-1=0 .\) thenWBJEE 2015 Medium