The degree of the differential equation \(\bigg(\frac{d^2y}{dx^2}\bigg)^3+\bigg(\frac{dy}{dx}\bigg)^2+\sin\bigg(\frac{dy}{dx}\bigg)+1=0\) is
Answer the following as true or false. (i)a→and -a→are collinear. (ii)Two collinear vectors are always equal in magnitude. (iii)Two vectors having same magnitude are collinear. (iv)Two collinear vectors having the same magnitude are equal.
In figure, identify the following vectors.
(i)Coinitial (ii)Equal (iii)Collinear but not equal
Classify the following as scalar and vector quantities. (i)Time period (ii)Distance (iii)Force (iv)Velocity (v)Work done
Represent graphically a displacement of 40km,30°east of north.
If A is an invertible matrix of order 2,then det(A-1) is equal to
Write Minors and Cofactors of the elements of following determinants: I. \(\begin{vmatrix}2&-4\\0&3\end{vmatrix}\)
II. \(\begin{vmatrix}a&c\\b&d\end{vmatrix}\)
Find the area of the region bounded by the parabola y=x2 and y=|x|
The area between x=y2 and x=4 is divided into two equal parts by the line x=a, find the value of a.
Find the area of the smaller part of the circle x2+y2=a2 cut off by the line x=a/√2
Find the area of the region in the first quadrant enclosed by x-axis,line x=√3y and the circle x2+y2=4
Determine order and degree(if defined)of differential equation y''+2y'+sin y= 0
Determine order and degree (if defined) of differential equation y''+(y')2+2y=0
Determine order and degree (if defined) of differential equation y'+ y=ex
Determine order and degree (if defined) of differential equation y'''+2y''+y'=0
Determine order and degree (if defined) of differential equation (y''')2+(y'')3 +(y')4 +y5 =0
Determine order and degree (if defined) of differential equation \(\frac{d^2y}{dx^2}=\cos 3x+\sin3x\)
Determine order and degree (if defined) of differential equation\(\Big(\frac{d^2y}{dx^2}\Big)\\^2+\cos\Big(\frac{dy}{dx}\Big)=0\)
Determine order and degree(if defined) of differential equation\((\frac{ds}{dt})^4+3s\frac{d^2s}{dt^2}=0\)
Determine order and degree(if defined) of differential equation y'+5y-0
Verify A(adj A)=(adj A)A=\(\mid A \mid I\).
\(\begin{bmatrix}1&-1&2\\3&0&-2\\1&0&3\end{bmatrix}\)
By using properties of determinants, show that:
\(\begin{vmatrix}a^2+1&ab&ac\\ab&b^2+1&bc\\ca&cb&c^2+1\end{vmatrix}\)=1+a2+b2+c2
