Find the value of $k$,if the angle between the straight lines represented by $2x^2 + 5xy + 3y^2 + 6x + 7y + 4 = 0$ is $\tan^{-1}(k)$.

$A$ bullet of mass $0.02 \ kg$ travelling horizontally with velocity $250 \ ms^{-1}$ strikes a block of wood of mass $0.23 \ kg$ which rests on a rough horizontal surface. After the impact,the block and bullet move together and come to rest after travelling a distance of $40 \ m$. Find the coefficient of sliding friction of the rough surface. (Take $g = 9.8 \ ms^{-2}$)

What is a conjugated protein called if it contains a carbohydrate as a prosthetic group?

The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is

Two infinite length wires carry currents $8A$ and $6A$ respectively and are placed along the $X$ and $Y$-axes. The magnetic field at a point $P(0, 0, d) \ m$ will be:

If $(a + \sqrt{2} b \cos x)(a - \sqrt{2} b \cos y) = a^2 - b^2$,where $a > b > 0$,then $\frac{dx}{dy}$ at $(\frac{\pi}{4}, \frac{\pi}{4})$ is