1. Tardigrade
  2. Question
  3. Mathematics
  4. Suppose u,v &w are twice differentiable functions of x , which satisfies the relations au+bv+cw=0 (where a,b &c are constants, not all zero simultaneously), the value of the determinant | u v w u' v' w' u'' v'' w'' | is

Q. Suppose $u,v\&w$ are twice differentiable functions of $x$ , which satisfies the relations $au+bv+cw=0$ (where $a,b\&c$ are constants, not all zero simultaneously), the value of the determinant $\begin{vmatrix} u & v & w \\ u^{'} & v^{'} & w^{'} \\ u^{''} & v^{''} & w^{''} \end{vmatrix}$ is

NTA AbhyasNTA Abhyas 2022 Report Error

Solution:

Given $ \, au+bv+cw=0 \, \, \ldots \left(\right.1\left.\right)$
$au^{′}+bv^{′}+cw^{′}=0 \, \, \ldots \left(\right.2\left.\right)$
And $au^{′ ′}+bv^{′ ′}+cw^{′ ′}=0 \, \, \, \ldots \left(\right.3\left.\right)$
For non trivial solution (non zero) solution of a, b and c. We must have $\begin{vmatrix} u & v & w \\ u′ & v′ & w′ \\ u′′ & v′′ & w′′ \end{vmatrix}=0$

Questions from NTA Abhyas 2022

1. Let points $A_{1},A_{2}$ and $A_{3}$ lie on the parabola $y^{2}=8x.$ If $\Delta A_{1}A_{2}A_{3}$ is an equilateral triangle and normals at points $A_{1},A_{2}$ and $A_{3}$ on this parabola meet at the point $\left(h , 0\right)$ , then the value of $h$ is

2. The lines represented by the equation $x^{2}+2\sqrt{3}xy+3y^{2}-3x-3\sqrt{3}y-4=0$ , are

Straight Lines

3. If the roots of the equation $ax^{2}+bx+c=0$ are in the ratio $m:n$ , then

Complex Numbers and Quadratic Equations

4. If $a,b,c,d,e,f$ are in arithmetic progression. Then $e - c$ is equal to

Sequences and Series

5. The sum to $n$ terms of $\left[\frac{1}{1.3} + \frac{2}{1.3 . 5} + \frac{3}{1.3 . 5.7} + \frac{4}{1.3 . 5.7 . 9} + . . . . . . . .\right]$ is

Mathematics Most Viewed Questions

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

WBJEE 2011 Differential Equations

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

COMEDK 2009 Differential Equations

3. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

KEAM 2016 Integrals

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

COMEDK 2009 Matrices

5. The value of $ \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx $ is

KEAM 2007 Integrals

Latest Updates