The angle between the lines represented by $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of $6000\, K$. Maximum intensity is emitted at a wavelength of about $4800\, \mathring{A}$. If the sun was cooled down from $6000\, K$ to $3000\, K$,then the peak intensity would occur at a wavelength of ......... $\mathring{A}$.

Match the following elements of the matrix $A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 4 & 2 \\ 3 & -4 & 6 \end{bmatrix}$ with their co-factors and choose the correct answer.

Element	Co-factor
$A$. $-1$	$(1)$ $-2$
$B$. $1$	$(2)$ $32$
$C$. $3$	$(3)$ $4$
$D$. $6$	$(4)$ $6$
	$(5)$ $-6$

In any $\triangle ABC$,$a(b \cos C - c \cos B)$ equals

$5.6 \, \text{liter}$ of helium gas at $STP$ is adiabatically compressed to $0.7 \, \text{liter}$. Taking the initial temperature to be $T_1$,the work done in the process is

The perimeter of a sector is a constant. If its area is to be maximum,the sectorial angle is: