List of top Physics Questions on Mathematics

For an even function, the Fourier coefficients are:
A. \(a_0 \neq 0\)
B. \(a_n \neq 0\)
C. \(a_n = 0\)
D. \(b_n = 0\)
Choose the correct answer from the options given below:

If \( x = r\cos\theta, y = r\sin\theta \) then Match the LIST-I with LIST-II

LIST-ILIST-II
A.\( \frac{\partial r}{\partial x} \)I.\( \frac{1}{r} \)
B.\( \frac{\partial r}{\partial y} \)II.\( \frac{y}{r} \)
C.\( \frac{\partial(x,y)}{\partial(r,\theta)} \)III.\( \frac{x}{r} \)
D.\( \frac{\partial(r,\theta)}{\partial(x,y)} \)IV.\( r \)


(Note: There is a typo in the question; it should be \( y = r \sin\theta \))

For the differential equation \(\left(1+\frac{d^2y}{dx^2}\right)^{3/2} = y\frac{d^2y}{dx^2}\) the order, degree and linearity respectively are:

For Particular Integral, Match the LIST-I with LIST-II

LIST-ILIST-II
A.\( \frac{1}{(D-1)} x^2 \)I.\( xe^x \)
B.\( \frac{1}{D^2+D+1} \cos x \)II.\( \sin x \)
C.\( \frac{1}{(D-1)^2} e^x \)III.\( \frac{x^2 e^x}{2} \)
D.\( \frac{1}{D^3-3D^2+4D-2} e^x \)IV.\( -(x^2 + 2x + 2) \)


(Note: List-I Item A is assumed to be \( \frac{1}{D-1} x^2 \) based on the options)