If the slope of one of the lines given by $ax^2+2hxy+by^2=0$ is two times the other,then:

The number of integral values of $k$ for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has a solution is:

The following diagram indicates the energy levels of a certain atom. When the system moves from the $4E$ level to the $E$ level, a photon of wavelength $\lambda_1$ is emitted. The wavelength of the photon produced during its transition from the $\frac{7}{3}E$ level to the $E$ level is $\lambda_2$. The ratio $\frac{\lambda_1}{\lambda_2}$ will be:

If $\hat{i}+2 \hat{j}+3 \hat{k}$ and $3 \hat{i}+2 \hat{j}+\hat{k}$ are sides of a parallelogram, then a unit vector parallel to one of the diagonals of the parallelogram is

If $\cos (A-B)=3/5$ and $\tan A \tan B=2$,then which one of the following is true?

In a reaction $N_{2(g)} + 3H_{2(g)} \to 2NH_{3(g)}$,the rate of appearance of $NH_3$ is $2.5 \times 10^{-4} \, mol \, L^{-1} \, s^{-1}$. The rate of reaction and rate of disappearance of $H_2$ will be (in $mol \, L^{-1} \, s^{-1}$):